Method and apparatus for determining liquid-solid work of adhesion

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 to determine the liquid-solid work of adhesion. [Background technology]

[0002] The liquid-solid work of adhesion is a quantity commonly used to characterize liquid-solid interfaces, whose value provides information about the interaction of solid and liquid phases in contact over a unit surface area. It is therefore a concrete quantity, and its unit of measurement is the surface tension (Nm / m 2 ), but it is denoted by the letter "W" which conventionally denotes the amount of work, and the specific amount of work may also be denoted by the lower case "w". It is of great importance in all such industrial branches where liquids come into contact with solid surfaces (e.g. electronics and cosmetics, paper, adhesives, paints, printing and textile industries, soldering and dental technology, etc.). This quantity is determined by measuring the contact angle formed at the liquid-solid boundary, according to the Young-Dupré equation:

[0003]

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[0004]

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[0005]

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[0006]

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[0007] This method reserves for itself various measurement and theoretical uncertainties that arise from the characteristics of the contact angle measurement method. In certain cases, the value of the contact angle may be determined with large uncertainties, especially when the contact angle is small (<10°-20°) and large (>150°). Furthermore, the equilibrium Young's contact angle

[0008]

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[0009]

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[0010] An apparatus and method are known in which the force required to eliminate a solid-liquid interface under specific geometric conditions and with specific parameters is measured to characterize the liquid-solid adhesion (Patent Document 1). Since the water contact angle of hydrophobic and superhydrophobic surfaces can usually be determined with large errors, an apparatus was developed (Patent Document 2) that measures the forces occurring during the approaching and retracting of a liquid droplet to a surface, including the time instances of forming and eliminating a solid-liquid interface, with the aid of a circular plate fixed to a force measuring device and using it to press the droplet to the surface (Patent Document 3). A similar apparatus and method is disclosed in Patent Document 3, in which the adhesive force (i.e., the capillary force, referred to as "adhesion force" in the specific disclosure, see also the explanation related to these terms below) originating from the liquid volume placed between the solid surfaces is measured during the process of further removing the solid surfaces and bringing them closer to each other.

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

[0012] A suitable device and method for measuring the dynamic contact angle is disclosed in US Pat. No. 5,399,633. This technique does not include a force measuring device. A similar technical technique is disclosed in US Pat. No. 5,399,633.

[0013] US Pat. No. 5,399,633 discloses an apparatus and method for measuring contact angle and dynamic surface tension.

[0014] An apparatus adapted to determine contact angles is disclosed in the technical article "Contact angle determination" by Friedrich Schmidt, "Electrochemical properties of contact angles in water", Journal of Applied Physics, Vol. 13, No. 1, 2003, pp. 1171-1175, 2003. The technical article deals with aspects related to contact angles.

[0015] A device similar to that described in the technical article is disclosed in the above-mentioned US Pat. No. 5,399,633.

[0016] In US Pat. No. 5,399,636, the identification of molecules located on a surface reverts to force measurements. In this process, the base surface of an elastic pillar with a known surface area is pressed directly against the surface to be tested, which contains the molecule. The force applied during compression is directed to deforming the elastic pillar, and the work put in is stored by the pillar in the form of elastic energy. In the method according to this document, the work of adhesion between a molecule and a surface with a known area is identified as a measure of molecular weight, as the difference in the integrals (over displacement) of the forces measured when compressing and pulling apart the surfaces.

[0017] A technique for determining the work of adhesion without measuring the contact angle is disclosed in US Pat. No. 6,399,633. This technique is fundamentally different from the techniques mentioned above and is based on rotational (centrifugal) measurements and on the fact that the force exerted on the drop at the moment it detaches from the surface can be calculated from the rotation speed.

[0018] In view of known techniques, there is a need for an apparatus and method for determining the liquid-solid work of adhesion that allows for a more efficient determination of the liquid-solid work of adhesion as compared to existing techniques. [Prior art documents] [Patent documents]

[0019] [Patent Document 1] JP 2011-191277 A [Patent Document 2] European Patent No. 3571483 [Patent Document 3] JP 2004-144573 A [Patent Document 4] German Patent No. 102012221490 [Patent Document 5] JP 2013-174478 A [Patent Document 6] Canadian Patent No. 2968623 [Patent Document 7] JP 20011-16675 A [Patent Document 8] U.S. Patent No. 6,537,499 [Patent Document 9] US Patent Application Publication No. 2011-118993 [Non-patent literature]

[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) Summary of the Invention

[0021] The main object of the present invention is to provide a method and an apparatus for determining the liquid-solid work of adhesion which, as far as possible, does not suffer from the disadvantages of the prior art approaches.

[0022] It is an object of the present invention to provide a method and an apparatus by application of which the liquid-solid work of adhesion can be determined independently of the contact angle measured at the liquid-solid interface (surface), i.e. the task set for the present invention was to determine the liquid-solid work of adhesion independently of the measurement of the contact angle.

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

[0024] The method and device according to the invention are based on the realization that if a cylindrically symmetric capillary bridge extending between a circular solid surface and a solid surface to be tested is formed from a liquid in a fluid medium surrounding them such that the contact line of the liquid is attached (pinned) to the edge of the circular solid surface, the capillary force is measured during the course of a cylindrically symmetric modification of the capillary bridge (i.e. its length or volume change), while determining the change in the liquid-fluid interfacial area (liquid-fluid interfacial area change) as well as the change in the interfacial area of ​​the liquid and the solid surface to be tested (liquid-solid surface to be tested) during the process, and then by integrating the capillary force, with knowledge of the energy change of the system and therefore the liquid-fluid interfacial tension, the solid-liquid work of adhesion can be determined. [Brief description of the drawings]

[0025] Preferred embodiments of the invention will now be described, by way of example only, with reference to the following drawings, in which: [Figure 1] FIG. 2 is a flow diagram of a method according to the present invention. [Diagram 2] 1 is a schematic diagram of an apparatus suitable for carrying out an embodiment of the method according to the invention; [Diagram 3] FIG. 2 is a schematic diagram of an apparatus suitable for carrying out another embodiment of the method according to the invention. [Figure 4A] 1 is a graph showing measurements performed on the hydrophilic surfaces tested. [Figure 4B] 1 is a graph showing measurements performed on the hydrophobic surfaces tested. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0026] The present invention is a method for determining the liquid-solid adhesion work (in connection with the method according to the invention, see FIG. 1 showing a flow diagram of the method, as well as FIGS. 2 and 3 showing an apparatus adapted to carry out the method according to the invention), during which the steps given below are carried out in connection with a liquid cylindrically symmetric capillary bridge (liquid cylindrically symmetric capillary bridge (real)) formed in a fluid medium between an end with a peripheral circular edge of a measuring element (end of a measuring element whose end has a peripheral circular edge) and a tested surface of a solid to be tested (see fluid medium 6, surface to be tested 4 and capillary bridge 9 in FIGS. 2 and 3). The (necessarily solid) surface to be tested (to be tested) of the solid to be tested (investigated) is referred to herein briefly as "solid surface to be tested" (see the description of FIGS. 2 and 3), to emphasize the necessity of the application of a solid surface in the method.

