Method and apparatus for determining liquid-solid bonding work

Abstract

The present invention is a method for determining the liquid-solid adhesion work, during which, in relation to a liquid cylindrically symmetric capillary bridge in a fluid medium between an end having a peripheral circular edge of a measurement element and a solid surface to be tested, a cylindrically symmetrical hold correction is performed on the capillary bridge to determine the change in interfacial area of ​​the capillary bridge and the fluid medium, as well as the capillary bridge and the surface to be tested (S110a), a capillary force is determined (S100) to determine the corresponding total mechanical work (S110b), and for the cylindrically symmetrical hold correction, a difference value of the solid-liquid interfacial tension and the solid-fluid interfacial tension is determined based on the interfacial area change, the total mechanical work, and the liquid-fluid interfacial tension (S120), and the liquid-solid adhesion work is determined by subtracting it from the liquid-fluid interfacial tension (S130). The present invention is further an apparatus for determining liquid-solid adhesion.

Description

[Technical Field]

[0001] The present invention relates to a method and apparatus adapted for determining the work of liquid-solid adhesion. [Background technology]

[0002] Liquid-solid bonding work is a quantity commonly used to characterize liquid-solid interfaces, and its value provides information about the interaction between the solid and liquid phases in contact on a unit surface area. Therefore, it is a specific quantity, and its unit of measurement is the surface tension (Nm / m²). 2 Although the unit of measurement is the same as that of work, it is conventionally represented by the letter "W" for work, and the specific amount of work may also be represented by the lowercase "w". It is very important in all such industrial fields where a liquid comes into contact with a solid surface (e.g., electronics and cosmetics, paper, adhesives, paints, printing and textile industries, soldering and dental technology, etc.). This quantity can be measured by the Young-Dupre equation by measuring the contact angle formed at the liquid-solid boundary:

[0003]

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[0004]

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[0005]

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[0006]

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[0007] This method retains the various measurement and theoretical uncertainties arising from the characteristics of the contact angle measurement method. In certain cases, the contact angle value may be determined with significant uncertainty, especially when the contact angle is small (<10°~20°) and large (>150°). Furthermore, the equilibrium Young contact angle...

[0008]

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[0009]

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[0010] Apparatus and methods are known for measuring the force required to eliminate a solid-liquid interface under specific geometric conditions and parameters in order to characterize liquid-solid adhesion (Patent Document 1). Since the water contact angles of hydrophobic and superhydrophobic surfaces can usually be determined with large errors, an apparatus has been developed (Patent Document 2) that measures the force generated while bringing a droplet closer to (approaching) a surface and moving the droplet away from a surface, including time instances of forming and eliminating a solid-liquid interface, by using a circular plate fixed to a force measuring instrument and pressing a droplet onto the surface with the help of the same. A similar apparatus and method is disclosed in Patent Document 3 in which the adhesive force (i.e., capillary force referred to as “adhesion force” in certain disclosures; see also the following explanation relating these terms) derived from the liquid volume placed between solid surfaces is measured during the process of further removing the solid surfaces and bringing them closer together.

[0011] Patent Document 4 discloses a method in which an object having specific parameters is immersed in a liquid, and a specific quantity is estimated based on this.

[0012] Apparatus and method suitable for measuring dynamic contact angle are disclosed in Patent Document 5. This method does not involve the use of a force measuring instrument. A similar technical method is disclosed in Patent Document 6.

[0013] Patent Document 7 discloses an apparatus and method for measuring contact angle and dynamic surface tension.

[0014] An apparatus adapted for determining the contact angle is disclosed in Non-Patent Document 4, which is a specialized article. The specialized article addresses aspects related to the contact angle.

[0015] A device similar to the one described in the specialist article is disclosed in the aforementioned Patent Document 2.

[0016] In Patent Document 8, the identification of the molecules located on the surface returns to force measurement. In this process, the base surface of an elastic column with a known surface area is directly pressed against the surface to be tested that contains molecules. The force applied during the compression process is directed at deforming the elastic column, and the amount of work input is stored by the column in the form of elastic energy. In the method according to this document, the amount of adhesion work between the molecules and the surface with a known area is identified as the difference in the integral (with respect to displacement) of the force measured when compressing and separating the surface, as an indicator of the molecular weight.

[0017] A technique for determining the amount of adhesion work without measuring the contact angle is disclosed in Patent Document 9. This technique is fundamentally different from the above technique and is based on the fact that based on rotational (centrifugal) measurement, the force exerted on the liquid droplet can be calculated from the rotational speed at the moment when the liquid droplet is separated from the surface.

[0018] Considering the known techniques, there is a need for an apparatus and method for determining the liquid-solid adhesion work amount that enables the liquid-solid adhesion work amount to be determined more efficiently compared to existing techniques.

Prior Art Documents

Patent Documents

[0019]

Patent Document 1

Patent Document 2

Patent Document 3

Patent Document 4

Patent Document 5

Patent Document 6

Patent Document 7

Patent Document 8

[0020] [Non-Patent Document 1] A.Marmur:Solid-Surface Characterization by Wetting.Annu.Rev.Mater.Res.39, pp. 473-89 (2009) [Non-Patent Document 2] J. Drelich et al.: The Effect of Drop(Bubble) Size on Advancing and Receding Contact Angles for Heterogeneous and Rough Solid Surfaces as Observed with Sessile-Drop and Captive-Bubble Techniques. J. Colloid Interface Sci. 179, pp. 37-50 (1996) [Non-Patent Document 3] R. Tadmor et al. Solid-Liquid Work of Adhesion. Langmuir 33, pp. 3594-3600 (2017) [Non-Patent Document 4] N.Nagy:Contact Angle Determination on Hydrophilic and Superhydrophilic Surfaces by Using r-θ-Type Capillary Bridges [Langmuir 35, page 5202 (2019) [Overview of the Initiative]

[0021] The main objective of the present invention is to provide a method and apparatus for determining liquid-solid bonding work that, as far as possible, avoids the drawbacks of prior art methods.

[0022] The object of the present invention is to provide a method and apparatus for applications in which the liquid-solid bonding work can be determined independently of the contact angle measured at the liquid-solid interface (surface). In other words, the problem set for the present invention was to determine the liquid-solid bonding work independently of the measurement of the contact angle.

[0023] The object of the present invention can be achieved by providing the method according to claim 1 and the apparatus according to claim 4. Preferred embodiments of the present invention are defined in the dependent claims.

[0024] The method and apparatus according to the present invention are based on the understanding that when a cylindrically symmetrical capillary bridge extending between a circular solid surface and a solid surface under test is formed from the liquid in the surrounding fluid medium such that the liquid contact line adheres (pins) to the edge of the circular solid surface, the capillary force is measured during the process of cylindrical symmetry-holding modification of the capillary bridge (i.e., change in its length or volume), determining the change in liquid-fluid interface area (change in liquid-fluid interface area) and the change in interface area between the liquid and the solid surface under test (change in liquid-tested solid surface area) during the process, and then integrating the capillary force to determine the work done by solid-liquid adhesion in knowledge of the energy change of the system, and therefore the liquid-fluid interface tension. [Brief explanation of the drawing]

[0025] Preferred embodiments of the present invention are described below, by example, with reference to the following drawings. [Figure 1] This is a flowchart of the method according to the present invention. [Figure 2] This is a schematic diagram of an apparatus suitable for carrying out one embodiment of the method according to the present invention. [Figure 3] This is a schematic diagram of an apparatus suitable for carrying out another embodiment of the method according to the present invention. [Figure 4A] This graph shows the measurements performed on the hydrophilic surface being tested. [Figure 4B] This graph shows the measurements performed on the hydrophobic surface being tested. [Modes for carrying out the invention]

[0026] The present invention relates to a method for determining liquid-solid bonding work (see Figure 1 showing a flow diagram of the method, and Figures 2 and 3 showing an apparatus adapted to perform the method according to the present invention), in which steps given below are performed in relation to a liquid cylindrical symmetric capillary bridge (liquid cylindrical symmetric capillary bridge (actual)) formed in a fluid medium between an end of a measuring element having a peripheral circular rim (the end of the measuring element having a peripheral circular rim) and the surface of the solid to be tested (see the fluid medium 6, the surface to be tested 4, and the capillary bridge 9 in Figures 2 and 3). The surface of the solid to be tested (to be tested) (which is necessarily a solid) of the solid to be tested (to be investigated) is referred to herein simply as the “solid surface to be tested” (see the description of Figures 2 and 3).

[0027] The formation of a capillary bridge is not considered part of the method according to the present invention. This is due to the fact that the method is based on the measurement taken with the capillary bridge itself, i.e., the capillary bridge is maintained throughout the entire process of the method. Alternatively, the formation of a capillary bridge may be handled in a separate step when the capillary bridge is formed by bringing a droplet located on or transferred to the end of a measuring element, which usually has a peripherally rounded edge, close to (or directly transferring) it to the surface being tested.

[0028] Furthermore, by requiring cylindrical symmetry of the capillary bridge in accordance with the above, it is also preferable that the circular edge of the end having a peripheral circular edge be perpendicular to the longitudinal axis of the measuring element (again, its axis of movement, i.e., the axis of symmetry corresponding to cylindrical symmetry) during the process of the method, thereby providing cylindrical symmetry of the bridge.

