Membrane utilizing a tiling and method of making same

Abstract

A membrane design utilizing a tiling. In some embodiments, the tiling design is employed in transport processes including filtration and particle capture, static mixing, catalyst support, and heat transfer. Membrane design includes selecting walls from each tile in the tiling to be removed.

Description

Attorney Docket No.: 104877-301TITLE MEMBRANE UTILIZING A TILING AND METHOD OF MAKING SAME CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application No. 63 / 722,272, filed November 19, 2024, and U.S. Provisional Application No. 63 / 920,515, filed November 19, 2025, which are both incorporated herein by reference as if disclosed in their entireties.BACKGROUND

[0002] Transport processes require an intervening medium. Many models have been developed to describe how transport processes occur through natural materials. These media are also very complicated geometrically so understanding how the geometry affects transport is often obscured. Mazes can be used as abstractions for natural transport processes. Transport processes of the type that may be more widely applicable generally involve multiple inlets and outlets.

[0003] Most common 2-D maze generation algorithms are based on the generation of a tiling of regular polygons. Maze generation is pseudo-random in that it uses a seeded, random number generator whenever a decision, such as which wall to remove upon visiting a cell, is required. The deterministic component of this approach is that by knowing the seed number, one can reproduce a maze geometry identically. Maze algorithms incorporate randomness in different forms and to different degrees, leading to vastly different generated mazes.

[0004] What is needed is a manner of making more effective transport structures that are easier to implement, study, fabricate, and that represent the inherent variability of natural systems better.SUMMARY

[0005] According to a first aspect of this technology, a tiling design is provided. In some embodiments, the tiling is aperiodic. In some embodiments, the tiling is chiral. In some embodiments, the tiling design is employed in transport processes including filtration and particle capture, static mixing, catalyst support, and heat transfer.132800068.1Attomev Docket No.: 104877-301

[0006] According to another aspect, a membrane filter is provided that includes a filtration section comprising a tiling, where each tile comprises a number of walls expect for a select number of removed walls. The performance of the filter is adjustable based on the tile walls selected for removal.

[0007] According to another aspect, a method for designing a membrane filter is provided, comprising selecting walls from each tile to be removed and producing a filtration section using the design.BRIEF DESCRIPTION OF THE DRAWINGS

[0008] The drawings show embodiments of the disclosed technology for the purpose of illustrating features and advantages of the disclosed technology. However, it should be understood that the present application is not limited to the precise arrangements and instrumentalities shown in the drawings, wherein:

[0009] FIG. 1 shows a tile consistent with several embodiments of the present technology.

[0010] FIG. 2 shows a tiling formed using the tile of FIG. 1.

[0011] FIG. 3 shows a schematic view of a filtration membrane using the tiling of FIG. 2.

[0012] FIG. 4 shows modified tile design according to an embodiment of the present technology.

[0013] FIG. 5 shows permeability data for various embodiments of the present technologyDETAILED DESCRIPTION

[0014] FIG. 1 shows a tile 100 according to a first embodiment of the present technology. The tile 100 has the shape defined by the points in the following table, with coordinates as shown.232800068.1Attomev Docket No.: 104877-301Point Coordinate® Point Coordinate®dumber (M) Numte* fx,y)

[0015] The above table shows the coordinates for an embodiment in which each wall length is 1. This length is dimensionless, however, as tiles according to embodiments of the present technology will have wall lengths selected according to the particular demands of the application. That is, the above table defines the tile shape, not the tile size, which varies.

[0016] Referring to FIG. 1, the tile 100 is defined by successive points 1-14. These points define walls 1-14 of the tile 100 as shown by the circled numbers in FIG 1. “Successive points” as referred to herein means points 1 and 2, points 2 and 3, points 3 and 4, and so on through points 14 and 1 to complete the tile 100 as shown.

[0017] FIG. 2 shows a tiling 200 formed using a plurality of tiles 100. As used herein, the term “tiling” refers to an arrangement of tiles that covers an area without overlapping. According to one embodiment, the tiling 200 is used to form a membrane filter 300, as shown in FIG. 3. In this embodiment, the membrane filter 300 comprises a filtration section 301. The filtration section 301 comprises a tiling formed using a plurality of tiles each having a shape defined by the points shown in the above table.

[0018] In the filtration section 301 according to a first embodiment, each tile comprises walls between successive points except for a first removed wall between a first set of successive points and any wall that is contiguous with a first removed wall of an adjacent tile. For example,332800068.1Attorney Docket No.: 104877-301in some embodiments, the first removed wall of each tile is the wall between points 6 and 7 (i.e., wall 7). FIG. 4 shows the tile shape 400 with wall 7 removed. In this embodiment, the wall in any neighboring tile that would be contiguous with wall 7 is also removed. This opens a flow path between the various tiles in the tiling.

[0019] In some embodiments, each tile in the filtration section also lacks a second removed wall between a second set of successive points as well as any wall contiguous with a second removed wall of an adjacent tile. For example, in one embodiment, the second removed wall of each tile is the wall between points 12 and 13 (i.e., wall 13). This design is shown in FIG. 4. Further, in this embodiment, the wall in any neighboring tile that would be contiguous with wall 13 is also removed. In another embodiment, the second removed wall of each tile is the wall between points 11 and 12 (i.e., wall 12). In another embodiment, the second removed wall of each tile is the wall between points 14 and 1 (i.e., wall 1). As discussed below, these embodiments have been found to provide relatively high permeability.