[0027] The formation of the capillary bridge is not considered to be part of the method according to the invention. This is according to the fact that the method is based on the measurements taken at the capillary bridge itself, i.e. the capillary bridge is maintained during the entire course of the method. It is also possible that the formation of the capillary bridge is treated in a separate step, when the capillary bridge is formed by bringing a drop located on or transferred to the end of a measuring element, usually with a peripheral circular edge, close to (or directly transferring) the surface to be tested.

[0028] Furthermore, by requiring cylindrical symmetry of the capillary bridge according to the above, it is also preferred that the circular edge of the end having a peripheral circular edge is perpendicular to the longitudinal axis of the measuring element (which again is its axis of movement, i.e. the axis of symmetry corresponding to the cylindrical symmetry) during the method, thereby allowing the cylindrical symmetry of the bridge to be achieved.

[0029] A cylindrically symmetric capillary bridge is formed thanks to an end with a peripheral circular edge (peripheral circular rim) that adheres to (against, on) its edge. At the same time, the requirement of cylindrical symmetry also requires that the surface to be tested does not break this cylindrical symmetry, i.e. is preferably a plane arranged parallel to the end with the peripheral circular edge, or a properly arranged spherical surface (see further below). In the latter case, due to the cylindrical symmetry, there is a dedicated 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 arranged in such a way as to preserve the cylindrical symmetry.

[0030] In the course of the method according to the invention (the description of the steps of the method according to the invention starts from this paragraph), a cylindrically symmetrical retention correction is performed on the cylindrically symmetrical capillary bridge, starting (started) from an initial state and ending (ended) in a final state (as their names suggest, the initial state and the final state are of course the states during which the method is performed, i.e. measurements are performed on the capillary bridge as required for each of the measurements, for the specific quantities see also the following formulas): a first interfacial area change (first surface area change) of a first interfacial area (first boundary area) of the capillary bridge and the fluid medium, and a second interfacial area change (second surface area change) of a second interfacial area (second boundary area) of the capillary bridge and the surface to be tested between the initial state and the final state are determined (the operational step S110a related to the determination of the interfacial area change corresponds to this, i.e. the first interface is the interface between the liquid - the capillary bridge - and the fluid, the change of which is the first interfacial area change, and the second interface is the interface between the capillary bridge and the surface to be tested - i.e. the surface where the capillary bridge contacts (touches) the surface to be tested, see Fig. 2 and Fig. 3 - the change of which is the second interfacial area change), ○ Based on at least one displacement value determined in the course of the cylindrically symmetrical holding correction and the force value respectively assigned thereto, by determining at least one displacement value of the work-related displacement (work execution displacement, work displacement, displacement corresponding to the work done) corresponding to the cylindrically symmetrical holding correction and therefore the respective force value of the capillary force corresponding to the capillary bridge (see below with regard to determining the displacement value, determining the force value is determining by measurement, which can also be referred to as being determined based on measurement, the operational step S100 related to determining the capillary force corresponds thereto, see also Figures 4A to 4B related to the graph (running) of the recorded values ​​and the aspects related to the range investigated by the method) in the course of the cylindrically symmetrical holding correction, the total mechanical work corresponding to the capillary force is determined for the cylindrically symmetrical holding correction (the operational step S110b related to determining the total mechanical work corresponds to this).

[0031] It is expressed above as "at least one displacement value of the work-related displacement corresponding to the cylindrically symmetrical holding correction". This is interpreted to mean that a total work-related displacement corresponds to the correction, the value of which is determined (measured as a whole or divided into parts) at a measurement time instance, i.e. the displacement value is typically determined (e.g. measured) at a number of points, and the respective force values ​​corresponding to this number of points are also determined. The total work-related displacement is obtained as the sum of one or more displacement values, which are measured (generally determined) in the course of the cylindrically symmetrical holding correction.

[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), force values ​​are also typically measured at both of its end points (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 state). If at least two displacement values ​​are determined, a respective capillary force value is determined for each of them and the total machine work is determined based on the displacement values ​​and the respective force values ​​assigned to each one.

[0033] According to the above, the work is determined based on one or usually several displacement values ​​and the respective force values ​​assigned to it or to each of them. Usually, for the discrete displacement values ​​(for typical cases, often the plural is used, but there may be only a single such value) recorded in the course of the measurement and the respective force values ​​assigned to them, the total machine work can be determined by summing (see Fig. 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 can be the force values ​​measured at either of both end points of a given displacement value, or for example their average, i.e. a 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 successive measurement time instances) and the respective force values ​​corresponding to each of the displacement values.

[0034] Also, based on the displacement values ​​and their assigned force values, 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 summation is essentially a numerical integration for sufficiently small displacement values), i.e., the total machine work is preferably determined by summation, numerical integration, or integration.

[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 can be calculated as their product in equation (2).

[0036] The capillary force corresponds to a capillary bridge, i.e. according to the capillary principle, the capillary bridge exerts this force on the surface it connects. In this connection, reference is made to the exemplary measurements disclosed in Fig. 4A-B, in which the evolution of the force values ​​is detailed. In connection with the work-related displacements corresponding to the cylindrically symmetrical holding correction, in other words the work-related displacements assigned to the capillary force, reference is made to the description of Fig. 2 and Fig. 3, which specifies which displacements (displacements of the ends of the measuring element, displacements of the liquid in the capillary conducting channel) are assigned to the capillary force, so that, for example by summation, the total mechanical work, i.e. the mechanical work corresponding to the entire cylindrically symmetrical holding correction, can be calculated (this term is also correct since gravitational effects are neglected, and can also be called the capillary force work, or simply the first work).

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

[0038] There is no hierarchy between the steps according to the above two points, i.e. their order here does not imply an order of execution. Since the forces are measured during the entire process of cylindrical symmetry preserving correction (or cylindrical symmetry preserving correction, which can also be called cylindrical symmetry preserving or sustaining correction), this can be interpreted as being earlier than the determination of the total machine work from the recorded force values ​​and the change in the interfacial area, although the latter two steps can be performed in any order or even simultaneously, as also indicated by their reference numbers.

[0039] It should also be noted that determining the interfacial area change is a measurement step preferably performed by obtaining optical recordings and utilizing them to calculate the interfacial areas at a given time instance and their difference between the initial and final states.