[0029] A cylindrical symmetric capillary bridge is formed thanks to an end having a peripheral circular rim (peripheral circular rim) that adheres to (or above) its edge. Simultaneously, the requirement for cylindrical symmetry necessitates that the surface to be tested not break this cylindrical symmetry, i.e., preferably a plane or appropriately positioned sphere parallel to the end having the peripheral circular rim (see further below). In the latter case, due to cylindrical symmetry, there is a specific arrangement of the object to be tested with respect to the end facing the measurement element (other such surfaces are also conceivable). The surface to be tested is generally positioned to maintain cylindrical symmetry.

[0030] In the course of the method according to the present invention (the description of the steps of the method according to the present invention begins in this paragraph), a cylindrical symmetry retaining modification is performed on a cylindrical symmetry capillary bridge, starting from an initial state and ending in a final state (as suggested by their names, the initial state and the final state are, of course, the states in which the method is performed between them, i.e., measurements are performed on the capillary bridge as necessary for each of the measurements, for specific quantities, see also the following formulas). ○Between the initial state and the final state, the first interface area change (first boundary area change) of the first interface area (first surface area change) of the capillary bridge and the fluid medium, and the second interface area change (second surface area change) of the second interface area (second boundary area) of the capillary bridge and the surface being tested are determined (operation step S110a related to the determination of interface area changes corresponds to this, i.e., the first interface is the interface between the liquid-capillary bridge- and the fluid, and its change is the first interface area change, and the second interface is the interface between the capillary bridge and the surface being tested - i.e., the surface that the capillary bridge contacts (touches) the surface being tested, see Figures 2 and 3, - its change is the second interface area change), ○Based on at least one displacement value and the force value assigned to it determined during the cylindrical symmetric holding correction process, the total mechanical work corresponding to the capillary force is determined for the cylindrical symmetric holding correction by determining at least one displacement value of the work-related displacement (work-executed displacement, work displacement, displacement corresponding to the work done) corresponding to the cylindrical symmetric holding correction, and the respective force values ​​of the capillary force corresponding to the capillary bridge therefor (see below regarding determining the displacement value; determining the force value is determined by measurement, which can also be said to be determined based on measurement; operation step S100 relating to determining the capillary force corresponds thereto; also see Figures 4A to 4B relating to the graph (running) of the recorded values, and aspects relating to the range investigated by the method) during the cylindrical symmetric holding correction process.

[0031] This is expressed above as "at least one displacement value of the work-related displacement corresponding to the cylindrical symmetry preservation modification." This is interpreted as meaning that the total work-related displacement corresponds to the modification, and its value is determined at measurement time instances (points in time) (either measured as a whole or divided into parts), i.e., the displacement value is usually determined (e.g., measured) at multiple points, and the force value for each of these multiple points is also determined. The total work-related displacement is obtained as the sum of one or more displacement values, and these displacement values ​​are measured (generally determined) during the process of the cylindrical symmetry preservation modification.

[0032] If a single displacement value is recorded (i.e., the entire work-related displacement corresponding to the cylindrical symmetry-holding correction is treated as a single unit), then force values ​​are also typically measured at both endpoints (i.e., it is thus possible to determine two or more (usually two) force values ​​for a single displacement value in the initial and final states). If at least two displacement values ​​are determined, the corresponding capillary force value is determined for each of them, and the total machine work is determined based on the displacement value and the respective force value assigned to each.

[0033] As described above, the amount of work done is determined based on one or usually more displacement values ​​and the respective force values ​​assigned to them or to each of them. Typically, for discrete displacement values ​​recorded during the measurement process (often plural for typical cases, but only a single such value may exist) and the respective force values ​​assigned to them, the total machine work can be determined by the sum (see Figures 4A-4B showing the force values ​​determined for each displacement value; however, the specific force value assigned to a given displacement is a matter of choice, see below; it may be the force value measured at either of the endpoints of the given displacement value, or, for example, their average, i.e., the force value derived from the measured force values). In this case, the total machine work is determined by summing the products of the displacement values ​​(occurring between consecutive measurement time instances) and the respective force values ​​corresponding to each displacement value.

[0034] Furthermore, based on the displacement values ​​and the force values ​​assigned to them, the points of the displacement-force function can be recorded, and the total machine work can even be determined by integrating the function fitted to the points (the sum is essentially a numerical integral for sufficiently small displacement values), i.e., the total machine work is preferably determined by sum, numerical integral, or integral.

[0035] As shown in the figure, the direction of displacement is parallel to the direction of capillary force (both are signed quantities), so the work done can be calculated as their product in equation (2).

[0036] The capillary force corresponds to the capillary bridge; that is, according to the principle of capillary action, the capillary bridge exerts this force on the surfaces it connects to. In this regard, the exemplary measurements disclosed in Figures 4A and 4B, which detail the evolution of the force values, are referred to. In relation to the work-related displacements corresponding to the cylindrical symmetry-holding modification, in other words, the work-related displacements assigned to the capillary force, the explanations in Figures 2 and 3 are referred to, specifying which displacements (displacements at the ends of the measuring elements, displacements of the fluid in the capillary conduction channels) are assigned to the capillary force, thereby allowing for the calculation, for example, by summation, of the total mechanical work, i.e., the mechanical work corresponding to the entire cylindrical symmetry-holding modification (this term is also correct as the effect of gravity is ignored, and can also be called the capillary force work, or simply the first work).

[0037] By performing this method, within the preferred dimensional range of the capillary bridge, the weight of the capillary bridge can usually be ignored, except for the forces arising from the interfacial tension of the liquid and fluid medium, and the forces arising from the curvature of the interface (boundary surface) between the liquid and fluid medium (the sum of these two forces is the capillary force). Therefore, gravity can also be ignored and omitted from the equation.

[0038] There is no hierarchy between the steps of the two points mentioned above; that is, their order here does not imply an order of execution. The force is measured during the entire process of the cylindrical symmetry preservation modification (or modification that preserves cylindrical symmetry, which can also be called a modification that preserves or sustains cylindrical symmetry), so this can be interpreted as being earlier than the determination of the total mechanical work from the recorded force values ​​and changes in interface area, although the latter two steps can be performed in any order or even simultaneously, as also indicated by their reference numbers.

[0039] Furthermore, it should be noted that determining the change in interface area is preferably a measurement step performed by acquiring optical recordings and using them to calculate the interface area at a given time instance and the difference between those of the initial and final states.

[0040] In relation to the summation for cylindrical symmetry maintenance correction, the explanation of equation (2) is referred to. In extreme cases (limit cases, border cases), the summation becomes an integral as shown in Figures 4A and 4B, as it is reflected in the notation of equation (2), however, because the measured values ​​are discrete, and a small but finite displacement value is applied to the calculation. The force value is the total mechanical work (the total mechanical work thus obtained is called the capillary force, and as a result, the capillary force is calculated by summing the capillary forces and integrating with the displacement, the following term in equation (2)

[0041]

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[0042] Furthermore, in the process of the method according to the present invention (further steps of the method according to the present invention are given in this paragraph), based on the first interface area change, the second interface area change, the total mechanical work, and the liquid-fluid interface tension of the (liquid) capillary bridge and the fluid medium, ○The solid-liquid interface tension (solid-liquid interface tension) of the surface and (liquid) capillary bridge being tested, ○The solid-fluid interface tension (solid-fluid interface tension) of the surface being tested in relation to the fluid medium and The first difference value (between) is determined for the cylindrical symmetry preservation correction (the operation step S120 related to the determination of the interface difference value corresponds to this), By subtracting a first difference value from the liquid-fluid interface tension, the liquid-solid bonding work, which is an indicator of the (liquid) capillary bridge and the surface being tested, is determined, corresponding to the cylindrical symmetry retention correction (operation step S130, which relates to the determination of the liquid-solid bonding work, corresponds to this).

[0043] The essence of the method and apparatus according to the present invention is that a cylindrical symmetrical capillary bridge is formed between a circular solid surface and a solid surface to be tested from a liquid in a surrounding fluid medium. The liquid thoroughly wets the circular solid surface, and the liquid meniscus adheres (pins) to the edge of the circular solid surface.

[0044] The end of the measuring element is referred to above in the introduction of the method as the end with a peripheral circular edge (the circular edge extends along its periphery, and for convenience, it is the edge of the preferably flat end of the cylindrical element). According to the cylindrical symmetric configuration of the capillary bridge, this also has a cylindrical symmetric configuration. In this description, the illustrated implementation of this is referred to as a "circular (solid) surface," and in the figure it is shown to have a flat configuration (therefore, the end with a peripheral circular edge also has a solid configuration, but can preferably have a flat configuration).

[0045] In the configuration of Figure 2, the circular surface is a (naturally flat) circular plate located at the bottom of the measuring element, and in the configuration of Figure 3, the channel 14 of the capillary tube 11 opens to a circular surface, so the end can be a planar (flat) circular ring shape, or a planar (flat) ring shape with a circular outer circumference, whose inner circumference is not circular, for example, a square or a rectangle.

