Reentrant structure on the surface of a porous material

Abstract

The filter material has a layer of porous material and a plurality of structures disposed on a surface of the layer, each structure having a re-entrant shape. The plurality of structures may be a plurality of ordered structures. The filter material may include a layer of porous material and a plurality of re-entrant structures disposed on a surface of the layer, each of the re-entrant structures including a stem and a cap, the caps of adjacent structures being attached to each other to form a plurality of pores, each pore being disposed between adjacent re-entrant structures.

Description

[Technical field]

[0001] Related Applications This application claims the benefit of U.S. Provisional Patent Application No. 63 / 193,807, filed May 27, 2021, the disclosure of which is incorporated by reference in its entirety herein.

[0002] FIELD OF THE DISCLOSURE The present disclosure generally relates to a number of structures having re-entrant features disposed on one or more surfaces of a porous material to increase the hydrophobicity and / or oleophobicity of the material, and methods of forming the same. [Background technology]

[0003] In some filtration applications, it may be desirable to prevent wetting and contamination of the filtration medium by liquids. Depending on the application, the liquid may be aqueous or oil-based. Water repellency to aqueous liquids (e.g., hydrophobicity) may be achieved by coating the filtration medium with a fluorinated polymer. However, achieving water repellency without fluorinated chemicals is desirable for environmental reasons. Additionally, it may be desirable to achieve oil repellency (e.g., oleophobicity) to oil-based liquids. Summary of the Invention [Means for solving the problem]

[0004]

[0003] Embodiments described herein relate to a filter material that includes a layer of porous material and a plurality of structures disposed on a surface of the layer. The structures have a re-entrant shape. Other embodiments relate to a filter element that includes the filter material.

[0005] A further embodiment relates to a filter material including a layer of porous material and a plurality of hoodoo structures disposed on a surface of the layer, each of the hoodoo structures including a stem and a cap, the caps of adjacent structures being attached to form a plurality of pores, each pore being disposed between adjacent hoodoo structures. Another embodiment relates to a filter element including the filter material.

[0006] The above summary is not intended to describe each disclosed embodiment or every implementation of the present disclosure. The following figures and detailed description more particularly exemplify exemplary embodiments.

[0007] The following description refers to the following figures, in which the same reference numbers may be used to identify similar / identical components in multiple figures. However, the use of a number to refer to a component in a given figure is not intended to limit the component in another figure labeled with the same number. The drawings are not necessarily to scale. [Brief description of the drawings]

[0008] [Figure 1A] FIG. 2 is a schematic diagram showing the normal contact line force of a droplet on a flat surface. [Figure 1B] 1 is a schematic diagram illustrating normal contact line forces of a droplet on multiple structures having re-entrant shapes, according to certain embodiments. [Figure 1C] FIG. 1 illustrates contact line forces according to certain embodiments. [Figure 2A] FIG. 13 is a cross-sectional view of a spherical re-entrant shape, according to certain embodiments. [Figure 2B] FIG. 13 illustrates a cross-sectional view of an inverted spherical re-entrant shape, according to certain embodiments. [Figure 2C] FIG. 13 is a cross-sectional view of a hoodoo re-entrant shape, according to certain embodiments. [Figure 3A] FIG. 2 illustrates a cross-sectional view of a porous material having a re-entrant layer on one surface, according to certain embodiments. [Figure 3B] FIG. 2 is a cross-sectional view of a porous material having re-entrant layers on opposing surfaces, according to certain embodiments. [Figure 4] FIG. 13 is a top perspective view of a spacing between structures having a re-entrant shape, in accordance with certain embodiments. [Figure 5A] FIG. 1 is a cross-sectional view of a structure having a hoodoo shape showing various dimensions, according to certain embodiments. [Figure 5B]FIG. 1 is a cross-sectional view of one half of a dual re-entrant hoodoo structure showing various dimensions according to certain embodiments. [Figure 5C] FIG. 1 is a cross-sectional view of one half of a single re-entrant hoodoo structure showing various dimensions in accordance with certain embodiments. [Figure 5D] 1A-1C are cross-sectional views of a pair of hoodoo structures illustrating contact line forces on a droplet, in accordance with certain embodiments. [Figure 5E] FIG. 1 is a cross-sectional perspective view of a continuous hoodoo structure showing various dimensions according to certain embodiments. [Figure 6A] FIG. 13 is a schematic diagram of contact line forces for a hoodoo structure geometry with low breakthrough pressure, in accordance with certain embodiments. [Figure 6B] FIG. 13 is a schematic diagram of contact line forces for a hoodoo structure geometry with high breakthrough pressure, in accordance with certain embodiments. [Figure 7A] 1A-1C are cross-sectional views of a pair of ordered hoodoo structures exhibiting a breakthrough pressure failure mode, in accordance with certain embodiments. [Figure 7B] 13A-13C are cross-sectional views of a pair of ordered hoodoo structures illustrating another breakthrough pressure failure mode in accordance with certain embodiments. [Figure 8] 1 is a chart illustrating various dimensions of nine hoodoo shapes and corresponding calculated breakthrough pressures, according to certain embodiments. [Figure 9] 1 is a graph illustrating breakthrough pressure as a function of various hoodoo dimensions, in accordance with certain embodiments. [Figure 10] 1 is a graph illustrating measured breakthrough pressure compared to modeled breakthrough pressure in accordance with certain embodiments. [Figure 11A] 2A-2C are various diagrams of a reentrant structure in accordance with certain embodiments. [Figure 11B] 2A-2C are various diagrams of a reentrant structure in accordance with certain embodiments. [Figure 11C] 2A-2C are various diagrams of a reentrant structure in accordance with certain embodiments. [Figure 12A]FIG. 2 is a perspective view of a re-entrant structure, according to certain embodiments. [Figure 12B] FIG. 12B is a cross-sectional bottom view of the re-entrant structure of FIG. 12A. [Figure 13A] FIG. 2 is a perspective view of a re-entrant structure, according to certain embodiments. [Figure 13B] FIG. 13B is a side view of the re-entrant structure of FIG. 13A. [Figure 13C] FIG. 13B is a cross-sectional bottom view of the re-entrant structure of FIG. 13A. [Figure 14A] FIG. 13 illustrates a cross-sectional side view of a continuous lattice having a re-entrant hoodoo structure and drainage channels, in accordance with certain embodiments. [Figure 14B] FIG. 14B is a bottom perspective view of the continuous grid of FIG. 14A. [Figure 14C] FIG. 14B is a bottom view of the continuous grating of FIG. 14A. [Figure 15A] FIG. 13 illustrates a bottom perspective view of a continuous grid having re-entrant hoodoo structures and drainage channels, in accordance with certain embodiments. [Figure 15B] FIG. 15B is a cross-sectional side view of the continuous grating of FIG. 15A. [Figure 16A] FIG. 13 illustrates a bottom perspective view of a continuous grid having re-entrant hoodoo structures and drainage channels, in accordance with certain embodiments. [Figure 16B] FIG. 16B is a cross-sectional side view of the continuous grid of FIG. 16A. [Figure 17] FIG. 13 is a schematic bottom view of a continuous lattice having a re-entrant hoodoo structure and drainage channels, in accordance with certain embodiments. [Figure 18] FIG. 13 is a schematic bottom view of a continuous lattice having a re-entrant hoodoo structure and drainage channels, in accordance with certain embodiments. [Figure 19] FIG. 13 is a schematic bottom view of a continuous lattice having a re-entrant hoodoo structure and drainage channels, in accordance with certain embodiments. [Figure 20] FIG. 13 is a schematic bottom view of a continuous lattice having a re-entrant hoodoo structure and drainage channels, in accordance with certain embodiments. [Figure 21]FIG. 13 is a schematic bottom view of a continuous lattice having a re-entrant hoodoo structure and drainage channels, in accordance with certain embodiments. [Figure 22] FIG. 2 is a schematic top view of a re-entrant layer having multiple zones, in accordance with certain embodiments. [Figure 23] FIG. 1 is a schematic top view of a re-entrant layer having multiple zones forming through-flow and cross-flow channels, according to certain embodiments. [Figure 24A] FIG. 1 is a schematic cross-sectional side view of a single pore of the test material of Example 5. [Figure 24B] FIG. 24B is a microscope image of a single pore of the test material of FIG. 24A. [Figure 24C] FIG. 24B is a microscope image of a single pore of the test material of FIG. 24A. [Diagram 25] FIG. 13 is a schematic side view of a sample testing device used in Example 6, in accordance with certain embodiments. [Figure 26A] 26 is a microscope image of a sample having a continuous lattice with a re-entrant hoodoo structure being tested in the sample testing apparatus of FIG. 25. [Figure 26B] 26 is a microscope image of a sample having a continuous lattice with a re-entrant hoodoo structure being tested in the sample testing apparatus of FIG. 25. [Figure 26C] 26 is a microscope image of a sample having a continuous lattice with a re-entrant hoodoo structure being tested in the sample testing apparatus of FIG. 25. [Figure 27A] 26 is a microscope image of a sample having a re-entrant hoodoo structure and a continuous lattice with drainage channels being tested in the sample testing apparatus of FIG. 25. [Figure 27B] 26 is a microscope image of a sample having a re-entrant hoodoo structure and a continuous lattice with drainage channels being tested in the sample testing apparatus of FIG. 25. [Figure 27C] 26 is a microscope image of a sample having a re-entrant hoodoo structure and a continuous lattice with drainage channels being tested in the sample testing apparatus of FIG. 25. [Figure 28] 1 is a schematic side view of a sample testing device, according to certain embodiments. [Figure 29A] 29 is a microscope image of a sample having a re-entrant hoodoo structure and a continuous lattice with drainage channels being tested in the sample testing apparatus of FIG. 28. [Figure 29B] 29 is a microscope image of a sample having a re-entrant hoodoo structure and a continuous lattice with drainage channels being tested in the sample testing apparatus of FIG. 28. [Figure 29C] 29 is a microscope image of a sample having a re-entrant hoodoo structure and a continuous lattice with drainage channels being tested in the sample testing apparatus of FIG. 28. [Figure 29D] 29 is a microscope image of a sample having a re-entrant hoodoo structure and a continuous lattice with drainage channels being tested in the sample testing apparatus of FIG. 28. [Figure 29E] 29 is a microscope image of a sample having a re-entrant hoodoo structure and a continuous lattice with drainage channels being tested in the sample testing apparatus of FIG. 28. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0009] definition All headings provided herein are for the convenience of the reader and should not be used to limit the meaning of any of the text that follows the heading, unless specifically stated.

[0010] Terms such as "a," "an," and "the" are not intended to refer to only a single entity, but include general classes of which specific examples can be used to illustrate. The terms "a," "an," and "the" are used interchangeably with the term "at least one." The phrases "at least one of" and "comprises at least one of," followed by a list, refer to any one of the items in the list, and any combination of two or more items in the list.