[0040] With regard to the summation for the cylindrical symmetry correction, reference is made to the explanation of equation (2). In extreme cases (limit cases, border cases), the summation becomes an integral as it is reflected in the notation of equation (2), however, since the measurements are discrete, a low but finite displacement value is applied in the calculation, as it is shown in Figures 4A-4B. The force value is calculated by the total mechanical work (the total mechanical work thus obtained is called corresponding to the capillary force, and as a result, the capillary force is calculated by summing the capillary forces and integrating with the displacement, the following terms of equation (2):

[0041]

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[0042] Furthermore, in the course of the method according to the invention (in this paragraph further steps of the method according to the invention are given), based on the first interfacial area change, the second interfacial area change, the total mechanical work and the liquid-fluid interfacial tensions of the (liquid) capillary bridge and the fluid medium (liquid-fluid interface tensions), the solid-liquid interfacial tension of the surface and (liquid) capillary bridge to be tested, ○ The solid-fluid interfacial tension of the surface being tested relative to the fluid medium (solid-fluid interface tension) A first difference value between (and) is determined for a cylindrically symmetry preserving correction (corresponding to the operational step S120 related to determining an interface difference value), By subtracting the first difference value from the liquid-fluid interfacial tension, the liquid-solid work of adhesion, which corresponds to the cylindrically symmetric retention correction and is indicative of the (liquid) capillary bridge and the surface being tested, is determined (corresponding to the operational step S130 related to determining the liquid-solid work of adhesion).

[0043] The essence of the method and device according to the invention is that a cylindrically symmetric capillary bridge is formed between a circular solid surface and the solid surface to be tested from a liquid in the fluid medium surrounding them, the liquid sufficiently wets the circular solid surface and the meniscus of the liquid adheres (pins) to the edge of the circular solid surface.

[0044] The end of the measuring element is referred to above at the beginning of the method as an 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 cylindrically symmetric configuration of the capillary bridge, it also has a cylindrically symmetric configuration. In this description, the illustrated implementation of this is referred to as a "circular (solid) surface" and is shown in the figures as having a flat configuration (therefore the end with a peripheral circular edge can also have a preferably flat configuration, although it naturally has a solid configuration).

[0045] In the configuration of FIG. 2, the circular surface is a (naturally flat) circular plate (located at the bottom of the measuring element), while in the configuration of FIG. 3, the channel 14 of the capillary 11 opens into the circular surface, so that the end can be a planar (flat) circular ring shape, or a planar (flat) ring shape with a circular outer periphery, the inner periphery of which is different from circular, e.g. square or rectangular.

[0046] Also, according to the previous identification, since the liquid wets the circular solid surface well, the meniscus of the liquid will adhere (pin) to the edge (rim) of the circular solid surface, i.e. the interfacial area of ​​the end and the capillary bridge with the peripheral circular edge can be considered to be constant. Preferably, a surface of a suitable material that facilitates adequate wetting can be applied to the end (e.g. glass or platinum), and the presence of the edge also ensures the permanence of the interfacial area between the end and the capillary bridge (i.e. the adhesion of the contact line helps), since it is not preferable to have the liquid separate from it. This is independent of whether the object to be tested (test object) is hydrophilic or hydrophobic.

[0047] With reference to the figures, the implementation of the method according to two different embodiments will be described. First, reference will be made to the implementation according to FIG. 2. In this case, the distance between the two solid surfaces is changed so that the direction of the relative displacement coincides with the axis of symmetry of the capillary bridge (i.e. a cylindrical symmetry preserving correction is applied, i.e. a correction that does not destroy the cylindrical symmetry of the capillary bridge). By changing the distance between the solid surfaces, the length of the capillary bridge is changed. When the two solid surfaces are brought closer to each other, the capillary bridge is shortened, when they are moved away from each other, the length of the capillary bridge is increased. For both processes, the size of the liquid-fluid interfacial area changes, as well as the size of the interfacial area of ​​the liquid and the solid surface to be tested. The interfacial area between the liquid and the circular solid surface does not change, since the meniscus of the liquid adheres (pins) to the edge of the circular solid surface.

[0048] The capillary force and the relative displacement of the solid surfaces are measured during the process. Integrating the measured force over the displacement gives the work (i.e., the amount of work done on or by the system) that is expended to change the size of the interfacial area (see the exemplary measurements shown in Figures 4A-B for the equation).

[0049]

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

[0051] When moving solid surfaces closer and further apart to determine the change in size of the interfacial area at the start and end points, the formula (γ SL -γ SF ) can be calculated. This remains the only parameter calculated in the formula, since the value of the integral on the left side of (2) is determined as the interfacial area changes. In the experiment, the unknown parameters (unknowns) are also the parameters of the surface being tested, i.e. the corresponding interfacial tensions, but also the liquid-fluid interfacial tension γ LF is assumed to be known. The detailed process above for calculating the liquid-solid work of adhesion is consistent with this.

[0052] By harmonizing the notation of the formula with the terminology (concepts) introduced above, the first difference value (see above) can be expressed by the formula (rearrangement of formula (2)):

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[0054]

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[0055] Liquid-solid adhesion work (W a )teeth,

[0056]

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[0057] If the method is carried out according to another embodiment, the above is slightly modified. In that connection, reference is made to FIG. 3. In this case, the circular solid surfaces are the cross-sections (ends) of the capillary, 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 volume change dV of the capillary bridge is measured. An increase and a decrease in volume correspond, respectively, to bringing the solid surfaces closer to each other and moving them away from each other. In this case, to calculate the work, the capillary force needs to be integrated over the relative displacement of the liquid column in 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 (according to the often applied convention) the attractive capillary force is considered to have a positive sign (in other words, one considers the capillary force to have a positive sign in the case of attractive forces), then according to equations (2) and (4) above, the difference between the mechanically performed work and the work required to change the liquid-fluid interfacial area, and the quotient of the liquid-solid interfacial area change, is subtracted from the liquid-fluid interfacial tension to obtain the liquid-solid adhesion work:

[0059] The liquid-solid work of adhesion can also be determined if one deviates from this convention and considers the attractive capillary forces 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 interfacial area, and the quotient of the liquid-solid interfacial area change, should be subtracted from the liquid-fluid interfacial tension to obtain the liquid-solid work of 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 is included with a negative sign). Thus, it is possible to determine the liquid-solid work of adhesion based on the quantities determined as described above, although the exact procedure of calculation depends on the sign convention chosen.

[0060] The work of adhesion determined during the advancement of a contact line of a liquid formed on a solid surface is an indication of the driving force behind the spreading of the liquid, whereas the work of adhesion determined in the receding regime characterizes the "liquid retention" of the surface (i.e., how difficult it is to separate the liquid from the surface). The mechanical work invested when the contact line is stationary is only utilized to change the liquid-fluid interfacial area, i.e., a stationary (non-moving) contact line does not allow obtaining information about the liquid-solid work of adhesion.

[0061] In accordance with the above, the present invention is based on the recognition that the work done to (or by) the system goes into modifying the liquid-fluid (medium) and liquid-solid interfacial areas, and thus the liquid-solid adhesion work can be determined with knowledge of the mechanical work, the liquid-fluid interfacial tension, and the change in size of the interfacial area.

[0062] Therefore, the present invention has a fundamentally new element (aspect) that has not been seen in the past, that is, the liquid-solid adhesion work can be separated and absolutely determined in addition to the advancement and retreat of the capillary bridge contact line from the mechanical work and the change in interfacial area for each advancement and retreat situation.

[0063] In the following, the manner of measuring or determining the amount applied in the method for determining the liquid-solid adhesion work is described. In this connection, reference is also made to the description of Figures 2 and 3.