[0046] Furthermore, as previously identified, since the liquid sufficiently wets the circular solid surface, the liquid meniscus adheres (pins) to the rim of the circular solid surface; that is, the interface area between the end with a peripheral circular rim and the capillary bridge can be considered constant. Preferably, a surface of a suitable material that facilitates proper wetting can be applied to the end (e.g., glass or platinum), and the presence of the rim ensures the persistence of the interface area between the end and the capillary bridge (i.e., adhesion of the contact line helps) since it is undesirable for the liquid to separate from it. This is independent of whether the object being tested (test object) is hydrophilic or hydrophobic.

[0047] Referring to the figures, the method is described to be performed according to two types of embodiments. First, the execution according to Figure 2 is referred to. In this case, the distance between the two solid surfaces is changed so that the direction of relative displacement coincides with the axis of symmetry of the capillary bridge (i.e., a cylindrical symmetry preservation modification, i.e., a modification that does not impair the cylindrical symmetry of the capillary bridge is applied). By changing the distance between the solid surfaces, the length of the capillary bridge is changed. When the two solid surfaces are brought closer together, the capillary bridge becomes shorter, and when they are moved further apart, the length of the capillary bridge increases. In both processes, the size of the liquid-fluid interface area changes, and the size of the interface area between the liquid and the solid surface being tested also changes. The interface area between the liquid and the circular solid surface does not change because the liquid meniscus adheres (pins) to the edge of the circular solid surface.

[0048] Capillary forces and relative displacements of solid surfaces are measured during the process. Integrating the forces measured in relation to the displacements gives the work done (i.e., the work done on or by the system), which is spent to change the size of the interface area (refer to the exemplary measurement results shown in Figures 4A and 4B in relation to the formula).

[0049]

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[0050] Here, F is the capillary force, dz is the relative displacement (work-related displacement) during the process of approximate (approaching) or separation (retreating) motion, ΔA is the change in the size of the liquid-solid interface area, and γ LF ΔB is the liquid-fluid interface tension (which is similar to the Greek gamma in the formula), ΔB is the change in the size of the interface area between the liquid and the solid surface being tested, and γ SL γ is the interfacial tension between the liquid and the solid surface being tested, SF This is the interfacial tension between the solid surface and the fluid medium being tested.

[0051] When approximating and separating the solid surfaces (from each other) and determining the change in the size of the interfacial area at the starting and ending points, the expression (γ SL -γ SF ) can be calculated. This remains the only parameter calculated by the expression since the value of the integral on the left side of (2) is determined such that the interfacial area changes. In an experiment, the unknown parameter (the unknown) is also the parameter of the surface being tested, i.e., the corresponding interfacial tension, but the liquid-fluid interfacial tension γ LF is considered known. The above detailed process for calculating the liquid-solid adhesion work is also consistent with this.

[0052] By reconciling the notation of the expression with the terms (concepts) introduced above, the first difference value (referenced above) is calculated according to the expression (represented by rearranging equation (2))

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[0055] The liquid-solid adhesion work (W a ) is

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[0057] The above is slightly modified when the method is carried out according to a different embodiment. In that regard, Figure 3 is referenced. In this case, the circular solid surfaces are the cross-sections (ends) of the capillaries, and instead of changing the distance between the solid surfaces, the volume of the capillary bridge formed from the liquid can be changed. Thus, in this case, the distance between the solid surfaces is kept constant, but the change in volume dV of the capillary bridge is measured. The increase and decrease in volume correspond to bringing the solid surfaces closer together and moving them further apart, respectively. In this case, in order to calculate the work done, the capillary force must be integrated over the relative displacement of the liquid column within the capillary (work-related displacement), i.e., the quantity "dV / a", where "a" is the internal cross-sectional area of ​​the capillary. Everything else is essentially the same as described above.

[0058] If the attractive capillary force is considered to have a positive sign (in other words, the capillary force is considered to have a positive sign in the case of attraction), then according to equations (2) and (4) above, the difference between the amount of work done mechanically and the amount of work required to change the liquid-fluid interface area, and the quotient of the change in the liquid-solid interface area, are subtracted from the liquid-fluid interface tension to obtain the liquid-solid adhesion work.

[0059] The work done by liquid-solid adhesion can also be determined if this convention is deviated from and the attractive capillary force is assumed to have a negative sign. In such a case, the difference between the negative value of the mechanically performed work and the work required to change the liquid-fluid interface area, and the quotient of the change in the liquid-solid interface area, should be subtracted from the liquid-fluid interface tension to obtain the work done by liquid-solid adhesion. Thus, if a different sign convention is used, it will reverse the sign of the integral on the left side of (2) (which also affects equation (3), where the integral will be included with a negative sign). Thus, although the exact procedure of the calculation depends on the chosen sign convention, it is possible to determine the work done by liquid-solid adhesion based on the quantities determined as described above.

[0060] The amount of adhesive work determined during the advance of a liquid contact line formed on a solid surface is an indicator of the driving force after the diffusion of the liquid, while the amount of adhesive work determined during the retreat is a quantity that characterizes the surface's "liquid retention" (i.e., how difficult it is to separate the liquid from the surface). The mechanical work applied when the contact line is stationary is used only to change the liquid-fluid interface area; that is, information about the liquid-solid adhesive work cannot be obtained from a stationary (not moving) contact line.

[0061] As described above, the present invention is based on the recognition that the amount of work done on (or by) a system is spent on changing the interfacial area of ​​the liquid-fluid (medium) and liquid-solid, and that the liquid-solid bonding work can be determined by knowledge of the mechanical work, the liquid-fluid interfacial tension, and the changes in the size of the interfacial area.

[0062] Therefore, the present invention has a fundamentally novel element (aspect) that is unprecedented in the conventional method, as it allows for the absolute determination of liquid-solid bonding work by separating it from the mechanical work, the advancement and retraction of the contact line of the capillary bridge, and the change in the interface area for each advancement and retraction situation.

[0063] The following describes methods for measuring or determining the quantities applied in a method for determining the liquid-solid bonding work. In this regard, see also the descriptions of Figures 2 and 3.

[0064] Capillary force can be measured when a circular solid surface is connected to a force gauge, or when a solid object (the object being tested) with a surface to be tested is placed on a force gauge.

[0065] Changes in the interfacial area and the volume of the capillary bridge can be determined by taking lateral images of the capillary bridge formed by the liquid, at least at the beginning and end, when the solid surfaces are close to each other and when they are separated from each other, and when the volume is increasing or decreasing.

[0066] The size of the interface area between the liquid and the solid surface being tested can be calculated by determining the distance between the contact points of the generatrixes of the capillary bridge and the solid surface being tested (i.e., the diameter of the circular contact line of the liquid) in the image, given that the capillary bridge is cylindrically symmetric (in relation to calculations based on camera images, refer to the aforementioned specialist article by N. Nagy, "Contact Angle Determination on Hydrophilic and Superhydrophilic Surfaces by Using r-θ-Type Capillary Bridges" [Langmuir 35, p. 5202 (2019)]). For example, if the solid surface being tested is a flat surface, the interface in question is a circular plate. For example, if the solid surface being tested is a sphere (with its uppermost or lowermost point coinciding with the axis of symmetry of the capillary bridge), the interface is the surface of a spherical cap.

[0067] The above requirements regarding the cylindrical symmetry of the capillary bridge, and other conditions mentioned above (i.e., the direction of relative displacement coincides with the axis of symmetry of the capillary bridge), support the idea that modifications made to the capillary bridge preserve (persist) cylindrical symmetry. Applying a linear motor for displacement also facilitates this. The same applies to volume changes, in which case image analysis can also be applied, as there are no situations that could cause changes that break cylindrical symmetry—such as changes in volume through the capillary channels.

[0068] The size of the liquid-solid interface area can be determined by performing an image analysis of the shape of the capillary bridge. The size of the interface area can be calculated by an analytical mathematical description of the shape of the capillary bridge, or by approximating the generatrix (contour) of the capillary bridge with an appropriate function (e.g., polynom) and calculating (integrating) the size of the plane of revolution obtained by rotating this curve around the axis of symmetry of the capillary bridge. According to another slightly different solution, the generatrix of a cylindrically symmetric capillary bridge is decomposed into distinct components, namely the plane of revolution is decomposed into a low-height cylinder mantle, and the size of the plane of revolution is calculated as the sum (numerical integral) of these.

[0069] The change in volume of a capillary bridge can be determined by a device that provides the volume change, in embodiments based thereon (see also in relation to Figure 3 below). The volume can also be determined by performing an image analysis of the shape of the capillary bridge. The volume of a capillary bridge can be calculated by providing an analytical mathematical description of its shape, or by calculating the volume of a solid of revolution obtained by rotating a curve of a function fitted to the generatrix of the capillary bridge, as well as determining the liquid-fluid interface area, or by numerical integration of the contour of the capillary bridge.

[0070] The change in distance between solid surfaces (in each embodiment), i.e., the change in the length of the capillary bridge, can be determined by a mechanism (mechanical arrangement) that provides linear motion, or by analyzing captured images of the capillary bridge.