[0011] As used herein, the term "or" is generally used in its ordinary sense, including "and / or," unless the content clearly dictates otherwise. The term "and / or" (when used) refers to one or all of the listed elements or a combination of any two or more of the listed elements. Additionally, "eg" is used as an abbreviation of the Latin phrase exempli gratia, meaning "for example."

[0012] The use of numerical ranges by endpoints includes all numbers within that range (e.g., 1 to 5 includes 1, 1.5, 2, 2.75, 3, 3.80, 4, and 5) and any range within that range. Additionally, unless otherwise indicated, all numbers expressing quantities and all terms expressing direction / orientation (e.g., vertical, horizontal, parallel, perpendicular, etc.) in this specification and claims are to be understood as being modified in all instances by the term "about." Thus, unless indicated to the contrary, the numerical parameters set forth in the foregoing specification and appended claims are approximations that may vary depending on the desired properties one of ordinary skill in the art is seeking to obtain utilizing the teachings disclosed herein. The term "about" is used herein in conjunction with numerical values ​​to include normal variations in measurements as would be expected by one of ordinary skill in the art, and is understood to have the same meaning as "approximately" and to cover typical error ranges, such as ±5% of the stated value.

[0013] In this disclosure, for ease of explanation, relative terms such as proximal, distal, left, right, front, rear, top, bottom, side, upper, lower, horizontal, vertical, etc. may be used. However, such relative terms are in no way intended to limit the scope of the invention. The terms left, right, front, rear, top, bottom, lateral, upper, lower, horizontal, vertical, etc. are from the perspective as viewed in a particular view.

[0014] Any directions referred to herein, such as "top", "bottom", "left", "right", "upper", "lower", and other directions or orientations, are described herein for clarity and brevity, and are not intended to limit the actual device or system. The devices and systems described herein can be used in several directions and orientations.

[0015] As used herein, "have," "having," "include," "including," "comprise," "comprising," and the like are used in an open-ended sense and generally mean "including, but not limited to." "Consisting essentially of," "consisting of," and the like are understood to be encompassed by "comprising," and the like. As used herein, "consisting essentially of," with respect to compositions, products, methods, and the like, means that the components of the composition, product, method, and the like are limited to the recited components and any other components that do not materially affect the basic and novel characteristics of the composition, product, method, and the like.

[0016] The terms "preferred" and "preferably" refer to embodiments that may provide certain benefits, under particular circumstances. However, other embodiments may also be preferred, under the same or other circumstances. Furthermore, the recitation of one or more preferred embodiments does not imply that other embodiments are not useful, and is not intended to exclude other embodiments from the scope of the present disclosure, including the claims.

[0017] The term "substantially" as used herein can be understood to have the same meaning as "significantly" and to modify the term that follows by at least about 90%, at least about 95%, or at least about 98%. The term "substantially free" as used herein can be understood to have the same meaning as "insignificantly" and to modify the term that follows by the opposite meaning of "substantially", i.e., by 10% or less, 5% or less, or 2% or less.

[0018] The present disclosure generally relates to a plurality of structures having reentrant features disposed on one or more surfaces of a porous material. Such structures can be utilized to selectively increase the liquid hydrophobicity (e.g., hydrophobicity or oleophobicity) of the material. The present disclosure also relates to methods of making such materials and structures.

[0019] In some cases, it may be desirable to provide a porous material that has the ability to resist contamination or repel contamination by liquids. For example, it may be desirable for a porous material (such as a venting medium or a filtration medium) to repel liquids (e.g., polar liquids, such as aqueous liquids, or non-polar liquids). Thus, depending on the intended application, the "contaminant" may be water or an aqueous (water-soluble) liquid or another polar liquid, or a non-polar liquid, such as an oil-based or organic solvent-based liquid.

[0020] In general, porous materials can offer a continuum of liquid repellency ranging from non-repellent (i.e., liquidphilic) to liquid repellent (i.e., hydrophobic) to very liquid repellent (i.e., superhydrophobic). The degree of repellency can be determined by measuring the contact angle of a liquid on the porous material. The contact angle is the angle measured through a drop of liquid where the liquid-vapor interface meets the solid surface. Liquid-phobic (e.g., hydrophobic and oleophobic) materials are defined as materials that have a contact angle greater than 90°, and superhydrophobic materials have a contact angle greater than 150°. The liquid repellency of a porous surface is determined by both the surface chemistry (surface energy) and the surface structure. The embodiments described herein relate to modifying the water repellency of a porous material by modifying the surface structure of the material.

[0021] The surface of a porous material can be patterned with a plurality of specific structures to enhance the liquid repellency of the material. For example, a wet material, such as a liquid porous material, can be made hydrophobic by disposing a plurality of ordered structures on the surface of the material. In another example, a hydrophobic porous material can be made oleophobic by disposing a plurality of structures on the surface of the material. This can be done by reducing or avoiding the use of coatings, particularly fluorine-containing coatings, such as environmentally unfriendly biologically persistent chemical coatings. Applying a predetermined pattern to a porous material can improve hydrophobicity and oleophobicity, but these liquid repellency properties can be improved when the resulting surface includes a plurality of structures, each having a reentrant shape.

[0022] A reentrant structure is any structure in which, when a straight line is drawn through a portion of the structure, the line passes through at least two interfaces of the structure. Reentrancy may be defined relative to a plane. That is, the structure may be reentrant relative to a horizontal plane (e.g., the plane of the substrate), and a line perpendicular to the horizontal plane (i.e., a vertical line) crosses at least two interfaces of the structure. A reentrant structure may be referred to as having a reentrant shape. A structure may also be multiply reentrant. For example, a structure may be doubly reentrant. In a doubly reentrant structure, a first line (e.g., a vertical line) drawn through a portion of the structure passes through two interfaces of the structure, and there is at least 1 / 2 a line perpendicular to the first line drawn through a portion of the structure that passes through at least four interfaces of the structure.

[0023] Hoodoos are a subcategory of reentrant structures. Hoodoos generally have a stem-and-cap structure, where the cap is wider than the stem. Hoodoos are discussed further below, for example, with respect to Figures 2C and 5A-5E.

[0024] A re-entrant structure can invert a meniscus of a liquid (e.g., a droplet) when the liquid wets the material that comprises the re-entrant structure. The inverted meniscus can reduce, minimize, or prevent the liquid from wetting through the underlying surface. Similarly, a re-entrant structure having a double re-entrant shape has the above properties of a re-entrant shape with an overhanging portion where the contact line of the liquid interface moves vertically on the overhanging portion of the structure as the contact line moves along the surface. Meniscus inversion is shown in Figures 1A and 1B. In Figure 1A, a droplet 106 is disposed in a gas environment 108 on a substantially flat surface of a substrate 102. The droplet adheres to the surface of the substrate 102 and the meniscus 104 of the droplet 106 is inverted by a contact line force F. CL The vertical component of F CLV The liquid curves outward from the surface of the substrate such that the liquid is directed toward or into the substrate 102. The liquid has a contact angle θ on the substrate 102. If the substrate 102 is a porous material, the droplet 106 may wet and possibly block and clog any pores covered by the droplet 106. In FIG. 1B, multiple structures 114A, 114B having a reentrant shape are disposed on the surface of the substrate 102. Here, the structures 114A, 114B have a droplet 106 attached thereto and the meniscus 112 is inverted compared to the meniscus 104. The inversion leaves a pocket 108 of gas between the droplet 106 between the structures 114A, 114B and the surface of the substrate 102. This may be particularly desirable if the substrate 102 is a porous material to maintain the porosity of the substrate 102. The normal component of the contact line force, indicated by the arrow 116, is also inverted to be directed away from the substrate 102. The contact line force F CL The vertical component of F CLV are directed towards or into the structures 114A, 114B.

[0025] Contact line force F CL The vertical component of F CLV is described by Equation 1:

number

[0026] Certain re-entrant shapes can be used to invert the meniscus of a droplet, such shapes are described further below.

[0027] 2A-2C show examples of various re-entrant structures that may be applied to the surface of a porous material. The re-entrant structures may have any suitable shape, size, pattern, and distance from one another (e.g., lattice pitch), as further described below. In some embodiments, the re-entrant structures may be applied in an ordered pattern. FIG. 2A shows a cross-section of a spherical shape where the structures of the pattern are regularly spaced spheres 204 arranged on the surface of a porous material substrate 202. FIG. 2B shows a cross-section of an inverted spherical shape where the structures 208 form spherical voids 206 between adjacent structures 208 on the surface of the porous material substrate 202. Although the structures in FIGS. 2A and 2B are shown as spheres (e.g., structures or voids having a radius of a single length), the structures may also be modified to form three-dimensional ellipses of various dimensions (e.g., structures or voids having at least two radii of different lengths) or other shapes modified from spheres. FIG. 2C shows a cross-section of a re-entrant structure 210 having a hoodoo shape arranged on the surface of a porous material substrate 202. The curved and overhanging configuration of each of these three geometric shapes allows for the meniscus of the liquid to be inverted. The inverted meniscus can reduce, minimize, or prevent the liquid from wetting through the underlying surface of the substrate 202.

[0028] A simple force balance equation can be used to explain when and why liquids repel or wet through reentrant structures. The contact line force (F CLV ) is the vertical component of the reentrant shape (F IN The droplet is repelled as long as the external normal force (F) on the droplet in the reentrant pore is greater than the normal component of the external force on the droplet (e.g., externally applied pressure, including gravity). IN ) overcomes the normal component of the contact line force pointing out of the structure, the liquid will wet through the structure. This can be expressed as Equations 2 and 3: F CLV <F IN Wet Type 2 F CLV ≧F IN Liquid repellency (no wetting) Formula 3

[0029] According to one embodiment, the reentrant structures are applied to one or more surfaces of the porous material. When discussing reentrant structures disposed on a porous substrate, two different types of pores can be distinguished: pores formed by or between reentrant structures, and inherent pores of the porous substrate itself. In this disclosure, any discussion of pores refers to pores formed by or between reentrant structures, unless otherwise specified.

[0030] Depending on the application of the porous material, multiple re-entrant structures can be applied to a first side of the layer as in FIG. 3A, or to two or more sides as in FIG. 3B. In certain applications, a first multiple re-entrant structures are disposed on a first side and a second multiple re-entrant structures are disposed on a second opposing side of the same layer of porous material as shown in FIG. 3B. FIGS. 3A and 3B show a composite or multi-layer material in which structured or re-entrant layers 304, 304A, 304B are bonded to an underlying porous material layer 302. By providing the re-entrant layers to the underlying porous material layer, the re-entrant structures can be incorporated without losing the permeability of the underlying porous material, and the original specifications of the porous material in terms of permeability as well as liquid (e.g., water) entry pressure and particle efficiency can be substantially maintained for a particular application.