[0064] Capillary forces can be measured when a circular solid surface is connected to a force measuring device (force gauge) or when a solid body with a surface to be tested (object to be tested) is placed on a force measuring device (gravimeter).

[0065] The change in interfacial area and volume of the capillary bridge can be determined by taking side images of the capillary bridge formed by the liquid at least at the beginning and end, when the solid surfaces are approaching each other and when they are moving away from each other, and when the volume is increasing and decreasing.

[0066] The size of the interface area of ​​the liquid and the solid surface to be tested can be calculated by determining in the image the distance between the contact points of the capillary bridge and the generatrix of the solid surface to be tested (i.e. the diameter of the circular contact line of the liquid) if the geometry of the solid surface to be tested is known, since the capillary bridge has cylindrical symmetry (for calculations based on camera images, reference is made to the specialized article mentioned above at the beginning by N.Nagy, "Contact Angle Determination on Hydrophilic and Superhydrophilic Surfaces by Using r-θ-Type Capillary Bridges" [Langmuir 35, page 5202 (2019)]). For example, if the solid surface to be tested is a flat surface, the interface in question is a circular plate. For example, if the solid surface to be 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 requirement for cylindrical symmetry of the capillary bridge, and the other conditions mentioned above (i.e. that the direction of the relative displacement coincides with the axis of symmetry of the capillary bridge) support that modifications made to the capillary bridge preserve (persist) cylindrical symmetry. Applying linear motors for the displacement also facilitates this. The case of volume change is similar, in which image analysis can also be applied, since there is no such situation - volume changing through the capillary channel - that could cause changes that destroy cylindrical symmetry.

[0068] The size of the liquid-solid interfacial area can be determined by performing an image analysis of the shape of the capillary bridge. The size of the interfacial 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 by a suitable function (e.g. polynom) and calculating (integrating) the size of the surface 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 separate components, i.e. the surface of revolution is decomposed into a cylindrical mantle of low height and the size of the surface of revolution is calculated as the sum (numerical integration) of these.

[0069] The change in the volume of the capillary bridge can be determined by a device that provides the volume change, in the case of an embodiment based thereon (see also in connection with FIG. 3 below). The volume can also be determined by performing an image analysis of the shape of the capillary bridge. The volume of the capillary bridge can be calculated by providing an analytical mathematical description of its shape or by calculating the volume of a body 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 interfacial area, or by numerical integration of the capillary bridge contour.

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

[0071] While the solids are approaching each other and while the volume of the capillary bridge is increasing, the contact line of the liquid formed on the solid surface being tested is advancing. The liquid-solid adhesion work determined in this way is therefore a measure of the spreading 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 (inserted) 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. The liquid-solid adhesion work determined in this way is therefore a measure 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 inserted into the Young-Dupré equation.

[0072] By using the Young-Dupré equation (i.e., using equation (1) above), from the value of the liquid-solid adhesion work thus determined, the (typical) values ​​of the advancing and receding contact angles of the liquid formed on the surface to be tested can be determined by calculation, i.e., without directly measuring them. This is preferable, for example, in cases where the uncertainty of the contact angle measurement significantly reduces the accuracy of the subsequent calculations. In this respect, the method of determining the liquid-solid adhesion work according to the invention is considered to be more efficient compared to known techniques.

[0073] In the following, Figures 2 and 3 are described which show details for carrying out a corresponding embodiment of the method, and in connection with carrying out the method, specific details of the apparatus are shown in Figures 2 and 3 (which also describe options and in many cases provide explanations at an exemplary level - giving which information can be generalized by analogy (if necessary)).

[0074] In FIG. 2, an embodiment of the method according to the invention is shown with the help of a schematic diagram of the corresponding device. In a preferred exemplary embodiment of the invention shown in FIG. 2, the circular solid surface 1 (according to the figure, this reference number (sign) can also indicate an end with a peripheral circular edge) can be, for example, the base of a glass cylinder with a diameter of 2 mm (as well as, as shown in FIG. 2, it can be implemented as another such object slightly slimmed down in the middle, with a suitably configured end, i.e. a circular solid surface), or a platinum disk with this same diameter. A drop (droplet) of liquid with a volume of more than 1 μL hangs from this surface. The upper end of the glass cylinder is connected to a force-compensating force measuring device 2, for example with a resolution of 5 μN or less (components with the same function, such as the force measuring device, are labeled with the same reference numbers in FIG. 2 and FIG. 3, but a slightly different configuration in one of the variants (for example this variant) can be indicated, for example, with an upper comma ('), such components can be, for example, the circular solid surface 1 and the sample chamber 5). Its movement in the vertical direction is provided by a linear mover (actuator) 3 with a lead (worm) screw driven by a stepper motor, the minimum available drive speed being <0.02 mm / s.

[0075] The solid surface 4 to be tested is placed below the base plate of the glass cylinder, parallel to its plane, on a support adapted to move in a plane, preferably along two directions (on an xy mover, which after the capillary bridge has been formed, is no longer used in the course of the method according to the invention). The lower end of the glass cylinder and the solid surface 4 to be tested are preferably placed in a common sample chamber 5, the fluid filling the sample chamber 5 (i.e. the fluid medium 6 surrounding the capillary bridge 9) being, for example, a nearly saturated (≧80%) vapor space of a liquid (if a gas-phase fluid medium is applied, it is of course feasible to seal the sample chamber in such a way that the ends of the measuring elements protrude into the chamber through small openings formed in the upper plate of the sample chamber, i.e. in an incomplete manner). The term "sample chamber" is used since the sample to be tested, i.e. the solid to be tested, is placed in it, but it can also be called "measurement chamber" since the measurements are focused on it or on the components placed in it (end with a peripheral circular edge, capillary bridge, solid to be tested).

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

[0077] Thus, the fluid medium may preferably be in a sample chamber, the solid to be tested having a surface to be tested in the course of the test is placed in the fluid medium thus arranged, and the end of the measuring element having a peripheral circular edge is also arranged here. Preferably, the device may comprise a sample chamber, i.e. the sample chamber may be a fixedly arranged component thereof (wherein the object to be tested is replaced if necessary), but the sample chamber may also be arranged for the time period during which the measurement (method) is performed, i.e. the object to be tested can be replaced together with the sample chamber.

[0078] Preferably, a light source 7 providing uniform illumination, in our case for example an LED light with a diffuser, is arranged on one side of the glass cylinder perpendicular to the axis of the glass cylinder, and on the other opposite side a camera 8, for example a CMOS (Complementary Metal Oxide Semiconductor) camera 8, with a resolution of at least 1024x768 pixels (preferably, more than one camera may be applied, or one can say at least one camera, since cylindrically symmetric bodies can be better investigated). The data of the force measuring device 2, the linear mover 3 and the camera 8 are preferably processed by an integrator unit 10 (summation unit, or integrator for short), which according to FIG. 2 preferably has a respective interconnection with the integrator unit 10.