[0071] As solids move closer to each other and as the volume of the capillary bridge increases, the contact line of the liquid formed on the solid surface being tested advances. Therefore, the liquid-solid adhesion work determined in this way is an indicator of the spread of the liquid on the surface being tested, i.e., it corresponds to the case where the advancing contact angle of the liquid measured on the surface being tested is substituted into the Young-Dupré equation (see equation (1) above). As the solids move further apart and as the volume of the capillary bridge decreases, the contact line of the liquid recedes. Therefore, the liquid-solid adhesion work determined in this way is an indicator of the separation of the liquid from the surface being tested, i.e., it corresponds to the case where the receding contact angle of the liquid measured on the surface being tested is substituted into the Young-Dupré equation.

[0072] By using the Young-Dupre equation (i.e., using equation (1) above), the (typical) values ​​of the liquid-advancing and receding contact angles formed on the surface under test can be calculated from the liquid-solid adhesion work value thus determined, without directly measuring them. This is preferable, for example, when the uncertainty of contact angle measurement would significantly reduce the accuracy of subsequent calculations. In this respect, the method for determining liquid-solid adhesion work according to the present invention is considered more efficient than known methods.

[0073] The following are Figures 2 and 3 illustrating details of carrying out corresponding embodiments of the method, and in connection with carrying out the method, specific details of the apparatus are shown in Figures 2 and 3 (also describing alternatives, and often at an illustrative level—giving (where necessary) which information can be generalized by analogy).

[0074] Figure 2 shows an embodiment of the method according to the present invention with the help of a schematic diagram of the corresponding apparatus. In the preferred exemplary embodiment of the present invention shown in Figure 2, the circular solid surface 1 (as shown in the figure, this reference number (symbol) may also indicate an end having a peripheral circular rim) may be, for example, the base of a glass cylinder having a diameter of 2 mm (and, as shown in Figure 2, it may be implemented as another such object that is slightly slimmed in the middle and has a well-configured end, i.e., a circular solid surface), or a platinum disc having the same diameter. A drop (droplet) of liquid having a volume greater than 1 μL hangs from this surface. The upper end of the glass cylinder is connected to a force-compensating force measuring instrument 2 having a resolution of, for example, 5 μN or less (components having the same function as the force measuring instrument are denoted by the same reference numbers in Figures 2 and 3, but slightly different configurations in one of the variants (e.g., this variant) may be indicated, for example, by an upper comma ('), and such components may be, for example, the circular solid surface 1 and the sample chamber 5). The vertical movement of this is provided by a linear mover (actuator) 3 having a lead (worm) screw driven by a stepper motor, with a minimum available drive speed of <0.02 mm / s.

[0075] The solid surface 4 to be tested is placed beneath the base plate of the glass cylinder on a support adapted to move in the plane parallel to its plane, preferably along two directions (on an xy mover, which is no longer used in the process of the method according to the present invention after the capillary bridge has formed). The lower end of the glass cylinder and the solid surface 4 to be tested are preferably placed in a common sample chamber 5, and the fluid filling the sample chamber 5 (i.e., the fluid medium 6 surrounding the capillary bridge 9) is, for example, a nearly saturated (≧80%) vapor space of a liquid (if a gaseous fluid medium is applied, it is of course possible to seal the sample chamber in an imperfect manner, i.e., so that the end of the measuring element protrudes into the chamber through a small opening formed in the upper plate of the sample chamber). The term “sample chamber” is used because the sample to be tested, i.e., the solid to be tested, is placed therein, but it can also be called a “measurement chamber” because the measurement is concentrated in it or on the components placed therein (the end with a peripheral circular rim, the capillary bridge, the solid to be tested).

[0076] The capillary bridge—the components applied to form it—does not necessarily have to be placed inside a sample chamber; in fact, they can even be placed in free air, and the measurement principle, the method for determining the liquid-solid adhesion work, is not affected by what kind of fluid medium surrounds the capillary bridge. Naturally, it may be preferable to add a suitable fluid medium inside the sample chamber (i.e., when a circular solid surface 1, a solid surface 4 to be tested, and a capillary bridge 9 are placed inside a common sample chamber 5).

[0077] Therefore, the fluid medium may preferably be located within a sample chamber, and the solid to be tested, having a surface to be tested during the test, is placed within the fluid medium in this manner, as is the end of a measuring element having a peripheral circular edge. Preferably, the apparatus may include a sample chamber, which may be a fixedly positioned component (from which the object to be tested is replaced if necessary), or it may be positioned only for the duration of the measurement (method) being performed, i.e., the object to be tested can be replaced along with the sample chamber.

[0078] Preferably, a light source 7 that provides uniform illumination, in our case, for example, an LED light with a diffuser, is positioned on one side of the glass cylinder perpendicular to the axis of the glass cylinder, and on the other side opposite, a camera 8 having a resolution of at least 1024 × 768 pixels, for example, a CMOS (complementary metal-oxide-semiconductor) camera 8 is positioned (preferably, two or more cameras may be applied, or it can also be said that at least one camera is applied so that the cylindrical symmetry can be better investigated). The data from the force measuring instrument 2, the linear mover 3, and the camera 8 are preferably processed by an integrator unit 10 (summation unit, or simply integrator), which, according to Figure 2, preferably has interconnections with the integrator unit 10.

[0079] During the measurement process, a droplet hanging from a circular solid surface 1 is first brought close to the solid surface 4 being tested. As soon as the droplet reaches the solid surface 4 being tested, i.e., from the time instance (point in time) of the formation of the capillary bridge 9, the speed of movement is set to, for example, 0.0025 mm / s, and the force measured by the force measuring instrument 2, the displacement of the circular solid surface 1, and the captured image of the capillary bridge 9 are recorded (memorized) every, for example, every 10 seconds. During the approximation (approach) process, the length of the capillary bridge 9 decreases, and the diameter of the interface area between the capillary bridge 9 and the surface 4 being tested increases.

[0080] A time instance selected based on the geometric situation of the approximating capillary bridge 9 is stopped, and the same parameters are applied to start moving the circular solid surface 1 away (removing the circular solid surface 1), which continues, for example, until the capillary bridge 9 breaks (cylindrical symmetry preservation modification to the capillary bridge by approximating and moving away).

[0081] During the evaluation, the second measurement point after the formation of the capillary bridge 9 is considered the starting point (initial state) of the approximation process, and the turning point is considered its final point (final state, see Figures 4A-4B; the circled point is the formation point, so the starting point is the second (or third if the circled point is also counted) point on the graph, the final point; in the case of Figure 4A, it is naturally the point before the "jump" in the turning point - at the bottom of the figure). The starting point (initial state) of the separation phase is considered, for example, the second measurement point after the turning point, and as its ending point (final state), the measurement point where the length of the capillary bridge 9 does not exceed the length of the bridge at the time of its formation is considered.

[0082] This effectively provides an empirical rule for determining the work of adhesion by calculating the approximation (approach) and separation (retreat) stages separately (as mentioned elsewhere, the work of adhesion calculated for the approximation and separation stages is an indicator of the diffusion and separation of the liquid, respectively).

[0083] Immediately after formation, the liquid-solid contact line is not necessarily progressing, so it is safer to investigate the process from the second point. In the case of separation, starting from the second point is also advantageous and provides practical guidance, as at this stage the contact line has usually already stopped receding, but it is not advisable to exceed the formation length as there is a risk of rupturing the capillary bridge. It is worthwhile to apply the method to sections where the contact line is truly moving and where empirical rules provide good support.

[0084] Therefore, the above should be treated only as an empirical rule; that is, the formula can be applied over much shorter periods, and deviations from it can be made as needed. Naturally, the shorter the range of change investigated, the greater the measurement error. The empirical rule defines a long measurement period for both the advance and retraction of the capillary bridge.

[0085] It will be understood that selecting a measurement period that is too short (between the initial and final states), i.e., investigating cylindrical symmetry preservation corrections that are too small in the method according to the present invention, is not worthwhile. For example, a change between two adjacent measurement points may be considered too small (high expected measurement error), but it can still be applied in the present invention. Investigating three consecutive measurement points during the process of cylindrical symmetry preservation correction will likely yield less error results, i.e., it may be preferable to record at least three measurement points (i.e., to operate over at least three measurement time instances covered by the cylindrical symmetry preservation correction).

[0086] In the following steps, the determination of the liquid-solid bonding work is performed according to the above description. The capillary force measured by the force measuring instrument 2 is integrated by the integrator unit 10 over the relative displacement of the circular solid surface 1 measured by the linear mover 3 (as needed). Based on the image recorded by the camera 8, the integrator unit 10 also calculates (integrates) the liquid-fluid interface area.

[0087] In another preferred embodiment of the apparatus according to the present invention shown in Figure 3, the sample chamber 5 is placed on a force measuring instrument 2, in this case an analytical (weighing) scale having a resolution of 0.05 mg or less. The fluid medium 6 in the sample chamber 5 is a liquid medium that does not mix with the liquid that forms the capillary bridge 9.

[0088] When a fluid medium in a liquid state that does not mix with the liquid is applied, the fluid medium can be filled into the chamber in one of the following two preferred subcases, and the fluid medium 6 in a liquid state that does not mix with the liquid is -After the capillary bridge 9 is formed, or - In such a state of the shortest or largest volume capillary bridge 9 It is filled into sample chamber 5.