[0020] In another embodiment, the first removed wall of each tile is the wall between points 2 and 3 (i.e., wall 3). In some embodiments, the second removed wall of each tile is the wall between points 5 and 6 (i.e., wall 6). As also discussed below, these embodiments provide relatively high particle capture.

[0021] In some embodiments, more than two walls per tile are selected for removal. For example, in some embodiments a third removed wall as well as any wall that is contiguous with a third removed wall of an adjacent tile is lacking in each tile of the tiling. In some embodiments, a fourth, a fifth, a sixth, a seventh, an eight, a ninth, a tenth, an eleventh, a twelfth, or a thirteenth are removed according to the performance objectives of the filtration section.

[0022] In some embodiments, walls are removed non-uniformly from tiles in the tiling. For example, a first set of tiles in the tiling may have walls 7 and 12 removed, while a second set of tiles in the tiling has walls 1 and 6 removed. In some embodiments, multiple sets of tiles with different wall removal patterns are used in a tiling. In some embodiments, the wall removal pattern varies by height within the filtration section, such that a top of the filtration section might have a first wall density that transitions to a second wall density at the bottom of the filtration section. In some embodiments, wall removal is performed by a random choice of walls to be removed for432800068.1Attomev Docket No.: 104877-301each tile using, for example, a pseudo-random number generator for each tile. This technique is used in some embodiments to select the number of walls to be removed per tile as well as which walls to be removed.

[0023] In some embodiments, the length of each wall is about 8 micrometers. In some embodiments with this wall length, the overall filtration section is about 475 micrometers tall and about 480 micrometers wide. As shown in FIG. 3, the membrane filter 300 also comprises an input section 302 and an output section 303. In some embodiments, the input and output sections are uniform regions into which a fluid to be filtered is provided to flow into the filtration section 301. In the embodiment shown, some of the upper and lower tiles protrude into the input and output sections. In some embodiments, the protruding tiles have permeable walls to permit flow into the filtration section. In some embodiments, the protruding tiles lack walls that would impede flow into the filtration section. For example, the uppermost walls of the tiles that protrude into the input section are removed and the lowermost walls of the tiles that protrude into the output section are removed.

[0024] FIG. 5 shows the correlation between the permeability of the filtration section and the wall number removed in addition to wall 7. The volumetric flow rate through the structure was calculated, and the pressure drop required to sustain it to determine permeability, K. In the following equation, / / is the viscosity of the fluid, AP is the pressure drop through the structure, V is the volumetric flowrate through the structure, and L is the overall thickness of the structure.VfiLK~ -& P

[0025] In general, and without wishing to be bound by theory, the permeability of the structure is highest when inlets and outlets are furthest apart. Also without wishing to be bound by theory, permeability is also highest when the velocity deviation is smallest. Most single inlet, single outlet systems are not permeable for all combinations of inlet and outlet walls. Walls 7 and 8 are permeable for all wall combinations paired with either of those two as the inlet.

[0026] The membrane filter design according to some embodiments can be adjusted for desired particle capture performance. Simulations were run using the structure shown in FIG. 3 for particle capture. Without wishing to be bound by theory, it is believed that the more interaction or close encounters a particle would have with the walls of the structure, the better the chances the 532800068.1Atomev Docket No.: 104877-301particle would have of being captured. The simulation was run using designs with various combinations of two walls removed plus any wall contiguous with a removed wall in any adjacent tile.

[0027] The finite element simulation with particle tracking assumed an inlet fluid velocity of 0.001 m / s, a particle size of 1 μm, and that particles would be captured if their centers approached the wall at a distance of less than one particle radius. The particles were assumed to be silica with a density of 2200 kg / m3. The Stokes drag force with Oseen correction on the particles and a simple van der Waals attraction between a sphere and flat surface (F = — Arparticle / 6δ2) was included, where 5 is the separation distance between the particle and the wall. A generic Hamaker constant, A = -1 x 10-21J was used. Wall lengths in this structure are 8 μm and the overall area occupied by a tile is 524.5 μm2. The pinch point in the structure between points 5 and 9 is 7.17 μm long.

[0028] Maximum capture in these simulations was achieved by removing walls 3 and 6, as well as walls contiguous with walls 3 and 6 in adjoining tiles.

[0029] According to another aspect of the present technology, a method for making a membrane filter is provided. The method comprises the steps of generating a tiling design using a plurality of tiles each having a shape defined by the points in the above table, then modifying the tiling design by selecting a first wall between a first set of successive points to remove from each tile and selecting each wall of a tile that is contiguous with a first removed wall of an adjacent tile to remove from each tile. The modified tiling design is used to produce a filtration section.

[0030] In some embodiments, the step of selecting a first wall comprises selecting the wall between points 6 and 7. In some embodiments, the step of modifying further comprises selecting a second wall between a second set of successive points to remove from each tile; and selecting each wall of a tile that is contiguous with a second removed wall of an adjacent tile to remove from each tile.