[0079] In the course of the measurement process, the drop hanging from the circular solid surface 1 is first brought close to the solid surface 4 to be tested. As soon as the drop reaches the solid surface 4 to be tested, i.e. from the time instance 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 device 2, the displacement of the circular solid surface 1 and the taken images of the capillary bridge 9 are recorded, for example every 10 seconds. In the course of the approximation 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 to be 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 (moving the circular solid surface 1 away), which continues, for example, until the capillary bridge 9 breaks (cylindrical symmetry retention modifications 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 taken as the starting point (initial state) of the approximation process, and the turning point is taken as its final point (final state, see Fig. 4A-B, the circled point is the formation point, so the starting point is taken as the second (or third, if you also count the circled point) point of the graph, the final point, which in the case of Fig. 4A is naturally the point before the "jump" in the turning - at the bottom of the diagram). As the starting point (initial state) of the separation phase, for example the second measurement point after the turning point, is taken as its end point (final state), the measurement point at which the length of the capillary bridge 9 just does not exceed the length of the bridge at its formation is taken as the final point.

[0082] This effectively provides a rule of thumb for determining the work of adhesion by calculating the approximation (approaching) and separation (retreating) phases separately (as noted elsewhere, the work of adhesion calculated for the approximation and separation phases are indicative of the spreading and separation of the liquids, respectively).

[0083] Immediately after its formation, the liquid-solid contact line is not necessarily advancing, so it is safer to investigate the process from the second point. In the case of separation, it is also expedient to start from the second point, and practical guidelines are given, at this stage the contact line has usually already stopped retreating, but it is not expedient to go beyond the formation length, since there is also a risk of rupturing the capillary bridge. It is worth applying the method to sections where the contact line is truly moving and where empirical rules give good support.

[0084] Therefore, the above should only be treated as a rule of thumb, i.e. the formula can be applied for much shorter periods and deviations from it can be made if necessary. Naturally, the shorter the range of changes investigated, the larger the measurement error. The rule of thumb defines long measurement periods for both the advancement and retreat of the capillary bridge.

[0085] It will be appreciated that choosing a measurement period (between the initial state and the final state) that is too short, i.e. investigating a cylindrically symmetrical retention correction in the method according to the invention that is too small, is not worthwhile. For example, a change between two adjacent measurement points can be considered as too small (expected measurement error is high), which can still be applied in the present invention. Investigating three consecutive measurement points in the course of a cylindrically symmetrical retention correction will likely result in less error, i.e. it may be preferable to record at least three measurement points (i.e. to operate with at least three measurement time instances covered by the cylindrically symmetrical retention correction).

[0086] In the following, the determination of the liquid-solid work of adhesion is carried out according to the above description: the capillary force measured by the force measuring device 2 is integrated by the integrator unit 10 over (as a function of) the relative displacement of the circular solid surface 1 measured by the linear mover 3. Based on the images recorded by the camera 8, the liquid-fluid interfacial area is also calculated (integrated) by the integrator unit 10.

[0087] In another preferred embodiment of the device according to the invention shown in figure 3, the sample chamber 5 is placed on a force measuring instrument 2, in this case an analytical (weighing) scale with a resolution of 0.05 mg or less. The fluid medium 6 present in the sample chamber 5 is a medium in liquid state that is immiscible with the liquid forming the capillary bridge 9.

[0088] When a fluid medium in a liquid state that is not miscible with the liquid is applied, the fluid medium can be filled into the chamber in any one of the following two preferred subcases, and the fluid medium 6 in a liquid state that is not miscible with the liquid is: after the capillary bridge 9 has formed, or in such a state that the capillary bridge 9 has the shortest or largest volume The sample chamber 5 is filled.

[0089] For example, in the latter case, the method is only applied in the backward case. Note that in general, it is often not convenient to perform searches in both directions (forward, backward), but this is not necessary.

[0090] A circular solid surface 1 (generally and end with a peripheral circular edge, or according to the description a circular solid surface with a capillary channel opening into it) is a cross section of a glass capillary tube 11, for example with an outer diameter of 2 mm, the capillary tube being connected via a preferably flexible tube to a liquid feeder 12 (liquid dispenser) device, in practice a syringe pump with a minimum supply rate (speed) of less than 0.2 μL / min, i.e. it is capable of supplying liquid at a speed of less than 0.2 μL / min. The linear movement of the capillary tube 11 is preferably provided by a linear mover 3, as described above in connection with the embodiment shown in FIG. 2.

[0091] The arrangement and characteristics of the light source 7 and the camera 8 are identical to those described above in connection with the embodiment shown in Figure 2. The data of the force measurer 2, the liquid feeder 12 and the camera 8 are processed by an integrator unit 10.

[0092] Prior to the measurement, the 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 expelled (squeezed) from the capillary tube 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 the previous preferred embodiment, i.e. by approximating and spacing the circular solid surface 1 (thus applying the cylindrical symmetry retention correction). In this case, the measurement is evaluated in the same manner as above (in this case the capillary tube 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 in the course of carrying out the corresponding embodiment of the method according to the invention. A liquid feeder 12 (e.g. a syringe pump) is applied to increase or decrease the volume of the capillary bridge 9 in a known amount, for example at a rate 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 device 2, the volume change of the capillary bridge 9 and the image of the capillary bridge 9 taken by the camera 8 are recorded (note) every 10 seconds. Again, an interconnection is established from the force measuring device 2, the camera 8 and the liquid feeder 12 (and preferably also the linear mover 3) to the integrator unit 10.

[0094] In the course of the evaluation, preferably in this embodiment the second measurement point after the formation of the capillary bridge 9 is considered as the start of the volume increase and the turning point is considered as the end point thereof, and the start of the volume decrease is considered to be preferably the second measurement point after the turning point and the end point is the measurement point at which the volume of the capillary bridge 9 just does not exceed the volume measured at its formation.

[0095] In the following, the liquid-solid work of adhesion is determined according to the description above, with the difference that the force measured during the process is integrated by the integrator unit 10 over the displacement (dV / a) of the liquid column in the capillary tube, rather than integrating it over the relative displacements of the solid surfaces (as these remain stationary).

[0096] Thus, in this case, the linear mover 3 is applied to move it to an appropriate distance from the solid surface 4 to be tested, after which it remains stationary (at a fixed distance from the solid surface 4 to be tested). However, in this latter embodiment, the device can also be configured without applying a (linear) mover, and instead the capillary is fixed at a predefined distance from the solid surface 4 to be tested (i.e. it is fixedly positioned at this distance) and the device is thus applied. Again, the liquid required 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 after the capillary bridge 9 has formed or after it has reached its maximum volume with a fluid medium 6 in a liquid state that is immiscible with the liquid forming the capillary bridge 9. The extent to which the presence of the fluid medium 6 facilitates the separation of the liquid from the surface 4 to be tested can be investigated with the help of this latter solution.