[0031] In FIG. 3A, a first layer 302 of porous material is provided. A second layer 304 of material including a plurality of re-entrant structures having one or more re-entrant shapes is disposed on and / or bonded to the first layer 302 to form a bi-layer composite. The re-entrant structures provide the advantages discussed herein with respect to liquid repellency. The re-entrant structures may be formed on the second layer 304 before bonding the layers to form the composite, or after the first layer 302 and the second layer 304 are laminated together. The first layer 302 is a porous material that can be designed to meet the airflow and / or liquid (e.g., water) inlet pressure specifications required for the desired application (e.g., ventilation or filtration) and can be used as is without modification. The second re-entrant layer 304 is designed for one or more anticipated contaminants in the desired application to reduce the wettability of the composite and reduce or minimize contact angle hysteresis (i.e., shedding). Without the second re-entrant layer 304 of material, the porous material would not be able to release contaminants and liquids could clog the pores of the substrate, reducing airflow and ventilation capacity. The second re-entrant layer 304 may also be a porous material, either the same material as the first layer 302 or a different type of porous material. In certain embodiments, the second re-entrant material may include at least one of polymer fibers, metal mesh, expanded polytetrafluoroethylene, laser etched material, colloids or other inorganic / hard particles, or another polymeric material.

[0032] Composite materials can be formed by laminating two layers of material together or can be combined in any of a variety of ways. Although the composite material is described as a bilayer material, the porous material may support re-entrant structures on opposing surfaces, either directly on one or more surfaces of the porous material or on one or more layers of material bonded to the surfaces of the porous material. Techniques for forming these structured surfaces are described below. For example, re-entrant structures may be formed with or without a residual thickness of the second layer 304 between the bottom of the structure and the top surface of the first layer 302.

[0033] The composite material may also include any of various combinations of materials. For example, in certain embodiments, the reentrant layer may be the same material as the porous material or a different material from the porous material. If there are two reentrant layers, the reentrant layers may be the same material or different materials, and one, both, or neither may be the same material as the porous material layer. For example, the porous material layer may include at least one of polypropylene, polyethylene, polyester, polyethersulfone, polysulfone, expanded polytetrafluoroethylene, polyvinylidene fluoride, polyamide, polyacrylonitrile, polycarbonate, cellulose acetate, and nylon. The reentrant layer 304 may be a solid (i.e., non-porous) material. The reentrant layer 304 may include a metal, a thermoplastic polymer (e.g., acrylic, polytetrafluoroethylene, polyethersulfone, polypropylene, polyethylene, polyethylene terephthalate, polycarbonate, polyamide, polymethyl methacrylate, etc.), a thermosetting polymer (e.g., epoxy, acrylate, urethane, thiol, etc.), a ceramic, or a combination thereof. When more than one re-entrant layer is present, the materials of the two or more layers may be independently selected. The material of the re-entrant layer may be selected to provide a predetermined amount of flexibility. The material of the re-entrant layer may include a coating that enhances the oleophobicity of the layer, such as a silicone-based, parylene-based, acrylic-based, wax-based, or fluorochemical coating. In some embodiments, the material does not include a fluorochemical coating.

[0034] In certain embodiments, the material of the reentrant material layer 304 can include a porous material. One example of a suitable porous material is expanded polytetrafluoroethylene. In further embodiments, the layer may be combined with an unstructured layer of expanded polytetrafluoroethylene. Certain materials having an open structure with aligned nodes to provide higher permeability can be structured as the reentrant layer 304. Examples of such open structure materials are described in a co-pending application entitled "Patterned Porous Material Surfaces," filed on April 2, 2021 as U.S. Provisional Patent Application No. 63 / 170,104. The material used to prepare the reentrant material layer may be designed to be compressible. Preferably, the material is not so compressible that it collapses the pore structure, to avoid requiring a very open initial pore structure before applying or forming the structure. In general, materials with high airflow and good compressibility can be configured as the layer 304. In certain embodiments, a material with many nodes and fibrils may be used to compress the nodes to create the structure of layer 304, avoiding compression of the fibrils / pores and thus avoiding loss of permeability. Alternative materials may include laser etched media to create reentrant structures, isolated polyester or other polymers to create reentrant structures, laminated nonwoven materials, apertured films, and aligned electrospun fibers. Depending on the wetting of the contaminant (e.g., θ<90°), the reentrant layer 304 may include reentrant structures of various shapes and dimensions as described herein. The orientation of the structure of layer 304 may be designed to provide liquid repellency against anticipated liquid contaminants as described herein. The surface tension of the reentrant and substrate materials as well as anticipated contaminants may contribute to design considerations.

[0035] One design consideration for the layer of reentrant structures is the lattice pitch (center-to-center spacing) between the reentrant structures. In certain embodiments, the reentrant structures are arranged as a plurality of ordered structures. As used herein, "ordered" refers to a plurality of reentrant structures having a regular, predetermined, at least partially uniform lattice pitch between adjacent reentrant structures. As such, the ordered structures are not randomly arranged on the surface of the porous material. However, the predetermined lattice pitch may be different in different directions between the structures or in different regions of the surface. For example, the structures may have a first lattice pitch in the x-direction along the plane and a second, different lattice pitch in the y-direction along the plane. In further embodiments, the structures may not necessarily be arranged as an ordered structure, such as when the structures form a continuous reentrant structure as further described below.

[0036] In certain embodiments, a plurality of ordered structures form a pattern on the material surface. The pattern may be an array of re-entrant structures with a consistent lattice pitch, but the pattern may also include re-entrant structures of different shapes, multiple shapes, varying lattice pitch, and / or unequal numbers of structures in rows and / or columns. In alternative embodiments, the pattern may take on complex shapes including complex combinations of re-entrant structures. The pattern shape may be regular or irregular.

[0037] The lattice pitch of a plurality of ordered re-entrant structures, according to various embodiments, is shown in Figure 4. Figure 4 shows a top view of a portion of a subset of four re-entrant structures (e.g., hoodoo structures) 402, 404, 406, 408. Each of the re-entrant structures 402, 404, 406, 408 are positioned adjacent to one another to define an area 410 between the structures 402, 404, 406, 408. A droplet 106 is shown as being supported or repelled by the re-entrant structures 402, 404, 406, 408. The lattice pitch is the center-to-center distance between two adjacent re-entrant structures (i.e., center-to-center spacing). The lattice pitch of structures 402, 404, 406, 408 is defined by a first lattice length L1 between structures 408 and 406 (e.g., in the x-direction) and a second lattice length L2 between structures 408 and 402 (e.g., in the y-direction). As described above, the first and second lattice lengths may be substantially the same or different. The lattice lengths may also be oriented with respect to each other at various angles, indicated by the lattice angle ψ, the angle between lattice lengths L1 and L2. The parallelogram formed by L1, L2, ψ is called a unit cell. The different measured dimension is the edge spacing, which is the distance D between the outermost edges of two adjacent reentrant structures (i.e., the edge-to-edge spacing).

[0038] The lattice pitch of the ordered structure is one parameter that controls the repulsive properties of the ordered structure. The maximum lattice pitch to maintain the repulsive properties of a particular reentrant structure can be determined using Equation 4:

number

[0039] Breakthrough pressure is the pressure on a droplet at which it penetrates through a reentrant structure to the underlying porous material. This occurs when the contact line shown in FIG. 4, located on the edge of the reentrant structure, moves along the reentrant structure to the underlying porous material or otherwise allows liquid to reach the underlying porous material. Using Equation 4, it can be seen that the smaller the edge spacing or lattice pitch, the smaller the area (A) and the larger the resulting breakthrough pressure for a given number of ordered reentrant structures. Conversely, the larger the lattice pitch and area A, the smaller the breakthrough pressure required to wet the material.

[0040] The critical point of a re-entrant structure is defined as the point where the angle a from Equation 1 is minimal. If repulsion is allowed, the pinning point will always be at the critical point or between the critical point and the outermost edge of the re-entrant structure, since for every point farther from the edge than the critical point, there exists a point closer to the edge than the critical point that has the same angle a, which means that the two points will be subjected to the same force F CL This means that the points closer to the edge will generate a higher repulsive pressure due to the reduced meniscus area (A). Thus, the coordinates of the reentrant structure from the critical point to the outermost edge, the lattice pitch and lattice angle, as well as the surface tension and contact angle are properties that affect the breakthrough pressure.

[0041] Additionally, the permeability of the re-entrant layer can be affected by the solids fraction of the re-entrant layer, which can be determined by the formula shown below as Equation 6:

number

[0042] By using these equations to predetermine the placement of re-entrant structures on a porous material, the repellency of the material to anticipated contaminants can be controlled. A well-designed re-entrant structure or structures will provide good release characteristics (i.e., roll-off angle) for anticipated contaminants.

[0043] Each of the above equations applies to reentrant structures of any reentrant shape.

[0044] 5A-5C show a cross-sectional view of a re-entrant structure shaped as a hoodoo 500 and various dimensions thereof, according to one embodiment. The hoodoo 500 includes a stem 502 extending from the surface 101 and a cap 504 extending from the stem 502. The cap 504 may include a lip or overhang 524 extending downward from the periphery of the cap 504 toward the surface 101. The hoodoo 500 defines a longitudinal axis A 500. The axis A 500 may be perpendicular to the surface 101. The hoodoo 500 may be defined by several parameters including a stem height H 502, a stem radius R 502, a cap height H 504, an inner radius R 520, an outer radius R 522, and a hoodoo angle α 526. FIG. 5A shows a cross-section of a hoodoo including a stem 502 and a cap 504 with an overhang 524. These hoodoos 500 may be arranged on the surface 101 as a plurality of ordered structures having one or more lattice pitches and lattice angles. The stems 502 have a radius R502. The radius R502 may have a length ranging from 0.5 to 100 μm, or in certain embodiments 2 to 90 μm, or in further embodiments 3 to 50 μm, and in further embodiments 5 to 40 μm. The stem radius R502 has little effect on the resulting breakthrough pressure if the edge spacing is held constant. However, a larger stem radius R502 provides greater mechanical stability at the expense of permeability. If the lattice pitch is held constant, increasing the stem radius decreases the edge spacing and increases the breakthrough pressure.

[0045] The height H502 of the stem 502 may be 0 μm or more, 2 μm or more, 5 μm or more, or 10 μm or more. The height H502 may be 100 μm or less, 65 μm or less, 50 μm or less, or 20 μm or less. The height H502 may range from 0 μm to 65 μm, 2 μm to 65 μm, 2 μm to 20 μm, or 10 μm to 50 μm. The stem height also has little effect on the resulting breakthrough pressure. The height H502 may be selected to correspond to the shape of the meniscus so that the liquid does not contact the underlying substrate. A shorter stem height H502 may increase the mechanical robustness of the hoodoo. The shape of the stem 502 may also have any number of sides and / or curves, and may have a form having a cross-sectional shape including, for example, a circle, a square, a triangle, a rectangle, a hexagon, and combinations thereof.