[0089] For example, in the latter case, the method applies only when retreating. Generally, it is often inconvenient to conduct surveys in both directions (forward and backward), but it should be noted that this is not necessary.

[0090] The circular solid surface 1 (generally, and having an end with a peripheral circular rim, or, as described, a circular solid surface having a channel of capillary tubes opening thereto) is, for example, the cross-section of a glass capillary tube 11 having an outer diameter of 2 mm, and the capillary tube is preferably connected via a flexible tube to a liquid feeder 12 (liquid dispenser) device, to a syringe pump having a minimum supply rate (speed) of less than 0.2 μL / min, i.e., it can supply liquid at a speed of less than 0.2 μL / min. Linear movement of the capillary tube 11 is preferably provided by a linear mover 3 described above in relation to the embodiment shown in Figure 2.

[0091] The arrangement and features of the light source 7 and camera 8 are the same as those described above in relation to the embodiment shown in Figure 2. Data from the force measuring instrument 2, liquid feeder 12, and camera 8 are processed by the integrator unit 10.

[0092] Before measurement, a circular solid surface 1 is moved close to the solid surface 4 to be tested, so that the distance between them is preferably 2 mm or less. A known amount of liquid is discharged (compressed) from the capillary 11 until a capillary bridge 9 is formed. At this point, the measurement can be performed as part of the method, as described above in relation to a previous preferred embodiment, i.e., by approximating and separating the circular solid surface 1 (and thus applying a cylindrical symmetry-retaining modification). In this case, the measurement is evaluated in the same manner as above (in this case, the capillary 11 can preferably be lowered close to the solid surface 4 to be tested using a linear mover 3, and then moved to change the length of the capillary bridge).

[0093] This preferred embodiment also allows for different measurement processes. In this case, preferably, the distance between the circular solid surface 1 and the solid surface 4 to be tested is not changed during the process of performing the corresponding embodiment of the method according to the present invention. A liquid feeder 12 (e.g., a syringe pump) is applied to increase or decrease the volume of the capillary bridge 9 by a known amount, for example, at a rate (speed) of 0.001 μL / s (applying a cylindrical symmetry retention correction due to volume change). During the measurement, as in the previous measurement, the force measured by the force measuring instrument 2, the volume change of the capillary bridge 9, and the image of the capillary bridge 9 taken by the camera 8 are recorded (memorized) every 10 seconds. Again, interconnections are established from the force measuring instrument 2, the camera 8, and the liquid feeder 12 (and preferably the linear mover 3 as well) to the integrator unit 10.

[0094] In the evaluation process, preferably in this embodiment, the second measurement point after the formation of the capillary bridge 9 is considered the starting point of the volume increase, and the turning point is considered its end point. The starting point of the volume decrease is preferably considered to be the second measurement point after the turning point, and its end point is the measurement point where the volume of the capillary bridge 9 does not exceed the volume measured at the time of its formation.

[0095] In the following, the liquid-solid bonding work is determined according to the above description, with the difference being that the forces measured during the process are integrated by the integrator unit 10 over the displacement of the liquid column in the capillary (dV / a) rather than integrating over the relative displacement of the solid surface (since these remain stationary).

[0096] Therefore, in this case, the linear mover 3 is applied to move to a suitable distance from the solid surface 4 being tested, and then it remains stationary (at a constant distance from the solid surface 4 being tested). However, in this latter embodiment, the apparatus can also be configured without applying the (linear) mover, and instead, the capillary is fixed at a predetermined distance from the solid surface 4 being tested (i.e., it is fixedly positioned at this distance), and the apparatus is applied in this manner. In this case as well, the liquid necessary to form the capillary bridge can be introduced through the capillary.

[0097] As partially mentioned above, in certain cases, it may be preferable to fill the sample chamber 5 with a fluid medium 6 in a liquid state that does not mix with the liquid forming the capillary bridge 9 after the capillary bridge 9 has formed or reached its maximum volume. The extent to which the presence of the fluid medium 6 facilitates the separation of the liquid from the surface 4 being tested can be investigated with the help of this latter solution.

[0098] Another advantage of the apparatus and corresponding method shown in Figure 3 is that capillary bridges can be formed easily and quickly, the volume of the capillary bridges can be precisely controlled, and therefore the capillary bridges can be easily automated, i.e., high-throughput measurements can also be obtained. A further advantageous characteristic is that, in contrast to the arrangement in Figure 2, when the fluid medium is in the liquid phase, capillary bridges can be formed easily, and it is more difficult for the initial suspension droplets to pass through the air-liquid medium interface. With the arrangement in Figure 3, in a particularly preferred manner, "under-liquid" measurements can be performed much more easily, and it is possible to study displacement-wetting (and dewetting) and washing processes, which are often applied in this field, more easily and accurately, and this involves determining the liquid-solid adhesion work.

[0099] In an embodiment of the method according to the present invention performed by the apparatus shown in Figure 3, a measuring element having a capillary conduction channel (see capillary conduction channel 14 in Figure 3) opening at its end having a peripheral circular rim is applied, the end of the capillary conduction channel opposite the end having a peripheral circular rim is connected to a liquid feeder (see liquid feeder 12 in Figure 3), the cylindrical symmetry-holding correction is performed on the cylindrical symmetry-holding capillary bridge by passing a liquid through the capillary conduction channel (this is a (adapted) liquid for constructing the capillary bridge, in other words, a liquid that constructs (constitutes) the capillary bridge which is also conveniently applied on which the cylindrical symmetry-holding correction is performed, and this will also appear below), and the work-related displacement is determined by a displacement determination unit adapted to determine the displacement of the liquid in the capillary conduction channel.

[0100] Therefore, on the one hand, a method for performing cylindrical symmetry-preserving correction in this embodiment is specified above (i.e., no new steps are introduced, but the method of execution is specified), in which case the cylindrical symmetry-preserving correction is performed only in this manner, i.e., the measuring element remains stationary, and therefore the length of the capillary bridge does not change, but the shape of the capillary bridge—volume and interface area—changes. Furthermore, a method for determining work-related displacement is also specified.

[0101] By allowing the liquid to pass through the capillary conduction channel, the volume of the capillary bridge can be increased (making the capillary bridge "thicker"), and the liquid can also be carried away (decreasing the volume of the capillary bridge). In this case as well, a bidirectional process can be carried out on the capillary bridge—advancing and retracting the liquid-solid contact line—which can also be carried out by moving the measuring element, and the corresponding work-related displacement can be determined.

[0102] As described above, a particular embodiment of the present invention relates to an apparatus adapted to determine the liquid-solid adhesive work. The apparatus according to the present invention is suitable for carrying out the method according to the present invention, that is, the apparatus according to the present invention is adapted to determine the liquid-solid adhesive work by carrying out the method according to the present invention.

[0103] The apparatus according to the present invention is - A measuring element having an end with a peripherally circular rim, which is placed in a fluid medium together with the solid to be tested, which has a surface to be tested, and which has an end with a peripherally circular rim. When the apparatus is in use, the measuring element and the surface to be tested are positioned relative to each other such that a liquid cylindrical symmetrical capillary bridge can be formed between the end having a peripheral circular rim and the surface to be tested (what kind of relative arrangement this requires of the components is addressed above, see also the fluid medium 6, the surface to be tested, and the capillary bridge 9 in Figures 2 and 3), and the measuring element has a capillary conduction channel 14 opening to the end having a peripheral circular rim (which is preferably formed within a capillary 11, shown filled with liquid in Figure 3).

[0104] In some cases, specific components of the apparatus may be defined below in relation to capillary bridges. On the one hand, this characterization also specifies the low-temperature configuration of these components, and on the other hand, in relation to these characteristics, it is understood that they perform their functions when the apparatus is used, as already specified in the definition above in relation to the formation of capillary bridges.

[0105] The device is - The end of the capillary conduction channel opposite the end with the peripheral circular rim (see capillary conduction channel 14 in Figure 3) is connected to a liquid feeder (see liquid feeder 12 in Figure 3) (of course, the channel has two ends, one of which opens to the end with the peripheral circular rim and the other is connected to the liquid feeder, i.e., the liquid feeder can supply liquid to this end or carry away (take out) liquid from this end), - An interface area determination device adapted to determine the first interface area of ​​the capillary bridge and the fluid medium, and the second interface area of ​​the capillary bridge and the surface under test. Furthermore, The liquid feeder is adapted (configured to be adapted) to perform a cylindrical symmetry retention correction on the capillary bridge by passing the liquid through capillary conduction channels.

[0106] As already mentioned, liquid feeders are suitable for supplying and carrying away liquid, that is, for performing cylindrical symmetry retention modifications by passing liquid through capillary conduction channels. In addition to supplying / removing, this also means adding or removing liquid corresponding to the cylindrical symmetry retention modification so that advancement or retraction modifications are made to the capillary bridge. To determine the displacement value, the liquid feeder can be used to conveniently determine how much liquid has been supplied or removed.