[0098] Another advantage of the device according to Fig. 3 and the corresponding method is that the capillary bridge can be easily and quickly formed, the volume of the capillary bridge can be precisely adjusted, and therefore it is also possible to easily automate the capillary bridge, i.e. to have high-throughput measurements. A further advantageous property is that the capillary bridge can be easily formed, in contrast to the arrangement according to Fig. 2, when the fluid medium is in the liquid phase, and it is more difficult to pass the initial suspension drop through the air-liquid medium interface. The arrangement according to Fig. 3, in a particularly preferred manner, allows much easier execution of measurements "under liquid", making it easier and more accurate to study the displacement-wetting (and dewetting) as well as cleaning processes often applied in the field, which involve the determination of the liquid-solid adhesion work.

[0099] In an embodiment of the method according to the invention performed by the device shown in Figure 3, a measuring element is applied having a capillary conducting channel (see capillary conducting channel 14 in Figure 3) opening at its end having a peripheral circular edge, the end of the capillary conducting channel opposite the end having a peripheral circular edge is connected to a liquid feeder (see liquid feeder 12 in Figure 3), a cylindrically symmetrical retention correction is performed on a cylindrically symmetrical capillary bridge by passing a liquid through the capillary conducting channel (this is a (adapted) liquid for building a capillary bridge, in other words a liquid that builds (constitutes) a capillary bridge which is also expediently applied for performing a cylindrically symmetrical retention correction on it, which also appears below), and the work-related displacement is determined by a displacement determination unit adapted to determine the displacement of the liquid in the capillary conducting channel.

[0100] Thus, on the one hand, the manner in which the cylindrically symmetrical retention correction is performed in this embodiment is specified above (i.e. no new steps are introduced, but the implementation scheme is specified), in which the cylindrically symmetrical retention correction is only performed in this case in this way, i.e. the measuring element remains stationary and therefore the length of the capillary bridge does not change either, but the shape of the capillary bridge - the volume and the interfacial area - changes. Furthermore, the scheme for determining the work-related displacement is also specified.

[0101] By passing a liquid through the capillary conducting 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), i.e. in this case too, a bidirectional process can be performed on the capillary bridge - advancing and retracting the liquid-solid contact line - which is also performed by moving the measuring element and the corresponding work-related displacement can be determined.

[0102] In accordance with the above, a particular embodiment of the present invention relates to an apparatus adapted to determine the liquid-solid adhesion work. The apparatus according to the invention is suitable for carrying out the method according to the invention, i.e. the apparatus according to the invention is adapted to determine the liquid-solid adhesion work by carrying out the method according to the invention.

[0103] The device according to the invention comprises: - a measuring element having an end with a peripheral circular edge (with an end) for placing said end with a peripheral circular edge in a fluid medium together with a solid to be tested having a surface to be tested and when the apparatus is utilised (in use), the measuring element and the surface to be tested are arranged relative to each other such that a liquid cylindrically symmetric capillary bridge can (is formable) be formed between the end with the peripheral circular edge and the surface to be tested (what kind of relative arrangement of components this requires has been addressed above, see also fluid medium 6, surface to be tested and capillary bridge 9 in Figures 2 and 3), the measuring element having a capillary conducting channel 14 opening out at the end with the peripheral circular edge (this is preferably formed in a capillary tube 11 and in Figure 3 is shown filled with liquid).

[0104] In some cases, certain components of the device may be defined below in relation to the capillary bridge, with the understanding that on the one hand, this characterization also specifies the cryo-state configuration of these components, and on the other hand, in relation to these characteristics, they perform their functions when utilizing (using) the device, as already specified in the definition above in relation to the formation of the capillary bridge.

[0105] The device is a liquid feeder (see liquid feeder 12 in FIG. 3 ) connected at its end to a capillary conducting channel (see capillary conducting channel 14 in FIG. 3 ) opposite the end with a peripheral circular edge (obviously the channel has two ends, one of which opens into the end with a peripheral circular edge and the other connected to the liquid feeder, i.e. the liquid feeder can supply liquid to this end or carry away (take) liquid from this end); an interfacial area determination device adapted to determine a first interfacial area of ​​the capillary bridge and the fluid medium, and a second interfacial area of ​​the capillary bridge and the surface to be tested; Further equipped with The liquid feeder is adapted (configured to be adapted) to perform a cylindrically symmetric retention correction to the capillary bridge by forcing liquid through the capillary conducting channel.

[0106] As already mentioned, the liquid feeder is suitable for supplying liquid and carrying it away, i.e. for carrying out a cylindrically symmetrical retention correction by passing the liquid through the capillary conducting channel. In addition to supplying / removing, this also means adding or removing liquid corresponding to the cylindrically symmetrical retention correction, so that a forward or backward correction is made to the capillary bridge. To determine the displacement value, it can be conveniently determined how much liquid has been supplied or removed by the liquid feeder.

[0107] When the device is applied (in use), the end with the peripheral circular edge and the surface to be tested enter into a fluid medium, which may even be free air, but also another appropriately selected fluid, since the liquid-fluid interface also plays a role in determining the liquid-solid work of adhesion. The solid to be tested with the surface to be tested may be replaceable, so that it does not form part of the device in the unapplied (not in use) state. Moreover, in certain embodiments, the circular end of the measurement element may apply a motion to enter into the fluid medium.

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

[0109] The device according to the invention comprises: a displacement determination unit adapted to determine, in the course of the cylindrically symmetrical retention correction, at least one displacement value of a work-related displacement of the liquid in the capillary conducting channel, which corresponds to the cylindrically symmetrical retention correction; a force measuring device adapted to determine (by measuring) a force value of a capillary force corresponding to the capillary bridge for at least one displacement value; an integrator unit adapted to determine a total mechanical work corresponding to a capillary force for the cylindrically symmetrical holding correction based on at least one displacement value determined by the displacement determination unit in the course of the cylindrically symmetrical holding correction and the force value assigned thereto respectively; -For cylindrical symmetry correction, based on a first interfacial area change of the first interfacial area and a second interfacial area change of the second interfacial area determined by the interfacial area determination device between an initial state and a final state of the cylindrically symmetric capillary bridge, for the total mechanical work and for the liquid-fluid interfacial tension of the capillary bridge and the fluid medium, The solid-liquid interfacial tension of the surface and (liquid) capillary bridge being tested, and · The solid-fluid interfacial tension of the surface and fluid medium being tested (i.e., the first difference value is determined based on these quantities, see equation above), a work determination unit adapted to determine a liquid-solid adhesion work corresponding to a cylindrical symmetry retention correction and indicative of a capillary bridge and of the surface being tested by subtracting a first difference value from the liquid-fluid interfacial tension; Prepare further.

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

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

[0112] The displacement determination unit expediently operates to divide the volume change caused by the liquid feeder (preferably a known volume is pumped 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 conducting channel, thereby determining the displacement (values ​​of the displacement in both directions causing both inward and outward liquid movement can be so determined).As described in the definition above, the integrator unit is adapted to determine the liquid-solid adhesion work based on suitable input data.

[0113] According to what has been described above in relation to the device, in order to determine the total mechanical work, the displacement can be related to a cylindrically symmetrical retention correction, which is carried out parallel to the axis of symmetry and targets the correction of the capillary bridge. As can be seen above, in relation to FIG. 2, the displacement is the change in the length of the capillary bridge caused by the vertical displacement of the measuring element. The displacement can be brought about similarly in relation to FIG. 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 work done. The displacement in both directions is therefore parallel to the axis of symmetry and the capillary forces also act in this direction.