[0046] Hoodoo 500 also includes a cap 504. The cap may be centered on the top of stem 502. Cap 504 has a height H504, which may be measured as the thickness of the major portion of cap 504 from the top / outer surface of cap 504 to the outer radius (discussed further below). Cap 504 height H504 may be greater than 0 μm and less than or equal to 3 μm, less than or equal to 5 μm, or less than or equal to 10 μm. Height H504 may range from 0 μm to 10 μm, 0 μm to 5 μm, or 0 μm to 3 μm. Cap height H504 may have little or no effect on breakthrough pressure, but may provide mechanical stability. Caps may also have a variety of shapes, including, in a top view, circular, square, triangular, rectangular, hexagonal, other geometric, regular, or irregular shapes, and combinations thereof.

[0047] The cap 504 of the hoodoo 500 includes an overhanging portion 524. The overhanging portion 524 is defined by an inner radius R 520, an outer radius R 522, and a hoodoo angle α 526. The effect of these parameters on breakthrough pressure depends on holding either the grating pitch or the edge spacing constant.

[0048] Generally, re-entrant structures, and hoodoos, have an overall radius R500. The overall radius R500 may be the maximum (widest) radius of the re-entrant structure or hoodoo 500 when the re-entrant structure or hoodoo 500 is viewed from above (e.g., from the direction of the cap 504). Often, the overall radius R500 is the radius of the widest portion of the cap 504. Various parameters, including the stem radius R502 described above, change the overall radius. Thus, if the grating pitch is held constant, changing the various parameters changes the edge spacing, thus affecting A in Equation 4. In contrast, if the edge spacing is held constant, changing the various parameters changes the grating pitch, thus affecting F in Equation 4. CLV and A. This effect can be greater, less, or opposite (i.e., positive or negative) to the breakthrough pressure. The constant lattice pitch also defines the boundaries of the inner radius, outer radius, stem radius, and hoodoo angle. These parameters affect the overall radius R500 and can be selected to allow space between re-entrant structures without overlapping structures when arranged as an ordered plurality.

[0049] As shown in FIG. 5B, the cross-sectional shape of the underside of the cap 504 may be approximated by a circle 520, while the tip of the overhang 524 may be approximated by a circle 522 that defines a double reentrant hoodoo. The circle 520, which is closer to the stem 502 of the hoodoo 500 and can be considered the inner circle, has an inner radius R520. The inner radius R520 defines an arc that forms a concave portion of the underside of the cap 504 that begins at the stem 502 and ends at the point where the inner circle 520 touches the outer circle 522. The slope of the cap underside 514 is a hoodoo angle α526, which is defined as the tangent to the outer circle 522 with a vertex 526 where the curvature of the underside 514 changes. The inner radius R520 may have any suitable length. In certain embodiments, the inner radius R520 is 0 μm or more, 1 μm or more, or 3 μm or more. The inner radius R520 may be 500 μm or less, 100 μm or less, 50 μm or less, or 40 μm or less. The inner radius R520 may be in the range of 0 μm to 500 μm, 0 μm to 100 μm, 1 μm to 50 μm, or 3 μm to 40 μm. Increasing the inner radius R520 increases the breakthrough pressure at the expense of permeability because the pinning points of the contact line are pushed outward, reducing the projected surface area of ​​the liquid and increasing the overall hoodoo radius.

[0050] As the inner radius R520 increases to infinity, the underside 514 approaches a straight line rather than a curve. In certain embodiments, the underside 514' is defined by a straight line emanating from the stem 502, as shown in FIG. 5C for the hoodoo 500'. The straight line may be slanted downward (towards the surface 101). In this case, an inner width W524 is defined. The inner width W524 is the length from the stem 502 to the hoodoo angle apex 526'.

[0051] Hoodoo 500' has an overhang 524' similar to hoodoo 500 of FIG. 5B, and outer radius R 522' is the radius of a circle 522' that approximates the shape of overhang 524'.

[0052] The outer radius R522, R522' can have any suitable length. In some embodiments, the outer radius R522, R522' is 0 μm or more, 1 μm or more, or 5 μm or more. The outer radius R522, R522' can be 100 μm or less, 50 μm or less, 25 μm or less, or 10 μm or less. The outer radius R522, R522' can be in the range of 0 μm to 100 μm, 0 μm to 50 μm, 0 μm to 25 μm, or 0 μm to 10 μm. The outer radius 0 μm is taken as the point. The outer radius has a large effect on the breakthrough pressure. For a constant edge spacing, a smaller outer radius reduces the normal component of the contact line force F CLV Increase the breakthrough pressure by increasing A and decreasing A (e.g., by pushing the contact line outward from the hoodoo). For a constant grating pitch, a smaller outer radius R522, R522' decreases the overall hoodoo radius R500, R500' and thus increases the edge spacing and the normal component of the contact line force F CLV decreases, A increases, and the breakthrough pressure decreases.

[0053] The hoodoo angles α526, α526' may be -10 degrees or more, 0 degrees or more, 30 degrees or more, 45 degrees or more, or 60 degrees or more. The hoodoo angles α526, α526' may be 90 degrees or less or 60 degrees or less. The hoodoo angles α526, α526' may be in the range of -10 degrees to 90 degrees, 0 degrees to 90 degrees, 45 degrees to 90 degrees, or 60 degrees to 90 degrees. The hoodoo angle increases the breakthrough pressure when it is close to 90 degrees. As the hoodoo angle approaches 90 degrees, the normal component of the contact line force increases, contributing to the increase in the breakthrough pressure. When the hoodoo structure has an inner radius approaching infinity and a hoodoo angle of 0 degrees, the hoodoo can be considered a single reentrant structure.

[0054] As described herein, the hoodoo structures (or re-entrant structures) are arranged as a plurality of structures on the surface of the material. The plurality may be arranged in an ordered arrangement as described above, and in certain embodiments, the structures are formed in an array. FIG. 5D shows two adjacent hoodoos 530, 532. The two structures are separated by a distance D530, referred to herein as edge spacing. When designing a re-entrant material, the edge spacing may be selected based on the expected contaminants that the porous material will come into contact with. For example, the edge spacing may be 1 μm or more, 2 μm or more, 5 μm or more, or 10 μm or more for low surface tension liquids (e.g., <30 mN / m). The edge spacing may be 50 μm or less, 30 μm or less, 20 μm or less, or 10 μm or less for low surface tension liquids (e.g., <30 mN / m). Edge spacing can range from 1 μm to 30 μm for low surface tension liquids (e.g., <30 mN / m). Edge spacing can be 10 μm or more, 30 μm or more, 50 μm or more, or 100 μm or more up to 2 mm for high surface tension liquids (e.g., >30 mN / m).

[0055] As described above in connection with FIG. 4, a plurality of re-entrant structures may be arranged in an array. The array of re-entrant structures may have a row of re-entrant structures oriented at an angle in a lattice, i.e., a lattice angle. The lattice angle may be 45 degrees or more, 60 degrees or more, or 75 degrees or more. The lattice angle may be 90 degrees or less, 75 degrees or less, or 60 degrees or less. In some embodiments, the lattice angle is in the range of 45 to 90 degrees. In certain embodiments, when the lattice is a square lattice, the angle is 90 degrees.

[0056] In some embodiments, the multiple hoodoos (or re-entrant structures) are arranged as multiple connected structures to form a continuous hoodoo structure (or continuous re-entrant structures). The multiple structures may be connected at one or more points. For example, the multiple hoodoos or re-entrant structures can be attached to the cap or the cap and stem in a continuous hoodoo structure. An exemplary embodiment of a continuous re-entrant structure is shown in FIG. 5E. A plurality of re-entrant structures 600 are attached to each other to form a continuous re-entrant lattice 601 and a plurality of pores 608 distributed throughout the lattice 601. The lattice 601 forms an outer surface 605. The lattice 601 is defined by a first lattice pitch L1 (center-to-center pore spacing in a first direction) and a second lattice pitch L2 (center-to-center pore spacing in a second direction) and a lattice angle α 601 defined as the angle between the first direction and the second direction. The re-entrant structures 600 in the continuous re-entrant lattice 601 may be arranged in an ordered plurality as shown, or may be arranged randomly. A single continuous re-entrant structure may form a re-entrant layer as described above, or may be combined with additional continuous re-entrant structures. In some embodiments, the re-entrant structures are arranged such that the spaces between the re-entrant structures form elongated channels.

[0057] The re-entrant geometric structure 600 of the continuous re-entrant lattice 601 of FIG. 5E includes a base 602 (comparable to the stem 502 of the hoodoo 500). The base 602 has a width W602, which refers to the width at the base of the re-entrant structure 600 as measured along the center-to-center line between two adjacent pores 608. The width W602 does not affect the breakthrough pressure, but contributes to the overall permeability of the continuous re-entrant lattice 601 and the permeability of the composite material when the continuous re-entrant lattice 601 is disposed on a porous material. The hoodoo base width W602 has a range of 0.5 to 100 μm, or in certain embodiments 2 to 90 μm, or in further embodiments 3 to 50 μm, or in still further embodiments 5 to 40 μm. The width may vary along the length of the stem, and the varying width may provide additional advantages in permeability or manufacturing.

[0058] The pores 608 of the continuous lattice structure 601 have a pore diameter D608. The pore diameter D608 is the spacing between the outermost edges of adjacent reentrant structures. The pore diameter D608 may be similar to the edge spacing D530 (spacing between hoodoos). The pore diameter D608 may be 1 μm or more, 2 μm or more, 5 μm or more, or 10 μm or more for low surface tension liquids (e.g., <30 mN / m). The pore diameter D608 may be 30 μm or less, 20 μm or less, or 10 μm or less for low surface tension liquids (e.g., <30 mN / m). The pore diameter D608 may range from 1 μm to 30 μm for low surface tension liquids (e.g., <30 mN / m). The pore size D608 can be 10 μm or more, 30 μm or more, 50 μm or more, or 100 μm or more up to 2 mm for high surface tension liquids (e.g., >30 mN / m). As can be seen, the pore size directly affects A in Equation 4.

[0059] As shown in Figure 5E, the permeability of a continuous hoodoo or re-entrant structure is also affected by the lattice pitch L1, L2. The lattice pitch of a continuous hoodoo or re-entrant structure is the center-to-center spacing between pores, so the lattice pitch encompasses the pore size and the cross-sectional dimensions of the re-entrant structure. A decrease in lattice pitch with a constant re-entrant structure length (or diameter) results in a decrease in pore size, decreasing A in Equation 4 and increasing the breakthrough pressure.