[0107] When the apparatus is in use, the liquid-fluid interface also plays a role in determining the liquid-solid adhesion work, so the end with the peripheral circular edge and the surface being tested enter a fluid medium, which may be free air or another appropriately selected fluid. The solid being tested, having the surface being tested, may be replaceable so as not to form part of the apparatus when it is not in use. Furthermore, in certain embodiments, the circular end of the measuring element can be moved into the fluid medium.

[0108] In relation to an interface area determination device (surface area determination device), Figures 2 and 3 show a light source and a camera (preferably a light source applicable with the camera, generally a device adapted to perform optical recording, usually used to provide illumination so that the camera can capture images of sufficient contrast and quality), they can preferably form part of the interface area determination device, with their help the camera can transfer such data to an interface area determination (calculation) unit (which is also preferably part of the interface area determination device), with their help it is possible to determine the first interface area of ​​the capillary bridge and the fluid medium, as well as the second interface area of ​​the capillary bridge and the surface being tested.

[0109] The apparatus according to the present invention is -A displacement determination unit adapted to determine at least one displacement value of the work-related displacement of the liquid in the capillary conduction channel, corresponding to the cylindrical symmetry retention modification, - A force measuring instrument adapted to determine (by measurement) the force value of the capillary force corresponding to a capillary bridge for at least one displacement value, - An integrator unit adapted to determine the total mechanical work corresponding to the capillary force for cylindrical symmetry correction, based on at least one displacement value determined by a displacement determination unit during the process of cylindrical symmetry correction, and the force values ​​assigned to each of them, - For cylindrical symmetry retention correction, Based on the first interface area change of the first interface area and the second interface area change of the second interface area, determined by the interface area determination device between the initial and final states of the cylindrical symmetrical capillary bridge, the total mechanical work is applied to the liquid-fluid interface tension of the capillary bridge and the fluid medium. • The solid-liquid interfacial tension of the surface and (liquid) capillary bridge being tested, and • Solid-fluid interface tension of the surface and fluid medium being tested Determine the first difference value (i.e., the first difference value is determined based on these quantities, see the formula above), ○A work determination unit adapted to determine the liquid-solid adhesion work, which is an indicator of the capillary bridge and the surface being tested, by subtracting a first difference value from the liquid-fluid interface tension, thereby accommodating cylindrical symmetry retention correction. Prepare further.

[0110] The units included in the device (displacement determination unit, integrator unit, work determination unit) are essentially computational units, which may be reflected in their names. The interface area determination unit (which can also form part of the interface area determination device described above) can also be included here.

[0111] Within the device, these units may be part of a central or main computing unit (their functions (tasks) may be implemented by a single central computing unit, but they may also be implemented by multiple computing units), but each computing unit may be independent (self-contained), or it may be implemented partially independently with a partially common configuration.

[0112] The displacement determination unit conveniently operates to divide the volume change brought about by the liquid feeder (preferably a known volume being fed out or carried away by the liquid feeder, and the volume change can also be determined by analyzing an image of the capillary bridge, see above) by the cross-sectional area of ​​the capillary conduction channel, thereby determining the displacement (the values ​​of the bidirectional displacement resulting in the movement of liquid both inside and outside can thus be determined). As described in the definition above, the integrator unit is adapted to determine the liquid-solid adhesion work based on appropriate input data.

[0113] As described above in relation to the apparatus, in order to determine the total mechanical work, displacement can be related to a cylindrical symmetry-holding correction, which is performed parallel to the axis of symmetry and targets the correction of the capillary bridge. As can be seen above, in relation to Figure 2, displacement is the change in the length of the capillary bridge caused by the vertical displacement of the measuring element. Displacement can be similarly brought about in relation to Figure 3, but in this case the length of the capillary bridge can also be fixed, in which case the displacement of the liquid column (thereby increasing or decreasing the volume of the capillary bridge) can be related to the amount of work done. Thus, displacement in both directions is parallel to the axis of symmetry, and the capillary force also acts in this direction.

[0114] Furthermore, in the apparatus according to the present invention, the force measuring instrument is a weighing scale (balance) having a measuring surface positioned opposite the end of a measuring element having a peripheral circular rim, and the measuring surface is adapted to position the solid to be tested such that its surface to be tested faces the end having a peripheral circular rim (see the force measuring instrument implemented as a weighing scale, and the relative arrangement of the weighing scale and the surface to be tested 4 in Figure 3, in such an arrangement of the force measuring instrument, the magnitude of the capillary force can be interpreted essentially as the degree to which the object being tested by the capillary force is lifted from the weighing scale or pressed against the weighing scale). Force measuring instruments typically measure force accurately when they are positioned in the apparatus shown in the figures, i.e., when the measuring surface of the weighing scale is horizontal, for example, as shown in Figure 3 (the force measuring instrument shown in Figure 2 is typically suited for measuring vertical forces).

[0115] When the fluid medium is free air, the object being tested is conveniently placed directly on the measurement surface. When the fluid medium is in a measurement chamber, the object being tested is placed on the measurement surface within the chamber.

[0116] The method according to the present invention can be carried out using a variety of apparatus, as suggested by its steps defined above, and these apparatuses are required to provide the functions introduced above in the description of the method. At the same time, the apparatus according to the present invention is required to have configuration details that ensure the method can be carried out. Furthermore, an important component of the common inventive concept of the method and apparatus according to the present invention is that the method according to the present invention can be carried out by the apparatus according to the present invention.

[0117] The apparatus may preferably form multiple capillary bridges, preferably arranged side by side (e.g., in a matrix arrangement), and the respective measuring elements corresponding to each capillary bridge may be moved together, or the volume of the capillary bridges may be changed together through their own capillary channels (i.e., preferably all having the same length) (the method, i.e., this variant also falls within the scope of the present invention, i.e., it can be performed to constitute an embodiment). An important feature is that since the capillary force is measured collectively over these capillary bridges, it is usually possible to measure a larger force than in the case of a single capillary bridge.

[0118] In this case, the determination of the interface area is naturally performed for all capillary bridges (the change in interface area is determined collectively), and an interface area determination device is suitable for doing so.

[0119] Below, the measurement results for both hydrophilic and hydrophobic cases are explained in relation to Figures 4A and 4B.

[0120] The measurements included below were performed in the configuration shown in Figure 2, following the measurement process described in relation to the figure. Circled measurement points indicate the formation of capillary bridges (i.e., capillary bridges are established at the circled locations, the bridges are first compressed, and then stretched according to the arrows). This is considered the zero point of the displacement scale (range) (see the zero points of the displacement axes in Figures 4A-4B). Further approximations of solid surfaces to each other are shown as negative displacements. The arrows in Figures 4A-4B indicate the direction of the process.

[0121] According to the commonly applied conventions mentioned above, the sign of the attractive capillary force is positive, that is, it is considered positive when, for example, "attempting" to attract solid surfaces together [EJDe Souza et al., Effect of Contact Angle Hysteresis on the Measurement of Capillary Forces, Langmuir 24, pp. 1391-1396 (2008)]. The following will follow this convention.

[0122] A typical force-displacement curve measured on a hydrophilic surface (the solid surface being tested / the material of the surface being tested is SiO2) is shown in Figure 4A. The measurement liquid was ultrapure water in a volume of 1.5 μl. The preferred applicable volume range of the capillary bridge is also influenced in various embodiments by the interfacial tension of the liquid and fluid media, as well as the difference in their densities. Images of the measured force and liquid bridge were recorded every 5 seconds (i.e., more frequently than specified above in relation to Figures 2-3).

[0123] The capillary forces measured in Figure 4A remain in the positive force region until the end; that is, the liquid bridge attempts to bring the boundary solid surfaces closer together. In the approximation stage (the portion extending from the circle in the direction of large negative values), (negative) mechanical work is performed by the system, which can be calculated by integrating the force-displacement curve recorded in the approximation stage (see equation (2)). This work is spent on the (energy-favorable) decrease (ΔA is negative) of the water-air interface area and the (similarly energy-favorable) increase (ΔB is positive) of the SiO2-water interface area.

[0124] Higher capillary force values ​​are encountered in the separation phase (which is the portion extending from the bend in the direction of positive displacement values, as indicated by the corresponding arrows). This is because separating water from the SiO2 surface is more difficult (energetically less favorable) compared to the magnitude of the driving force after the wetting process (this phenomenon is also evident at higher advancing and lower receding contact angles). Therefore, the geometry of the capillary bridge, and thus the dimensions (and changes) of the interface area, differ between the approximation phase and the separation phase. In the separation phase, work (of a positive sign) is performed on the system, in which the water-air interface area increases (which is energetically less favorable, ΔA is positive) and the SiO2-water interface area decreases (which also increases the energy of the system, ΔB is negative).

[0125] A typical force-displacement curve measured on a hydrophobic (cycloolefin polymer) surface is shown in Figure 4B. The measurement solution was 1.8 μl of ultrapure water, and in this case, force values ​​and images of the liquid bridge were recorded every 5 seconds (as described above, this measurement was also performed using the setup shown in Figure 2).

[0126] In the approximation stage (extending from the circle in the direction of similarly larger negative displacement values), the initially positive (contractile) capillary forces change sign, and in the range of negative forces, they attempt to move the solid surfaces further away from each other. In this range, work is done on the system, i.e., the value of the integral is positive (both force and displacement are negative), so the value of the integral calculated over the entire approximation stage increases. Similarly, at the beginning of the separation stage, work is done by the system, giving a negative contribution to the equation (force is negative, but displacement is positive due to separation).