[0114] Moreover, in the device according to the invention, the force measuring device is a weighing scale (scale, balance) with a measuring surface arranged opposite the end of the measuring element with a peripheral circular edge, the measuring surface being adapted to arrange the solid to be tested so that its surface to be tested faces the end with the peripheral circular edge (see the force measuring device implemented as a weighing scale and the relative arrangement of the weighing scale and the surface to be tested 4 in FIG. 3, in such an arrangement of the force measuring device the magnitude of the capillary force can essentially be interpreted as the degree to which the object to be tested is lifted from the weighing scale or pressed against the weighing scale by the capillary force). Force measuring devices usually measure forces accurately when they are arranged in the device shown in the figures, i.e. for example when the measuring surface of the weighing scale is horizontal as shown in FIG. 3 (the force measuring device shown in FIG. 2 is usually suitable for measuring forces in the vertical direction).

[0115] If the fluid medium is free air, the object to be tested is expediently placed directly on the measurement surface. If the fluid medium is in a measurement chamber, the object to be tested is placed on a measurement surface in the measurement chamber.

[0116] The method according to the invention, as suggested by its steps defined above, can be carried out using various devices, which are required to provide the functionality introduced above in the description of the method. At the same time, the device according to the invention requires configuration details that ensure that the method can be carried out. Moreover, an important component of the common inventive concept of the method and the device according to the invention is that the method according to the invention can be carried out by the device according to the invention.

[0117] The device can preferably be configured such that it is possible to form a number of capillary bridges, preferably arranged side by side (e.g. in a matrix arrangement) and the respective measuring elements corresponding to each of the capillary bridges are moved together or the volume of the capillary bridges is changed together (i.e. preferably all have the same length) via their own capillary channels (the method can be carried out so as to constitute an embodiment, i.e. this variant also falls within the scope of the invention (this variant is also the subject of the invention). An important feature is that since the capillary forces are measured for these capillary bridges together, it is usually possible to measure forces that are larger than for a single capillary bridge.

[0118] In this case, the determination of the interfacial area is naturally carried out for all capillary bridges (the change in the interfacial area being determined collectively), and the interfacial area determination device is suitable to do so.

[0119] In the following, the measurement results for both hydrophilic and hydrophobic cases are explained with reference to Figures 4A and 4B.

[0120] The measurements included below were performed in the arrangement shown in Figure 2 and according to the measurement process described in connection with the figure. The circled measurement points indicate the formation of a capillary bridge (i.e. a capillary bridge is established at the circled position, the bridge is first compressed and then stretched according to the arrows). This is considered as the zero point of the displacement scale (range) (see the zero point of the displacement axis in Figures 4A-4B). Further approximation of the solid surfaces to each other is indicated as a negative displacement. The arrows in Figures 4A-4B indicate the direction of the process.

[0121] According to the commonly applied convention mentioned above, the sign of the attractive capillary force is positive, i.e. it is considered positive if it "tries" to bring, for example, solid surfaces together [EJ De Souza et al., Effect of Contact Angle Hysteresis on the Measurement of Capillary Forces, Langmuir 24, pp. 1391-1396 (2008)]. This convention will be followed below.

[0122] A typical force-displacement curve measured on a hydrophilic surface (tested solid surface / tested surface material is SiO2) is shown in FIG. 4A. The measurement liquid was ultrapure water with a volume of 1.5 μl. The preferred applicable volume range of the capillary bridge is also influenced by the interfacial tensions of the liquid and fluid media, as well as the differential values ​​of their densities, in various embodiments. Measured forces and images of the liquid bridge were recorded every 5 seconds (i.e. more frequently than specified above in connection with FIGS. 2-3).

[0123] The capillary force measured in Fig. 4A remains in the positive force region until the end, i.e. the liquid bridge tries to bring the bounding solid surfaces closer together. During the approximation phase (extending from the circle towards larger negative values), (negative) mechanical work is performed by the system, which can be calculated by integrating the force-displacement curve recorded during the approximation phase (see equation (2)). This work is expended on the (energetically favorable) decrease of the water-air interfacial area (ΔA is negative) and on the (also energetically favorable) increase of the SiO2-water interfacial area (ΔB is positive).

[0124] Higher capillary force values ​​are encountered in the separation phase (which is the part extending from the bend in the direction of positive displacement values, as indicated by the corresponding arrow). The reason for this is that it is more difficult (energetically less favorable) to separate the water from the SiO2 surface compared to the magnitude of the driving force after the wetting process (this phenomenon is also evident in higher advancing and lower receding contact angles). Therefore, the geometry of the capillary bridge and therefore the dimensions (and their changes) of the interfacial area are different in the approximation and separation phases. In the separation phase, work (with positive sign) is performed on the system, in the process increasing the water-air interfacial area (which is energetically unfavorable, ΔA is positive) and decreasing the SiO2-water interfacial area (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 measuring liquid was ultrapure water with a volume of 1.8 μl, and again the measured force values ​​and images of the liquid bridge were recorded every 5 seconds (following the explanation above, this measurement was also performed applying the arrangement shown in Figure 2).

[0126] During the approximation phase (also extending from the circle in the direction of more negative displacement values), the initially positive (contractile) capillary forces change sign and, in the negative force range, attempt to move the solid surfaces further away from each other. In this range, work is performed on the system, i.e., the value of the integral calculated for the entire approximation phase increases, since the value of the integral is positive (both force and displacement are negative). Similarly, at the beginning of the separation phase, work is performed by the system, giving a negative-signed contribution to the equation (force is negative, but displacement is positive due to separation).

[0127] The method and device according to the invention are therefore directed to determining the work of adhesion, which is an indicator of the liquid-solid interface (without measuring the contact angle). The device can therefore be preferably operated and the method can be carried out such that a cylindrically symmetric capillary bridge is formed from the liquid in the surrounding fluid medium between the circular solid surface and the solid surface to be tested, with the contact line attaching (pinning) to the edge of the circular solid surface. The capillary force is measured while changing the length or volume of the capillary bridge. By processing the image of the capillary bridge, the change in size of each interfacial area resulting from the change in length or volume of the capillary bridge is determined. The liquid-solid work of adhesion 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 size of the interfacial area, and from the change in the size of the interfacial area, provided that the liquid-fluid interfacial tension is known, without determining the contact angle of the liquid forming on the solid surface to be tested. Furthermore, based on the determined work of adhesion, the value of the contact angle can be determined by calculation (from (1) expressing the angle) without measurement.

[0128] In the following, a distinction is provided from the prior art approaches referenced at the beginning.

[0129] A common feature of the approaches according to JP2011191277A, EP3571483A1 and JP2004144573 is that although the forces associated with liquid-solid adhesion are determined, they are unable to determine the change in the size of the interfacial area. A common drawback of these approaches stems from this: the solid-liquid adhesion work cannot be determined applying these methods, i.e. the adhesive properties of various solid-liquid material pairs can only be compared by carrying out measurements with identical parameters and applying the same arrangement with a given geometry of a particular device.