[0031] In some embodiments, the step of selecting a second wall comprises selecting the wall between points 12 and 13. In some embodiments, the step of selecting a second wall632800068.1Attomev Docket No.: 104877-301comprises selecting the wall between points 11 and 12. In some embodiments, the step of selecting a second wall comprises selecting the wall between points 14 and 1.

[0032] In some embodiments, the step of selecting a first wall comprises selecting the wall between points 2 and 3. In some embodiments, the step of selecting a second wall comprises selecting the wall between points 5 and 6.

[0033] In some embodiments, the step of producing comprises use of an additive manufacturing technique. In some embodiments, the thickness of the walls of the tile is scaled nonuniformly.

[0034] The tiling designs are used for other types of transport processes in other embodiments. For example, in some embodiments, the tiling designs disclosed herein are extruded into a 3-D structure and employed as a static mixer. In some embodiments, the tiling designs are used in a heat transfer application, such as a chip cooling structure. In some embodiments, singlephase cooling is used such as flowing water, refrigerant, or liquid metal, like gallium, through the channels formed in the structure. The flow is structured as desired to vary which areas are most efficiently cooled by selecting which walls we remove. In some embodiments, phase change heat transfer is utilized wherein vapor can flow either from top to bottom of the structure, or in embodiments in which the system is encapsulated, holes are drilled in the top at the big regions of the tiles and vent the vapor out.

[0035] In some embodiments, the tiling designs are used as catalyst support to promote chemical reactions.

[0036] Although the disclosed subject matter has been described and illustrated with respect to embodiments thereof, it should be understood by those skilled in the art that features of the disclosed embodiments can be combined, rearranged, etc., to produce additional embodiments within the scope of the technology, and that various other changes, omissions, and additions may be made therein and thereto, without parting from the spirit and scope of the present technology.732800068.1

Claims

Attorney Docket No.: 104877-301CLAIMS1. A membrane filter, comprising:a filtration section, comprising a tiling formed using a plurality of tiles each having a shape defined by points:Point Coordinate® Point Cour toate®Number {x,y) Number (Xy)I (0,0) (2,3) 2 Wl) / 3 6 — v 3 X 3.2 2 / 8 io ( -3 V <3 & — V <3 5 4 H 5 12 6 1314wherein each tile in the filtration section comprises walls between successive points except for:a first removed wall between a first set of successive points; andany wall contiguous with a first removed wall of an adjacent tile.

2. The filtration membrane of claim 1, wherein the first removed wall of each tile is the wall between points 6 and 7.

3. The filtration membrane of claim 1, further comprising that each tile lacks a second removed wall between a second set of successive points and any wall contiguous with a second removed wall of an adjacent tile.

4. The filtration membrane of claim 3, wherein the first removed wall of each tile is the wall between points 6 and 7.

5. The filtration membrane of claim 4, wherein the second removed wall of each tile is the wall between points 12 and 13.

6. The filtration membrane of claim 4, wherein the second removed wall of each tile is the wall between points 11 and 12.832800068.1Attomev Docket No.: 104877-3017. The filtration membrane of claim 4, wherein the second removed wall of each tile is the wall between points 14 and 1.

8. The filtration membrane of claim 3, wherein the first removed wall of each tile is the wall between points 2 and 3.

9. The filtration membrane of claim 8, wherein the second removed wall of each tile is the wall between points 5 and 6.

10. The filtration membrane of claim 1, further comprising that the length of each wall is about 8 micrometers.

11. A method for making a membrane filter, comprising the steps of:generating a tiling design using a plurality of tiles each having a shape defined by points:Point Coordinates Point CoordinatesNumber (x,y) Number (x,y)9 10u 12 13 14modifying the tiling design by:selecting a first wall between a first set of successive points to remove from each tile; andselecting each wall of a tile that is contiguous with a first removed wall of an adjacent tile to remove from each tile; andproducing a filtration section using the modified tiling design.

12. The method of claim 11, wherein the step of selecting a first wall comprises selecting the wall between points 6 and 7.

13. The method of claim 11, wherein the step of modifying further comprises:932800068.1Attomev Docket No.: 104877-301selecting a second wall between a second set of successive points to remove from each tile; andselecting each wall of a tile that is contiguous with a second removed wall of an adjacent tile to remove from each tile.

14. The method of claim 13, wherein the step of selecting a first wall comprises selecting the wall between points 6 and 7.

15. The method of claim 14, wherein the step of selecting a second wall comprises selecting the wall between points 12 and 13.

16. The method of claim 14, wherein the step of selecting a second wall comprises selecting the wall between points 11 and 12.

17. The method of claim 14, wherein the step of selecting a second wall comprises selecting the wall between points 14 and 1.

18. The method of claim 13, wherein the step of selecting a first wall comprises selecting the wall between points 2 and 3.

19. The method of claim 18, wherein the step of selecting a second wall comprises selecting the wall between points 5 and 6.

20. The method of claim 11, wherein the step of producing comprises use of an additive manufacturing technique.1032800068.1

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