[0127] Therefore, the method and apparatus according to the present invention are intended to determine the work of adhesion, which is an indicator of the liquid-solid interface (without measuring the contact angle). Thus, the apparatus can be preferably operated so that a cylindrical symmetric capillary bridge is formed from the liquid in the surrounding fluid medium between a circular solid surface and the solid surface under test, and the contact line adheres (pins) to the edge of the circular solid surface, and the method can be performed. The capillary force is measured while varying the length or volume of the capillary bridge. By processing images of the capillary bridge, the change in the size of each interface area resulting from the change in the length or volume of the capillary bridge is determined. The work of adhesion of the liquid can be calculated from the measured force (by integrating the capillary force over the change in length or essentially the change in volume of the capillary bridge), from the change in the length or volume of the capillary bridge, and from the change in the size of the interface area, provided that the liquid-fluid interfacial tension is known, without determining the contact angle of the liquid forming on the solid surface under test. Furthermore, based on the determined work of adhesion, the value of the contact angle can be determined by calculation (representing the angle from (1)) without measurement.

[0128] The following provides a distinction from the conventional techniques referenced at the beginning.

[0129] A common feature of the methods described in Japanese Patent Publication No. 2011191277A, European Patent No. 3571483A1, and Japanese Patent Publication No. 2004144573 is that while the forces related to liquid-solid adhesion are determined, they cannot determine the change in the size of the interface area. A common drawback of these methods is that the solid-liquid bonding work cannot be determined by applying these methods; that is, the adhesive properties of various solid-liquid material pairs can only be compared by performing measurements using the same parameters and applying the same arrangement having a given geometry of a particular apparatus.

[0130] In contrast to the specialist article by N. Nagy (Contact Angle Determination on Hydrophilic and Superhydrophilic Surfaces by Using r-θ-Type Capillary Bridges, Langmuir 35, page 5202 (2019)), in which the changes in work and interface area performed by or on the system are not determined, and the determination of adhesive work independent of the contact angle is not disclosed, the present invention determines the changes in work and interface area size performed by or against capillary forces based on appropriate measurements (preferably by applying an integrator, utilizing an integrator based on an integral quantity, such as the method according to the present invention, in relation thereto, see also below, but not included in the specialist article), and the liquid-solid adhesive work is also determined in a very preferred manner independent of the contact angle.

[0131] According to the present invention, the inventors have recognized that a method for determining liquid-solid bonding work can be constructed in a highly preferred manner based on observing changes in capillary bridges, and that the liquid-solid bonding work is determined from the quantities measured in the process. In the process of the method, contact angles are not utilized (they are not measured), and instead, the work performed by or against capillary forces is measured in addition to the changes in the respective interface areas, and the liquid-solid bonding work is determined based on these measured quantities.

[0132] Therefore, the inventors have come to the realization that determining liquid-solid adhesive work should be based on the measurement of an integral quantity, rather than on methods based on instantaneous values ​​(i.e., for contact angles which involve uncertainty in determining work according to the initial method) (in a preferred manner, the contact angle can also be calculated thereafter, thus allowing the adhesive work to be obtained without utilizing the value of the contact angle). The method of the present invention based on an integral quantity also has the advantage that the integral quantity can usually be measured with higher precision because uncertainty and measurement errors (noise) with a zero mean are integrated during the process. In summary, the inventors have recognized that in order to determine liquid-solid adhesive work, it is necessary to apply a measurement method different from that of the prior art to measure a different parameter.

[0133] To put the above in a slightly different way, according to the present invention, changes are investigated in the process (investigating the balance of work done, i.e., determining what the total mechanical work corresponding to the cylindrical symmetry retention change (modification) of the capillary bridge is spent on and how, as a result, the interface area of ​​the capillary bridge changes), that is, the measurement points are investigated in particular in relation to each other. Thus, the inventors preferably apply an integrator to take into account changes related to interface area, such as the interface area formed between the capillary bridge and the surrounding fluid, and the interface area between the capillary bridge and the surface being tested (in this regard, the description relating to the investigated section and the empirical rules applicable thereto is referred to).

[0134] In relation to the technical article, it should also be noted that the value of the capillary force (referred to as “adhesion force” in the technical article in particular), as supported by the formulas of this application (see formula (2) in particular), depends only partially on the interaction between the liquid and the solid surface being tested. Its value is also determined by the size of the interface area between the liquid and the solid surface being tested, the surface tension of the liquid, and the shape and geometric dimensions of the liquid bridge. As a result, the quantity obtained by integrating the capillary force over a change in length (while the length of the liquid bridge changes) is not the liquid-solid adhesion work. The latter cannot be determined without taking into account the change in interface area.

[0135] In contrast to the disclosure of U.S. Patent No. 6,537,499B1, which studies the adhesion of molecules bonded to a surface, the present invention investigates cylindrical symmetry-retaining modifications performed on liquid capillary bridges. In connection with the present invention, the liquid-solid adhesion work can be determined bidirectionally, i.e., during the “increase” and “decrease” of the capillary bridge (in both forward and backward situations), which, on the one hand, orders the concept of adhesion work as the difference between the contributions resulting from movement in both directions, and on the other hand, differs from the amount in the document, as between the two processes, the column pushing the molecules downward undergoes elastic deformation, i.e., two mutually opposing solid surfaces are forced to press against each other. The latter is clearly contrary to the method according to the present invention, and pressing mutually opposing measuring surfaces against each other should be particularly avoided (in the present invention, either the forward or backward situation is investigated, and in addition to compression, the turn from the forward situation to the backward situation is also avoided in the method according to the present invention, and integration is not usually performed for that purpose, see the explanation of the empirical rule above).

[0136] Therefore, in the present invention, the work of adhesion is the work of solid-liquid adhesion, which can only be determined by knowledge of the mechanical work, liquid-solid interfacial tension, and changes in the size of the interfacial area performed during the process of cylindrical symmetry retention correction of the capillary bridge. Accordingly, U.S. Patent No. 6,537,499B1 does not disclose such a method for determining the work of liquid-solid adhesion similar to the present invention.

[0137] In the case of Japanese Patent Publication No. 2013174478A and Chinese Patent No. 2968623 mentioned at the beginning, in addition to the capillary liquid introduction (specifically the introduction of a certain amount of liquid), the volume change of the capillary bridge is not investigated, and the amount of liquid-solid bonding work according to the process of the present invention is not determined based on the change in the interfacial area.

[0138] Equation (1) for determining the liquid-solid adhesion work based on the contact angle measurement described at the beginning is also referenced in other documents mentioned above as part of the prior art (see Chinese Patent No. 2968623 above). The present invention eliminates the drawbacks associated with calculations based on contact angle measurement (the uncertainty of theoretical measurement) and provides a solution, i.e., a direct method, for determining the liquid-solid adhesion work independently of contact angle measurement.

[0139] In summary, the method and apparatus according to the present invention have the advantage that the liquid-solid adhesion work is determined based on force measurements without knowing the contact angle of the liquid formed on the solid surface being tested. A further advantage is that it is sufficient to utilize only a very small volume of liquid, and the measurement can be performed in a sample chamber, i.e., the fluid medium can be selected. Thus, the measurement can be performed in a nearly saturated vapor space of liquid, or in another unmixed liquid medium.