[0060] Additionally, the hoodoos or reentrant structures that make up a continuous hoodoo or reentrant structure (lattice) share many of the same dimensions as the individual hoodoos or reentrant structures described above in connection with the ordered plurality of hoodoos. For example, the stem height H602 of each structure may be 0 μm or more, 2 μm or more, 5 μm or more, or 10 μm or more. The stem height H602 may be 100 μm or less, 65 μm or less, 50 μm or less, or 20 μm or less. The height H602 may range from 0 μm to 65 μm, 2 μm to 65 μm, 2 μm to 20 μm, or 10 μm to 50 μm. In a continuous hoodoo or reentrant structure (lattice), the stem height is substantially uniform across the continuous structure because the hoodoos are attached to each other to form a substantially flat outer surface 605. As used herein, "substantially flat" refers to a surface that is planar but may deviate within manufacturing tolerances. If a hoodoo structure is attached to the cap, the cap height H604 may be measured from the top / outer surface of the cap to the outer radius. The height H604 of the cap 604 may be 0 μm or more and 3 μm or less, 5 μm or less, or 10 μm or less. The height H504 may be in the range of 0 μm to 10 μm, 0 μm to 5 μm, or 0 μm to 3 μm.

[0061] The reentrant geometric structure 600 of the continuous reentrant lattice 601 may be a double reentrant structure (as shown in FIG. 5E) or may be configured as a single reentrant structure. Similar to the individual hoodoo structures of FIGS. 5B and 5C, the connected hoods (reentrant geometric structures 600) of the continuous lattice structure 601 may be contoured and approximated by an inner circle 520, an inner radius R520, an outer circle 522, and an outer radius R522, or may have an underside defined by a straight line and an inner width W524. The dimensions of the inner radius R520, the outer radius R522, the inner width W524, and the hoodoo angle α526 may be as described above with respect to FIGS. 5B and 5C.

[0062] The inverted meniscus can reduce, minimize, or prevent liquid from wetting through the surface underlying the substrate 202. When the hoodoo structures, in their ordered multiple or continuous lattice structure, are in contact with a liquid (e.g., a contaminant), the hoodoo structures perform their repelling function by inverting the meniscus 112 of the liquid (i.e., reversing the contact line force). CL is indicated by an arrow. The contact line force F CLindicates a point 551 on each hoodoo structure cap 504 where the liquid meniscus 112 is pinned to the structure. As mentioned above, the edge spacing D530 is selected to keep the structures close enough to prevent liquid from penetrating the multiple re-entrant structures 500 to reach and wet the surface of the porous substrate 202. As can be appreciated by the equation for breakthrough pressure (Equation 4) and the equation for normal contact line force (Equation 1), there are three competing parameters for maximizing the breakthrough pressure: 1) the length of the contact line l (connected pinning points 551), 2) the projected area of ​​the liquid surface (A), and 3) the angle a (optimize angle a in Equation 1 by making θ-a as close to 90 degrees as possible). The maximum pressure is a balance between increasing or maximizing l in Equation 1 and decreasing or minimizing A in Equation 4. This balance contributes to the re-entrant geometry of the multiple structures, whether ordered or continuous, and therefore the selection of the specific parameters. When liquids (eg, contaminants) penetrate, the pores of the substrate material can become clogged and the escaping air flow can be reduced or redirected.

[0063] 6A-7B, the geometry and dimensions of the re-entrant structure can invert the meniscus of the liquid in contact with the re-entrant structure and can be designed to increase the breakthrough pressure for a given liquid (e.g., anticipated contaminant). FIG. 6A shows a first example where the hoodoo 800 has a gradual slope at the cap overhang 824, resulting in a structure with a low hoodoo angle α 826, a large outer radius R 822, and a small inner radius R 820. The contact line is pinned near the hoodoo corner point 826, where the two arcs that form the inner radius R 820 and the outer radius R 822 meet. In FIG. 6A, the meniscus 112 is pinned to the hoodoo along the gradual slope 806. F CL The combination of a low hoodoo angle α826 and an inner radius R820 that is significantly smaller than the outer radius R822 results in a small F in the vertical direction because the angle of CLV This contact line force angle results in a low breakthrough pressure of the liquid and the hoodoo shape.

[0064] To increase the breakthrough pressure of the same liquid, the dimensions of the hoodoo structure can be altered. Figure 6B shows a modified hoodoo structure 900 that has a higher breakthrough pressure than the hoodoo structure 800 of Figure 6A. In Figure 6B, the inner radius R 920 is significantly larger than the outer radius R 922, and the hoodoo angle α 926 is larger than that of Figure 6A. The meniscus 112 is still pinned close to the hoodoo angle point 926, where the contact line is pinned close to the tip of the hoodoo 900 at an angle nearly perpendicular to the porous substrate surface. The corresponding contact line force F CL also extends at an angle of approximately 90 degrees to the horizontal, and F CL This contact line force F CL provides a much higher breakthrough pressure and increases the resilience of the re-entrant layer.

[0065] Various parameters affect the breakthrough pressure of a liquid on a reentrant structure, and these parameters are described in relation to Figures 7A-7B. The breakthrough pressure is the pressure at which a liquid is likely to penetrate the reentrant structure and penetrate the porous material surface. The normal component of the contact line force of the droplet can be used to determine the breakthrough pressure of a given liquid. The breakthrough pressure varies depending on the surface tension of the liquid involved as well as the geometric parameters of the reentrant structure.

[0066] As shown in FIG. 7A, liquid may reach a breakthrough pressure and be released into the hoodoo from one or more of the points where the liquid pins. This is called contact line runaway and occurs when the contact line passes its pinning point at a pressure threshold (e.g., maximum pressure or breakthrough pressure). The point where runaway occurs is typically near a hoodoo corner point (e.g., where two arcs meet). Here, the meniscus 113 of the droplet between the hoodoo structures 500 is released from the cap 504 of the hoodoo 500 to contact the stem 502 and "flow down" the stem. Thus, the liquid is no longer repelled by the surface of the reentrant structure and can reach the pores of the porous material of the substrate 202. Contact line runaway is the most likely failure mode for lower surface tension liquids because their contact line forces are lower.

[0067] An alternative breakthrough scenario is shown in FIG. 7B, a failure mode called surface collapse. This failure mode is most likely to occur with higher surface tension liquids with high contact line forces. The droplet 106 maintains a pinning point in the hoodoo cap 504, but the weight of the droplet 106 pushes the meniscus 113 down to the substrate surface 202. Shortening the hoodoo spacing D530 to bring the hoodoo structures 500 closer together or increasing the height of the stems 502 can increase the breakthrough pressure for a given liquid. For example, even if the hoodoo cap 504 provides a high breakthrough pressure, if the stem height is too low such that the meniscus 113 still reaches the underlying substrate 202, the liquid will seep through and the reentrant structure cannot repel the liquid.

[0068] 11A-13C show reentrant structures 1500, 1530, 1550 according to alternative embodiments. These reentrant structures 1500, 1530, 1550 have a double reentrant shape including a reentrant shape relative to a horizontal plane (xz-plane) and an additional reentrant shape in at least one plane orthogonal to the horizontal plane (xy-plane and / or yz-plane). The xz-plane is a plane parallel to the substrate on which the reentrant structures 1500, 1530, 1550 are disposed. The reentrant structures 1500, 1530, 1550 include a first reentrant shape around their caps 1504, 1534, 1554. Additionally, the reentrant structures 1500, 1530, 1550 include a second reentrant shape around their stems 1502, 1532, 1552. Re-entrant structures with re-entrant features in the xz plane can be used to reduce or prevent contamination or cross-wetting of adjacent structures in case of breakthrough. Furthermore, the additional planes of the re-entrant features can help improve imperfections that may result from the fabrication of very small structures.

[0069] 11A-11C, the re-entrant structure 1500 includes a stem 1502 extending from the surface 101 of the substrate 102 and a cap 1504 extending from the stem 1502. The cap 1504 provides a first re-entrant shape, for example as described with reference to FIGS. 2A-2C. The cap 1504 may define a continuously contoured upper surface. In some embodiments, the cap 1504 may have a hemispherical surface. However, other shapes are possible, including a substantially flat upper portion. A lower edge of the cap 1504 may form an overhang 1524 that extends downwardly toward the surface 101. The re-entrant structure 1500 defines a central longitudinal axis A 1500. The axis A 1500 may be perpendicular to the surface 101.

[0070] The stem 1502 may extend along a central longitudinal axis A1500. The stem 1502 has a height H1502. The stem 1502 may be formed as a webbed beam and may include a webbed core portion 1521 and lobes 1523. The webbed core portion 1521 may have a trifurcated cross section including three webs 1522 as shown in FIG. 11B. Other shapes are possible, such as a four-pronged or star-shaped cross section. The lobes 1523 may extend axially along and laterally from the edges of the core portion 1521. The lobes 1523 may be slightly curved outward (away from the central longitudinal axis A1500). The lobes 1523 form a second reentrant shape in the xz plane (parallel to the surface 101 of the substrate 102).

[0071] The dimensions of the re-entrant structures 1500, 1530, 1550 may be similar to the hoodoo 500 described above, including stem height, cap height, and overall radius. However, due to the stem structure, the stem width may be wider than the width of the hoodoo 500 and may be similar to the overall radius.

[0072] The re-entrant structures 1530, 1550 of Figures 12A-13C are similar to the re-entrant structure 1500, except for the curvature of the webs 1542, 1562 and lobes 1543, 1563. The stem 1532 of the re-entrant structure 1530 of Figures 12A and 12B has a core 1541 with a web 1542 having straight edges parallel to the central longitudinal axis A 1530. The lobes 1543 that extend along the edges of the web 1542 are also parallel to the central longitudinal axis A 1530.

[0073] 13A-13C has a core 1561 with a web 1562 that has edges that are concave relative to the central longitudinal axis A 1550. Lobes 1563 extending along the edges of the web 1562 are also concave relative to the central longitudinal axis A 1550.

[0074] In some embodiments, it may be desirable to provide a continuous re-entrant structure (lattice) with a drain. In practice, when a continuous re-entrant structure (lattice) is applied to a relatively large surface area, the lattice may contain one or more imperfections, such as pores that are larger than intended. Such imperfections may cause liquid breakthrough even if the lattice and re-entrant structure are otherwise designed and configured to repel the intended contaminants. The continuous re-entrant structure (lattice) may be provided with a drain or outlet structure to allow any possible breakthrough liquid to escape rather than penetrating adjacent pores. The term breakthrough liquid is used herein to refer to liquid that has penetrated the liquid-repellent barrier provided by the re-entrant structure. The breakthrough liquid may have come into contact with the substrate surface. Various examples of drain and outlet structures for directing the breakthrough liquid are shown in Figures 14A-19.

[0075] 14A-14C, a continuous re-entrant structure (lattice) 1601 includes a plurality of re-entrant structures 1600 connected to one another and a plurality of pores 1608 formed between the plurality of re-entrant structures 1600. The re-entrant structure 1600 includes a cap 1604 that forms an outer surface 1605 of the lattice. The re-entrant structure 1600 includes a stem 1602 that defines a bottom surface 1606 of the lattice. The cap 1604 can include an overhang 1624 as described above. In some examples, the liquid 1006 can penetrate and enter one of the pores 1608. The bottom surface 1606 can include one or more grooves or drains 1610. Any liquid 1006 that enters the pores 1608 can flow into the drain 1610. The drain 1610 can be sized to allow the liquid to flow out of the pores by capillary action. A bottom perspective view of the bottom surface 1606 having a hexagonal drain 1610 around the pores 1608 is shown in FIG. 14B.