[0140] To characterize the present invention, the following points define further embodiments. Paragraph 1 below should be interpreted as including further features of the present invention not described therein, but certain features given in Paragraph 1 can be made to correspond to certain features of the present invention, and any other features may also appear. Further subpoints add other optional features to the embodiments according to cross-references between paragraphs. 1. An apparatus for determining solid-liquid bonding work without contact angle measurement, comprising a circular solid surface 1, a force measuring instrument 2, a linear mover 3, a solid surface 4 to be tested, at least one light source 7, at least one camera 8, at least one capillary bridge 9, and at least one integrator unit 10, wherein the capillary force measured by the force measuring instrument 2 is integrated by the integrator unit 10 over a change in the length of the capillary bridge 9, and the size of the interface area of ​​the capillary bridge 9 is calculated by the integrator unit 10 based on the image from the camera 8. 2. An apparatus for determining solid-liquid bonding work without contact angle measurement, comprising a circular solid surface 1 forming a base plate of a capillary tube 11, a force measuring instrument 2, a linear mover 3, a solid surface 4 to be tested, at least one light source 7, at least one camera 8, at least one capillary bridge 9, at least one integrator unit 10, and at least one liquid feeder 12 (the apparatus may optionally consist of these), wherein the capillary force measured by the force measuring instrument 2 is integrated by the integrator unit 10 over the change in volume of the capillary bridge 9, and the size of the interface area of ​​the capillary bridge 9 is calculated by the integrator unit 10 based on the image from the camera 8. 3. The apparatus according to point 1 or point 2, wherein the material of the circular solid surface 1 is glass. 4. The apparatus according to point 1 or point 2, wherein the material of the circular solid surface 1 is platinum. 5. The apparatus according to point 1 or point 2, wherein the liquid meniscus adheres to (pins) the edge of a circular solid surface 1. 6. The apparatus as described in point 1 or point 2, wherein a circular solid surface 1, a solid surface to be tested 4, and a capillary bridge 9 are placed in a common sample chamber 5. 7. The apparatus described in point 6, wherein the fluid medium 6 filling the sample chamber 5 is a nearly saturated vapor space of liquid. 8. The apparatus according to point 6, wherein the fluid medium 6 that forms the environment of the capillary bridge 9 in the sample chamber 5 is a medium in a liquid state that does not mix with the liquid. 9. A method for determining liquid-solid adhesion work based on changing the length of a cylindrical symmetric capillary bridge 9 formed in a liquid-to-fluid medium 6 between a circular solid surface 1 and a solid surface 4 under test, and measuring the capillary force, wherein, in the process of changing the length of the capillary bridge 9 and measuring the capillary force and the change in the length of the capillary bridge 9, the change in the size of the liquid-fluid interface area and the change in the size of the interface area between the liquid and the solid surface 4 under test are determined, and the liquid-solid adhesion work is calculated based on these. 10. A method for determining liquid-solid adhesion work based on measuring the capillary force of a cylindrical symmetric capillary bridge 9 formed in a liquid-to-fluid medium 6 between a circular solid surface 1 and a solid surface 4 under test, wherein the volume of the capillary bridge 9 is changed, and in the process of measuring the capillary force and the change in the volume of the capillary bridge 9, the change in the size of the liquid-fluid interface area and the change in the interface area between the liquid and the solid surface 4 under test are determined, and the liquid-solid adhesion work is calculated based on these. 11. The method according to point 9 or point 10, wherein the material of the circular solid surface 1 is glass. 12. The method according to point 9 or point 10, wherein the material of the circular solid surface 1 is platinum. 13. The method according to point 9 or point 10, wherein a liquid meniscus adheres to (pins) the edge of a circular solid surface 1. 14. The method according to point 9 or point 10, wherein the contact angle occurring at the phase boundary between the liquid, fluid medium 6 and the solid surface 4 being tested is calculated from the liquid-solid bonding work. 15. The method according to point 9 or point 10, wherein the size of the interface area between the liquid and the fluid medium 6, and the size of the interface area between the liquid and the solid surface 4 to be tested are determined based on processing images of the capillary bridge 9. 16. The method according to point 10, wherein the volume of the capillary bridge 9 is calculated based on processing an image of the capillary bridge 9. 17. The method according to point 9 or point 10, wherein a circular solid surface 1, a solid surface to be tested 4, and a capillary bridge 9 are placed in a common sample chamber 5. 18. The method according to point 17, wherein the fluid medium 6 filling the sample chamber 5 is a nearly saturated vapor space of liquid. 19. The method according to point 17, wherein the fluid medium 6 that forms the environment of the capillary bridge 9 in the sample chamber 5 is a medium in a liquid state that does not mix with the liquid. 20. The method according to point 19, wherein a fluid medium 6 in a liquid state that does not mix with the liquid is filled into the sample chamber 5 after a capillary bridge 9 has been formed. 21. The method according to point 19, wherein a fluid medium 6 in a liquid state that does not mix with the liquid is filled into the sample chamber 5 of the capillary bridge 9 in such a state, and it has a minimum or maximum volume.

[0141] The present invention is, of course, not limited to the preferred embodiments described in detail above, and can be further modified, altered, and developed within the scope of protection as determined by the claims.

Claims

1. A method for determining the liquid-solid bonding work, wherein, in the process, a liquid cylindrical symmetrical capillary bridge (9) is formed in a fluid medium (6) between the end of a measuring element having a peripheral circular edge and the surface (4) of the solid to be tested, the following: -By performing a cylindrical symmetry retention modification on the cylindrical symmetrical capillary bridge (9), starting from the initial state and ending in the final state, ○ A step (S110a) to determine the first interface area change of the first interface area of ​​the capillary bridge (9) and the fluid medium (6), and the second interface area change of the second interface area of ​​the capillary bridge (9) and the surface to be tested (4), between the initial state and the final state, and ○In the process of correcting the cylindrical symmetry, the steps include determining at least one displacement value of the work-related displacement corresponding to the cylindrical symmetry correction and the respective force values ​​of the capillary force corresponding to the capillary bridge (9) for that purpose (S100), thereby determining the total amount of mechanical work corresponding to the capillary force for the cylindrical symmetry correction based on the at least one displacement value determined in the process of correcting the cylindrical symmetry and the force values ​​assigned to each of them (S110b), - In the cylindrical symmetry maintenance modification, based on the first interface area change, the second interface area change, the total mechanical work, and the liquid-fluid interface tension of the capillary bridge (9) and the fluid medium (6), ○The solid-liquid interface tension of the surface (4) and the capillary bridge (9) being tested, and ○ The solid-fluid interface tension of the surface (4) and the fluid medium (6) being tested. The first step of determining the difference value (S120), - A step (S130) to determine the liquid-solid bonding work, which is an indicator of the capillary bridge (9) and the surface (4) being tested, by subtracting the first difference value from the liquid-fluid interface tension, corresponding to the cylindrical symmetry retention correction. The method by which it is executed.

2. formula [Math 1] The first difference value is calculated according to the formula, in which, -γ ＳＬ The solid-liquid interface tension is γ ＳＦ This is the solid-fluid interface tension, － [Math 2] This is the total amount of machine work, -γ ＬＦ This is the liquid-fluid interface tension, -ΔA is the first interface area change, and ΔB is the second interface area change. The method according to claim 1.

3. The method according to claim 1 or 2, characterized in that a measuring element having a capillary conduction channel (14) opening at an end having a peripheral circular rim is applied, the end of the capillary conduction channel (14) opposite to the end having a peripheral circular rim is connected to a liquid feeder (12), the cylindrical symmetry retention modification is performed on the cylindrical symmetry capillary bridge (9) by passing the liquid through the capillary conduction channel (14), and the work-related displacement is determined by a displacement determination unit adapted to determine the displacement of the liquid in the capillary conduction channel (14).

4. A device for determining the amount of work done in liquid-solid adhesion, - A measuring element having an end with a peripheral circular edge for positioning its end having a peripheral circular edge in a fluid medium (6) together with a solid to be tested having a surface (4), wherein, when the apparatus is used, the measuring element and the surface to be tested (4) are positioned relative to each other so that a liquid cylindrical symmetric capillary bridge (9) can be formed between the end having a peripheral circular edge and the surface to be tested (4), and the measuring element has a capillary conduction channel (14) that opens to the end having a peripheral circular edge, - A liquid feeder (12) to which the end of the capillary conduction channel (14) opposite to the end having a peripheral circular edge is connected, - An interface area determination device adapted to determine the first interface area of ​​the capillary bridge (9) and the fluid medium (6), and the second interface area of ​​the capillary bridge (9) and the surface to be tested (4), Equipped with, The liquid feeder (12) is adapted to perform a cylindrical symmetric retention correction on the cylindrical symmetric capillary bridge (9) by passing the liquid through the capillary conduction channel (14), and the apparatus further, - A displacement determination unit adapted to determine at least one displacement value of the work-related displacement of the liquid in the capillary conduction channel (14) corresponding to the cylindrical symmetry retention modification process, - A force measuring instrument (2) adapted to determine the force value of the capillary force corresponding to the capillary bridge (9) for at least one of the displacement values, - An integrator unit (10) adapted to determine the total mechanical work corresponding to the capillary force for the cylindrical symmetry correction, based on the at least one displacement value determined by the displacement determination unit during the process of the cylindrical symmetry correction, and the force value assigned to each thereof. - In the cylindrical symmetry retention modification, ○Based on the first interface area change of the first interface area and the second interface area change of the second interface area, determined by the interface area determination device between the initial state and the final state of the cylindrical symmetrical capillary bridge (9), the total mechanical work and the liquid-fluid interface tension of the capillary bridge (9) and the fluid medium (6) are applied to the total mechanical work and the liquid-fluid interface tension of the capillary bridge (9) and the fluid medium (6). - The solid-liquid interfacial tension of the surface (4) and the capillary bridge (9) being tested, and - The solid-fluid interface tension of the surface (4) and the fluid medium (6) being tested. Determine the first difference value, and ○A work determination unit adapted to determine the liquid-solid adhesion work, which is an indicator of the capillary bridge (9) and the surface (4) being tested, by subtracting the first difference value from the liquid-fluid interface tension, in accordance with the cylindrical symmetry retention correction. A device equipped with the following features.

5. formula [Math 3] The first difference value is calculated according to the formula, in which, -γ ＳＬ The solid-liquid interface tension is γ ＳＦ This is the solid-fluid interface tension, － [Math 4] This is the total amount of machine work, -γ ＬＦ This is the liquid-fluid interface tension, -ΔA is the first interface area change, and ΔB is the second interface area change. The apparatus according to claim 4.

6. The apparatus according to claim 4 or 5, characterized in that the force measuring instrument (2) is a weighing scale having a measuring surface positioned opposite to the end of the measuring element having a peripheral circular edge, wherein the measuring surface is adapted to position the solid to be tested such that the surface to be tested (4) faces the end having a peripheral circular edge.

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