[0076] 15A-15B and 16A-16B show embodiments in which the lattices 1630, 1650 include imperfections in the form of larger pores 1618. The larger pores 1618 may result in liquid breakthrough. The lattices 1630, 1650 include drains 1640, 1660 that allow any breakthrough liquid to drain out of the pores. The drains 1640, 1660 may be such that each pore 1608 is surrounded by a drain 1640 (as in FIG. 15A) or multiple pores 1608 are grouped together and surrounded by a drain 1660 (as in FIG. 16A).

[0077] The drains may be configured in any suitable manner and may include different shapes and pore groups, as shown in Figures 17-21. While many possible configurations and shapes can be used, structures utilizing hexagonal or honeycomb-like structures may result in a more densely packed and more efficient lattice structure. The pores may be grouped in various ways within the drain shapes. The number of pores within the drainage structures may be determined based on, among other things, the desired drainage efficiency (fewer pores per drainage structure results in more efficient drainage), the impact on structural integrity (more spaced drainage structures result in better structural integrity), and the estimated drainage needs (estimated population density of breakthrough structures). In some embodiments, the number of pores per drainage structure (one continuous drain loop) is 1 or more, up to 50, up to 25, up to 10, up to 7, or up to 4. In some embodiments, each pore of the lattice is adjacent to a drain. The lattice may include drainage structures of different shapes and sizes. In some embodiments, various tessellation patterns of the drainage structures may be used to adjust the group size. In some embodiments, the drainage structures form channels that extend across the entire width of the substrate, while in other embodiments, the channels extend across only a portion of the width of the substrate.

[0078] In some embodiments, the drain 1610, 2610 includes a stem 1611, 2611 leading from the pore 1608, 2608 to the main drain conduit 1610, 2610. The drain 1610, 2610 may further include an outlet structure 1612, 2612 through which the liquid 1006 flowing in the drain may exit. In many embodiments, the drain 1610, 2610, 4610, 5610 is formed by a groove in the bottom surface 1606, 2606, 4606, 5606. However, in some embodiments, the grate 3601 may include a protrusion forming a hood 3610 over the pore 3608. Some drain structures may be suitable for directing flow in a vertical or inclined arrangement, with the bottom surface 1606, 2606, 3606, 4606, 5606 being vertically oriented or inclined. Some drain structures, such as those shown in Figures 17, 20, and 21, may be suitable for directing flow in any orientation, whether vertical, inclined, horizontal, or "upside down" (bottom surface 1606, 4606, 5606 facing up).

[0079] The drain and outlet structures can have any suitable dimensions. In some embodiments, the drain and outlet structures are sized to promote capillary flow. For example, the drain and outlet structures can be sized based on the desired capillary pressure according to Equation 7 below:

number

[0080] The layered material may further include an absorbent or adsorbent material intended to absorb or adsorb any breakthrough liquid. Such an absorbent or adsorbent material may optionally be located near the drain outlet structure 1612, 2612.

[0081] In some embodiments, the reentrant layer may be configured to have regions or zones. For example, in some embodiments, the reentrant layer is as two or more different types of reentrant structures grouped together as a subset of structures. The reentrant structures in a given region may be discrete reentrant structures or may form a continuous reentrant structure (e.g., a lattice). In some cases, the reentrant layer may include alternating regions of discrete reentrant structures and regions of continuous reentrant structures. In some embodiments, the reentrant layer may include alternating regions of different types of reentrant structures. For example, the reentrant layer may include alternating regions of a first type of reentrant structure and a second type of reentrant structure. Providing regions of different types of reentrant structures and / or reentrant structures and continuous reentrant structures may be desirable to provide the material with different properties that can be achieved in different regions. For example, one region may provide good liquid repellency and another region may provide good drainage. Or, one region may promote throughflow and another region may provide crossflow. The use of distinct regions can also reduce manufacturing complexity by reducing the number of structures that may have desirable properties but may be difficult to manufacture. Such structures can be balanced with structures that are easier to manufacture.

[0082] Examples of reentrant layers with multiple zones are shown in Figures 22 and 23. In Figure 22, a first type of reentrant structure 2201 is alternated with a second type of reentrant structure 2202. The first type of reentrant structure 2201 forms a first zone 2210 and the second type of reentrant structure 2202 forms a second zone 2220. In Figure 23, the first type of reentrant structure 2301 forms a first region 2310 that provides a through-flow channel and a second type of reentrant structure 2302 for a second region 2320 that provides a cross-flow channel. The first type of reentrant structure 2301 may be a hoodoo with a stem and a cap. The second type of reentrant structure 2302 may be similar to the reentrant structures 1500, 1530, 1550 of Figures 11A-13C, except that the second type of reentrant structure 2302 lacks a cap.

[0083] The re-entrant structures may be formed using a variety of methods, including embossing, etching, and micromachining. The formation method for creating the re-entrant structures may be selected based on the desired dimensions of the structures. Various methods for forming the re-entrant structures are described below.

[0084] One exemplary method involves microfabrication using a polymer substrate. First, a polymer substrate is prepared. Then, a photoresist pattern is deposited on the substrate surface. The photoresist pattern includes forming a ring. Using mixed gas reactive ion etching under the photoresist, a ring feature is formed in the polymer substrate. A material layer is deposited (e.g., sputter coated) on the surface to fill the ring feature. In a particular embodiment, the material layer is a metal layer (e.g., nickel-chromium and gold) to provide adhesion and structural support. A photoresist is applied and the previous material layer is removed except for the portions protected by the photoresist. These portions form a reentrant structure (e.g., hoodoo) cap. Using a mixed gas, a reactive ion etch is performed anisotropically to undercut the overhanging portion of the hoodoo cap. A coating such as parylene or another polymer can be optionally applied to protect the structure and / or improve the omniphobicity of the structure. Using this method, a reentrant structure can be created in which the stem and cap are composed of different materials. This method can include a polymer stem and a metal cap, although various combinations of materials can be used.

[0085] An alternative forming method uses micromachining and molding. A molding material, such as a silicon wafer, is patterned with photoresist and etched to form a mold. A filler material is then deposited in the mold and cured. For example, the filler material may be a polymer. Any portion of the filler material that protrudes from the mold can be optionally etched to further shape the hoodoo cap. Compared to the above method, this method can be used to form a single-material hoodoo structure.

[0086] One exemplary method includes fabricating a master stamp. The master stamp can be fabricated by a subtractive method, for example, by etching glass with a femtosecond laser to form the reentrant structure. The master stamp can also be formed by an additive method, for example, using a 3D printer (e.g., two-photon lithography). Either positive or negative master stamps can be made by both techniques. The master stamp can be further replicated to produce a robust stamp for further processing. The master stamp can be directly replicated via electroforming to create multiple metal stamps (e.g., nickel stamps), or a polymer replica can be molded from the master stamp prior to electroforming. In either case, multiple metal stamps can be electroformed to create a repository for further embossing processes. The replica stamp is then used in an embossing process to make the final reentrant structure. The stamp can be used in a hot embossing process, where a thermoplastic polymer is heated above its glass transition temperature and then embossed with a metal stamp. The polymer is then cooled back before removing the metal stamp. A UV embossing process can also be used, for example, where a thermosetting polymer is used. A stamp is used to emboss the polymer, where UV exposure hardens the polymer in place before the stamp is removed.

[0087] To make the through holes for the pore structure a continuous reentrant structure (e.g., as shown in FIG. 5E), the stamp can have long pins that penetrate the polymer film during embossing. In this case, a sacrificial layer may be included on top of the polymer film during embossing.

[0088] A further method for forming a hoodoo structure includes forming the hoodoo with two different materials, such as polymers with different parameters. In certain embodiments, polymers with different glass transition temperatures can be used. A layer of a first polymer having a glass transition temperature is provided as a substrate, and a second polymer having a lower glass transition temperature than the first polymer is deposited (e.g., spin-coated) on the surface of the first polymer. The second polymer layer can be thinner than the first polymer layer. For example, the second polymer layer is deposited at a thickness slightly higher than the desired hoodoo cap thickness. The composite polymer layer is patterned and etched to form discrete structures. The structure is then heated to partially flow the second polymer layer and form the cap overhang.

[0089] The spherical and inverse spherical structures can be achieved with known deposition and etching processes.

[0090] Once the re-entrant structures are formed (regardless of the re-entrant shape), they need to be placed on the porous material. In certain embodiments, the re-entrant structures are formed directly on the porous material layer. In further embodiments, the re-entrant structures may be fabricated from a portion of the porous material layer using techniques such as embossing, nanoimprinting, etching, etc. Any of the formation techniques described herein may be performed by roll-to-roll or roll-to-plate processing.

[0091] In yet further embodiments, the re-entrant structures are bonded to a porous material layer. For example, the re-entrant structures may be transfer printed onto a layer of porous material. Certain re-entrant shapes, such as inverted spheres and continuous arrays of hoodoos, can be formed as one layer or entity, making them easier to manufacture and / or print onto a porous material substrate. These layers may appear in top view as an array of discrete holes or inverted hoodoo structures.

[0092] Transfer printing is a known technique that will not be discussed in further detail. Although transfer printing controls the production of the reentrant structures, the reentrant structures must be bonded to the porous material layer. In certain embodiments, the reentrant structures are applied directly to the porous material using thermocompression bonding (e.g., using heat and force, but without an intermediate layer on the porous material). For example, a layer of the reentrant structures can be applied to the porous material, with gaps (e.g., laser drilling) between the stems of each structure to expose the underlying porous material. In other embodiments, a plasma bond is formed directly between the reentrant structures and the porous material, without the presence of an intermediate layer. In alternative embodiments, the reentrant structures may be bonded to the porous material using an intermediate layer, such as a chemical bond (e.g., a layer applied by roll-on, spin-on, or dip coating techniques) and / or an adhesive bond. When an intermediate layer is used, the porosity and compatibility with the underlying porous material are taken into consideration so as not to reduce the breathability of the original porous material.

[0093] As described herein, by patterning the surface of a porous material with a plurality of structures having re-entrant features, the repellency of the material can be increased. For example, the hydrophobicity and / or oleophobicity of a porous material can be increased by including a plurality of re-entrant features without the use of additional chemical coatings.

[0094] Example embodiment The technology described herein is defined in the claims. However, a non-exhaustive list of non-limiting embodiments is provided below. Any one or more of the features of these embodiments can be combined with any one or more features of another example, embodiment, or aspect described herein.

[0095] Embodiment 1 is a filter material having a layer of porous material and a plurality of structures disposed on a surface of the layer, each of the structures including a re-entrant feature.

[0096] Embodiment 2 is the filter material according to any one of embodiments 1 and 3 to 23, wherein the plurality of structures is a plurality of ordered structures.

[0097] Embodiment 3 is the filter material according to any one of embodiments 1 to 2 and 4 to 23, wherein the structure is a discrete structure.

[0098] Embodiment 4 is the filter material according to any one of embodiments 1 to 3 and 5 to 23, in which a plurality of structures form a continuous reentrant structure.

[0099] Embodiment 5 is the filter material according to any one of embodiments 1 to 4 and 6 to 23, wherein each of the plurality of structures is spherical.

[0100] A sixth embodiment is the filter material according to any one of the first to fifth and seventh to twenty-third embodiments, wherein each of the plurality of structures has an inverted spherical shape.

[0101] Embodiment 7 is the filter material of any one of embodiments 1 to 6 and 8 to 23, wherein each of the plurality of structures has a hoodoo shape.

[0102] Embodiment 8 is the filter material of embodiment 7, wherein the hoodoo geometry is determined based on a plurality of parameters including a stem radius in the range of 0.5 to 100 μm, a stem height in the range of 0 to 65 μm, an inner radius in the range of 0 to 200 μm, an outer radius in the range of 0 to 100 μm, a hoodoo angle in the range of -10 to 90 degrees, a cap height in the range of 0 to 10 μm, a hoodoo spacing in the range of 1 μm to 1 mm, and a lattice angle in the range of 45 to 90 degrees.

[0103] Embodiment 9 is the filter material of embodiment 7, wherein the hoodoo geometry is determined based on a plurality of parameters including a stem radius in the range of 0.5 to 100 μm, a stem height in the range of 0 to 65 μm, an inner radius in the range of 0 to 100 μm, an outer radius in the range of 0 to 100 μm, a hoodoo angle in the range of -10 to 90 degrees, a cap height in the range of 0 to 10 μm, a hoodoo spacing in the range of 1 to 30 μm, and a lattice angle in the range of 45 to 90 degrees.

[0104] Example 10 is the filter material of any one of Examples 1-9 and 11-23, wherein the hoodoo geometry includes a stem portion and a cap portion, and the cap portions of adjacent structures are attached to one another.

[0105] An eleventh embodiment is the filter material of any one of the first to tenth and twelfth to twenty-three embodiments, wherein a plurality of structures are formed on the layer.

[0106] A twelfth embodiment is the filter material according to any one of the first to eleventh and thirteenth to twenty-third embodiments, in which the plurality of structures are formed of a material different from the porous material.

[0107] Embodiment 13 is the filter material of any one of embodiments 1-12 and 14-23, wherein the plurality of structures are formed on a second layer bonded to the layer of porous material.

[0108] Embodiment 14 is the filter material of embodiment 13, wherein the second layer and the first layer comprise the same material.

[0109] Embodiment 15 is the filter material of embodiment 13, wherein the second layer is a different material than the first layer.

[0110] A sixteenth embodiment is the filter material according to any one of the first to fifteenth and seventeenth to twenty-third embodiments, wherein the porous material is a membrane.

[0111] Embodiment 17 is the filter material of embodiment 16, wherein the membrane comprises one of polypropylene, polyethylene, polyester, polyethersulfone, polysulfone, expanded polytetrafluoroethylene, polyvinylidene fluoride, polyamide, polyacrylonitrile, polycarbonate, cellulose acetate, and nylon.

[0112] Embodiment 18 is the filter material of any one of embodiments 1-17 and 19-23, wherein a plurality of structures are disposed on opposing surfaces of the layer.

[0113] Embodiment 19 is the filter material according to any one of embodiments 1 to 18 and 20 to 23, wherein the re-entrant shape is a double re-entrant shape.

[0114] Embodiment 20 is the filter material of any one of embodiments 1-19 and 21-23, wherein the re-entrant shape includes a substantially flat outer surface.

[0115] Embodiment 21 is the filter material of any one of embodiments 2-20 and 22-23, wherein each of the plurality of ordered structures is arranged in an array having a first dimension and a second dimension disposed at an angle relative to the first dimension, the array having a grating pitch in the first dimension and the second dimension. An edge spacing between each structure in the array can be determined based on expected contaminants.

[0116] Embodiment 22 is the filter material of embodiment 21, wherein a lattice pitch between structures in a first dimension of the array is different from a lattice pitch between structures in a second dimension of the array.

[0117] Embodiment 23 is the filter material of any one of embodiments 1-22, wherein the outer surface of the layer of porous material further comprises a coating that increases the oleophobicity of the layer.

[0118] A twenty-fourth embodiment is a filter element including the filter material according to any one of the first to twenty-third embodiments.

[0119] Embodiment 25 is a filter material that includes a layer of porous material and a plurality of re-entrant (e.g., hoodoo) structures disposed on a surface of the layer, each of the re-entrant (e.g., hoodoo) structures comprising a stem and a cap, the caps of adjacent structures being attached to form a plurality of pores, each pore being disposed between adjacent hoodoo structures.

[0120] Embodiment 26 is the filter material of any one of embodiments 25 and 27-36, wherein a plurality of structures are formed on the layer.

[0121] Embodiment 27 is the filter material according to any one of embodiments 25-26 and 28-36, wherein the plurality of structures are formed from a material different from the porous material.

[0122] Embodiment 28 is the filter material of any one of embodiments 25-27 and 28-36, wherein the plurality of structures includes a second layer bonded to the layer of porous material.

[0123] Embodiment 29 is the filter material of embodiment 28, wherein the second layer and the first layer comprise the same material.

[0124] Embodiment 30 is the filter material of embodiment 28, wherein the second layer is a different material than the material of the first layer.

[0125] Embodiment 31 is the filter material according to any one of embodiments 25 to 30 and 32 to 36, wherein the porous material is a membrane.

[0126] Embodiment 32 is the filter material of embodiment 31, wherein the membrane comprises one of polypropylene, polyethylene, polyester, polyethersulfone, polysulfone, expanded polytetrafluoroethylene, polyvinylidene fluoride, polyamide, polyacrylonitrile, polycarbonate, cellulose acetate, and nylon.

[0127] Embodiment 33 is the filter material of any one of embodiments 25-32 and 34-36, wherein a plurality of structures are disposed on opposing surfaces of the layer.

[0128] Embodiment 34 is the filter material according to any one of embodiments 25 to 33 and 35 to 36, wherein the re-entrant structure forms a substantially flat outer surface.

[0129] Embodiment 35 is a filter material of any one of embodiments 25-34 and 36, wherein each of the plurality of structures is arranged in an array having a first dimension and a second dimension, and a first lattice pitch between the structures in the first dimension of the array is different from a second lattice pitch between the structures in the second dimension of the array.

[0130] Embodiment 36 is the filter material of any one of embodiments 25-35, wherein the outer surface of the layer of porous material further comprises a coating that increases the oleophobicity of the layer.

[0131] A thirty-seventh embodiment is a filter element including the filter material according to any one of the twenty-fifth to thirty-sixth embodiments.

[0132] Embodiment 38 is a filter material that includes a layer of porous material and a first plurality of structures disposed on a surface of the layer, each of the structures having a re-entrant shape, at least some of the structures having re-entrant shapes along two orthogonal planes, and optionally, at least some of the first plurality of structures include re-entrant shapes along three orthogonal planes.

[0133] Embodiment 39 is a filter material described in any one of embodiments 38 and 40 to 64, wherein the first plurality of structures including re-entrant shapes along three orthogonal planes includes a first re-entrant shape in a plane substantially perpendicular to the layer of porous material and a second re-entrant shape in a plane substantially parallel to the layer of porous material.

[0134] Embodiment 40 is a filter material described in any one of embodiments 38-39 and 41-64, wherein the first plurality of structures including re-entrant shapes along three orthogonal planes includes a webbed stem including a plurality of connected webs and a rib extending from an edge of each web.

[0135] Embodiment 41 is the filter material of any one of embodiments 38-41 and 42-64, wherein the lobes define a re-entrant shape in a plane parallel to the surface of the substrate.

[0136] Embodiment 42 is the filter material of embodiment 41, wherein each of the ribs includes a similar second re-entrant shape.

[0137] Embodiment 43 is the filter material of any one of embodiments 40-42, wherein the ribs run parallel to the longitudinal axis of the structure.

[0138] Embodiment 44 is the filter material of embodiment 43, wherein the ribs define a convex curve away from the stem.

[0139] Embodiment 45 is the filter material of embodiment 43, wherein the ribs define a concave curve toward the stem.

[0140] Embodiment 46 is the filter material of any one of embodiments 38-45 and 47-64, wherein the subset of structures are discrete structures.

[0141] Embodiment 47 is the filter material of any one of embodiments 38-46 and 48-64, wherein a subset of the structures form a continuous re-entrant structure.

[0142] Embodiment 48 is the filter material of any one of embodiments 38-47 and 49-64, wherein the subset of structures are spherical.

[0143] Embodiment 49 is the filter material of any one of embodiments 38-48 and 50-64, wherein a subset of the structures have an inverted spherical shape.

[0144] Embodiment 50 is the filter material of any one of embodiments 38-49 and 51-64, wherein the subset of structures has a hoodoo shape.

[0145] Embodiment 51 is a filter material according to any one of embodiments 38-50 and 52-64, wherein the structures in the subset are arranged in a pattern configured to control the movement of breakthrough fluid.

[0146] Embodiment 52 is the filter material of embodiment 51, wherein the pattern forms a circumference of the shape.

[0147] Embodiment 53 is the filter material of embodiment 52, wherein the circumferentially disposed structures are not part of the subset of structures.

[0148] Embodiment 54 is a filter material according to any one of embodiments 38-53 and 55-64, further comprising a second plurality of structures having re-entrant shapes along three orthogonal planes, the second plurality of re-entrant structures being different from the first plurality of structures.

[0149] Embodiment 55 is the filter material of embodiment 54, wherein the first plurality of structures includes a first number of webs and the second plurality of structures includes a second number of webs.

[0150] Embodiment 56 is the filter material of embodiment 54, wherein the first plurality of structures includes a cap and the second plurality of structures does not include a cap.

[0151] Embodiment 57 is a filter material as described in embodiment 54, in which a structure having re-entrant shapes along three orthogonal planes is placed in close proximity to a structure having re-entrant shapes along two orthogonal planes to control the movement of breakthrough fluid.

[0152] Embodiment 58 is the filter material of any one of embodiments 38-57, wherein the second plurality of structures has an average diameter smaller than the average diameter of the first plurality of structures.

[0153] Embodiment 59 is a filter element including the filter material according to any one of embodiments 38 to 58.

[0154] Embodiment 60 is a filter material described in any one of embodiments 1 to 37 and 59, wherein the plurality of structures form a continuous structure defining a second layer having a first surface and a second surface opposite the first surface, the second layer including a plurality of pores formed between the plurality of structures, and the second surface including one or more grooves disposed between the pores.

[0155] Embodiment 61 is the filter material of embodiment 60, wherein the one or more grooves form continuous shapes, each continuous shape surrounding one or more pores.

[0156] Embodiment 62 is a liquidphobic material comprising a first layer including a lattice having a first surface and a second surface opposite the first surface, and a plurality of pores extending from the first side to the second surface, each pore including a reentrant structure adjacent the first surface, rendering the first surface liquidphobic. The first layer may optionally further include a plurality of drainage structures disposed along the second surface.

[0157] Embodiment 63 is the liquidphobic material of embodiment 62, wherein the plurality of drainage structures comprises protrusions extending from the second surface.

[0158] Embodiment 64 is the liquidphobic material of embodiment 62 or 63, wherein the plurality of drainage structures comprises grooves in the second surface.

[0159] Embodiment 65 is the liquidphobic material of embodiment 64, wherein the channels comprise continuous shapes, each continuous shape surrounding one or more pores.

[0160] Embodiment 66 is the liquidphobic material of any one of embodiments 62-65, further comprising a second layer disposed along the second surface of the first layer.

[0161] Embodiment 67 is the liquidphobic material of embodiment 66, wherein the second layer comprises a filtration medium. EXAMPLES

[0162] Example 1 The predicted value of breakthrough (wetting) pressure is calculated using the formula above. In Example 1, edge spacing is held constant for hoodoos with various parameters identified as geometries 1-9 in Figure 8. The values ​​in Figure 8 are provided for a liquid with a surface tension of 26 mN / m and a contact angle of 44 degrees.

[0163] The values ​​of stem height and cap height, as shown by geometries 2 and 3, are cropped in FIG. 8 to show that they do not affect the breakthrough pressure.

[0164] Geometries 4 through 9 are iteratively varied one feature dimension at a time (indicated by the shaded values) and the resulting breakthrough pressures are shown at the bottom of Figure 8. The greatest effects on breakthrough pressure are observed for geometries 5 through 9 and are discussed in Example 2.

[0165] Example 2 The predicted value of breakthrough (wetting) pressure is calculated using the formula above. In Example 2, edge spacing is held constant for hoodoos with various parameters identified as geometries 1-9 in Figure 8. The values ​​in Figure 8 are provided for a liquid with a surface tension of 26 mN / m and a contact angle of 44 degrees.

[0166] Figure 9 further analyzes the parameters that change the breakthrough pressure the most. As seen in Figure 9, the hoodoo angle increases the breakthrough pressure as the hoodoo angle increases. As the outer radius decreases, the F CL Increasing the inner radius increases the breakthrough pressure by changing the pinning location of the contact line, F. Reducing the edge spacing increases the breakthrough pressure by decreasing A (the projected surface area of ​​the liquid). Increasing the inner radius increases the breakthrough pressure by changing the pinning location of the contact line, F. CL Affects both A and B.

[0167] Examples 3-5 tested the breakthrough pressure of 3D printed structures using a stereolithography (SLA) printer (Form 3B, Formlabs, Somerville, MA, USA).

[0168] Example 3 Re-entrant structures (i.e., hoodoos) were 3D printed as described above with various tip radii and spacings as shown in Table 1 below. Breakthrough pressure was measured by gluing a syringe to the 3D printed structure and continuously adding water to the syringe until breakthrough was observed. Breakthrough pressure was calculated from the head pressure of the water prior to breakthrough. The experimental breakthrough pressure was compared to the predicted value using the equation above.

[0169] [Table 1]

[0170] The measured breakthrough pressure is consistently about 70% of the predicted breakthrough pressure, as can be seen in Figure 10. Table 1 shows that, as predicted, smaller spacing results in increased breakthrough pressure and sharper tips (i.e., reduced outer radius) result in increased breakthrough pressure.

[0171] Example 4 Re-entrant structures (i.e., hoodoos) were 3D printed as described above with various tip radii and spacings as shown in Table 2 below. Breakthrough pressure was measured with a drop of water. The drop was forced into the re-entrant structure by a hydrophobic plate. A balance recorded the change in mass as the drop was forced into the re-entrant structure and converted to breakthrough pressure.

[0172] [Table 2]

[0173] As shown in Table 2, the measured and predicted breakthrough pressures are relatively close at low breakthrough pressures. This method can generate artificially high breakthrough pressures from droplets moving laterally across the hoodoo rather than downward into the structure, and therefore should be used with caution for structures with high breakthrough pressures. This may also be the reason for the large standard deviation in Table 2.

[0174] Example 5 The reentrant structures were replicated on a microscale and designed to repel low surface tension (>20 mN / m) liquids without the use of any chemical coatings. The reentrant structures (hoodoos) were fabricated by molding and hot embossing processes described below. Figure 24A is a schematic side view of one of the pores of the printed structure with reentrant sides, turned upside down so that the outlet side is on top. Figures 24B and 24C are microscopic images of a single pore with reentrant sides in the orientation shown from Figure 24A (i.e., outlet side up).

[0175] A master stamp was fabricated by etching glass with a femtosecond laser to form reentrant structures (hoodoos). The master stamp was designed with tall pin structures that puncture through holes in the resulting hot embossed film. The master stamp was then directly replicated by electroforming to create a nickel stamp. A 200 nm gold layer was sputter coated onto the glass master prior to electroforming to ensure ease of demolding. The nickel stamp was then used in a hot embossing process to create the final reentrant structures. A polymethyl methacrylate (PMMA) film (50 μm thick), available as product ME 30-FM-000150 from Goodfellow Corporation, Pittsburgh, PA, was used in the hot embossing process with the silicone layer on top to act as a sacrificial layer. The tall pin structures penetrate the 50 μm PMMA film into the sacrificial silicone layer to form through holes. The PMMA film was embossed for 5 min at a temperature of 135 °C and a force of 2 kN. After the PMMA film was cooled to below 100° C., the force was released.

[0176] Example 6 Re-entrant structures (hoodoos) were 3D printed as described above. Single re-entrant structures were printed with pore sizes of 500 μm or 1000 μm. The outlet structure channel width was either 500 μm or 1000 μm and surrounded all pores. Continuous lattices with pores with re-entrant sides were prepared with and without outlet structures (drains).

[0177] The test liquid was water containing 0.5% sodium dodecyl sulfate (SDS). The test liquid was pressurized with a syringe to induce breakthrough while imaging the droplet propagation. Tests were performed with pressurized liquid volumes either below (FIG. 25) or above (FIG. 28) the reentrant structure array. Figures 26A-27C and 29A-29E are images captured from footage taken during the experiment.

[0178] Figures 26A-C show a reentrant structure array with 1000 μm pore size with no outlet structures, tested with a pressurized volume applied from below the sample (as shown in Figure 25). Liquid penetrates at point B, indicated by the arrow in Figure 26A, and propagates across the array, causing extensive failure by wetting the pores across the array.

[0179] Figures 27A-C show a reentrant structure array with 1000 μm outlet structure channels surrounding all pores, 500 μm and 1000 μm pore sizes, with the 1000 μm pores acting as "defects", tested with a pressurized volume applied from below the sample. Liquid penetrates at point B, indicated by the arrow in Figure 27B, filling the channel volume and propagating around the pores, preventing extensive failure.

[0180] FIG. 28 shows the test setup of a reentrant structure array with 1000 μm outlet structure channel surrounding all pores, pore sizes of 500 μm and 1000 μm, with the 1000 μm pore acting as a "defect", tested with a pressurized volume applied from above the sample. In some cases, breakthrough occurs (point B indicated by arrow in FIG. 29A), and in some cases, liquid continues to drip out of the sample, as shown at point B indicated by arrow in FIG. 29A. In other cases, liquid penetrates a single pore and fills some volume of the outlet structure channel, as shown, for example, at point D in FIG. 29D and FIG. 29E. The outlet structure in this case prevented extensive failure of the array. Unless otherwise indicated, all numbers expressing size, quantity, and physical properties of features used in this specification and claims should be understood to be modified in all cases by the term "about". Accordingly, unless indicated to the contrary, the numerical parameters set forth in the foregoing specification and attached claims are approximations that may vary depending upon the desired properties that one of ordinary skill in the art would seek to obtain using the teachings disclosed herein. The use of numerical ranges by endpoints includes all numbers within that range (e.g., 1 to 5 includes 1, 1.5, 2, 2.75, 3, 3.80, 4, and 5) and any range within that range.

[0181] The above description has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the embodiments to the precise form disclosed. Many modifications and variations are possible in light of the above teaching. Any or all features of the disclosed embodiments may be applied individually or in any combination and are not meant to be limiting but are purely exemplary. It is intended that the scope of the invention be determined not by this detailed description but rather by the appended claims.

Claims

1. A filter material comprising: a layer of porous material; a plurality of re-entrant structures, each of the re-entrant structures including a stem and a cap, the caps of adjacent structures being attached to one another to form a plurality of pores, each pore being disposed between adjacent re-entrant structures; Equipped with A filter material, wherein the pores are through holes extending through a layer of the porous material.

2. The filter material of claim 1, wherein the porous material is a membrane, and optionally the membrane comprises one or more of polypropylene, polyethylene, polyester, polyethersulfone, polysulfone, expanded polytetrafluoroethylene, polyvinylidene fluoride, polyamide, polyacrylonitrile, polycarbonate, cellulose acetate, and nylon.

3. A filter material as described in any one of claims 1 and 2, wherein each of the plurality of structures is arranged in an array having a first dimension and a second dimension, and a first lattice pitch between structures in the first dimension of the array is different from a second lattice pitch between structures in the second dimension of the array.

4. A filter element comprising a filter material described in any one of claims 1 and 2.

5. A liquidphobic material, comprising: A first layer, a grating having a first surface and a second surface opposite the first surface; a first layer including a plurality of pores extending from the first surface to the second surface, each pore including a re-entrant structure adjacent the first surface, rendering the first surface liquidphobic.

6. The liquidphobic material of claim 5, further comprising a plurality of drainage structures arranged along the second surface, optionally, the plurality of drainage structures comprising protrusions extending from the second surface, and optionally, the plurality of drainage structures comprising grooves in the second surface.

7. A liquidphobic material as described in any one of claims 5 and 6, further comprising a second layer disposed along the second surface of the first layer, optionally the second layer comprising a filtration medium.

8. A liquidphobic material described in any one of claims 5 and 6, wherein the pores have a pore diameter in the range of 1 μm to 30 μm, or in the range of 30 μm to 2 mm.

9. The liquidphobic material described in any one of claims 5 and 6, wherein the liquidphobic material comprises a filtration medium or a ventilation medium.

10. The liquidphobic material of any one of claims 5 and 6, wherein the liquidphobic material is a membrane, and optionally the membrane comprises one or more of polypropylene, polyethylene, polyester, polyethersulfone, polysulfone, expanded polytetrafluoroethylene, polyvinylidene fluoride, polyamide, polyacrylonitrile, polycarbonate, cellulose acetate, and nylon.

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