[0130] In contrast to the technical 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 work done by or on the system and the change in the interfacial area are not determined and no determination of the adhesion work independent of the contact angle is disclosed, in the present invention the work done by or against the capillary forces and the change in the size of the interfacial area are determined on the basis of suitable measurement quantities (preferably by applying an integrator, the use of an integrator such as the method according to the invention on the basis of integral quantities, see also below in this connection, but which is not included in the technical article), and the liquid-solid adhesion work is also determined in a highly preferred manner independent of the contact angle.

[0131] According to the present invention, the inventors have realized that a method for determining the liquid-solid adhesion work can be constructed in a very favorable manner based on observing the changes in the capillary bridge, and the liquid-solid adhesion work is determined from the quantities measured in the process. In the process of the method, the contact angles are not utilized (they are not measured), instead the work done by or against the capillary forces is measured in addition to the changes in the respective interfacial areas, and the liquid-solid adhesion work is determined on the basis of these measured quantities.

[0132] Therefore, the inventors have come to the realization that instead of an approach based on instantaneous values ​​(i.e. for contact angles with uncertainties for determining the work according to the introduction), the determination of the liquid-solid adhesion work should be based on the measurement of integral quantities (in this way the adhesion work can be obtained without utilizing the value of the contact angle, although in a preferred manner the contact angle can also be calculated therefrom afterwards). The inventive approach based on integral quantities also has the advantage that the integral quantities can usually be measured with higher accuracy, since uncertainties and measurement errors with zero mean value (noise) are integrated in the process. Thus, in summary, the inventors have realized that in order to determine the liquid-solid adhesion work, it is necessary to apply a measurement method different from the prior art approach and to measure another parameter.

[0133] Writing the above in a slightly different way, one can say that according to the invention, changes are investigated in the process (investigating the balance of the work done, i.e. establishing what is spent on the total mechanical work corresponding to the cylindrically symmetrical retention modification (correction) of the capillary bridge and, as a result, how the interfacial area of ​​the capillary bridge changes), i.e. the measurement points are investigated in particular in relation to each other. Thus, we preferably apply an integrator, taking into account changes related to the interfacial areas, such as the interfacial area constituted between the capillary bridge and the surrounding fluid and the interfacial area between the capillary bridge and the surface to be tested (in this connection, reference is made to the explanations related to the investigated sections and the rules of thumb applicable therein).

[0134] In relation to the technical article, it should also be noted that, as supported by the formulas of the present application (see in particular formula (2)), the value of the capillary force (called "adhesion force" in the technical article in certain cases) only partially depends on the interaction between the liquid and the solid surface being tested. Its value is also determined by the size of the interfacial area of ​​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 of this, the quantity obtained by integrating the capillary force over the 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 interfacial area.

[0135] In contrast to the disclosure of US Pat. No. 6,537,499 B1, i.e. studying the adhesion of molecules bound to a surface, in the present invention a cylindrically symmetrical retention correction is investigated, which is carried out on the liquid-capillary bridge. In the context of the present invention, the liquid-solid adhesion work can be determined in both directions, i.e. during the "increase" and "decrease" of the capillary bridge (in both the forward and backward situations), which, on the one hand, orders the concept of adhesion work to the difference between the contributions resulting from the movement in both directions, and on the other hand, differs from the documented quantity, since during the two processes the pillars that push the molecules downward undergo elastic deformations, 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 specifically avoided (in the present invention, either the forward or backward situations are investigated, and in addition to compression, turns from the forward to the backward situations are also avoided in the method according to the present invention, and integration is not usually carried out for that, see the explanation of the rule of thumb above).

[0136] Therefore, in the present invention, the adhesion work is the solid-liquid adhesion work, which can be determined only with the knowledge of the mechanical work performed in the process of cylindrically symmetric holding modification of the capillary bridge, the liquid-solid interfacial tension, and the change in the size of the interfacial area. Therefore, US Patent No. 6,537,499 B1 does not disclose such a method for determining the liquid-solid adhesion work similar to the present invention.

[0137] In the case of JP 2013174478A and CN 2968623 mentioned at the beginning, besides the capillary liquid introduction (wherein the introduction of a specific fixed amount of liquid is mentioned), the volume change of the capillary bridge is not investigated, and the liquid-solid adhesion work is not determined according to the process of the present invention based on the change in the interfacial area.

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

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

[0140] In order to characterize the present invention, the following points are described to define further embodiments. Paragraph 1 below should be interpreted as including further features of the present invention not mentioned therein, but the specific features given in paragraph 1 can be made to correspond to specific features of the present invention, and optional features also appear. Further subpoints add other optional features to the embodiments according to the cross-references between paragraphs. 1. An apparatus for determining solid-liquid adhesion work without contact angle measurement, comprising a circular solid surface 1, a force measuring device 2, a linear mover 3, a solid surface to be tested 4, 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 device 2 is integrated over the change in length of the capillary bridge 9 by the integrator unit 10, and the size of the interfacial area of ​​the capillary bridge 9 is calculated by the integrator unit 10 based on an image of the camera 8. 2. An apparatus for determining the solid-liquid adhesion work without contact angle measurement, comprising (optionally consisting of) a circular solid surface 1 forming a base plate of a capillary 11, a force measuring device 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, wherein the capillary force measured by the force measuring device 2 is integrated over the change in volume of the capillary bridge 9 by the integrator unit 10 and the size of the interfacial area of ​​the capillary bridge 9 is calculated by the integrator unit 10 based on an image of the camera 8. 3. The apparatus according to point 1 or 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. An apparatus as described in point 1 or point 2, in which the meniscus of the liquid adheres (pins) to the edge of the circular solid surface 1. 6. An apparatus according to point 1 or point 2, in which the circular solid surface 1, the solid surface to be tested 4 and the capillary bridge 9 are arranged in a common sample chamber 5. 7. An apparatus according to point 6, in which the fluid medium 6 filling the sample chamber 5 is a vapor space substantially saturated with liquid. 8. An apparatus according to point 6, in which the fluid medium 6 forming the environment of the capillary bridge 9 in the sample chamber 5 is a medium in the liquid state that is immiscible with liquids. 9. A method for determining the liquid-solid work of adhesion based on varying the length of a cylindrically symmetric capillary bridge 9 formed from a liquid to a fluid medium 6 between a circular solid surface 1 and a solid surface 4 to be tested and measuring the capillary force, wherein in the course of varying 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 interfacial area and the change in the size of the interfacial area between the liquid and the solid surface 4 to be tested are determined, and the liquid-solid work of adhesion is calculated based thereon. 10. A method for determining the liquid-solid work of adhesion based on measuring the capillary force of a cylindrically symmetric capillary bridge 9 formed from a liquid to a fluid medium 6 between a circular solid surface 1 and a solid surface 4 to be tested, wherein the volume of the capillary bridge 9 is changed and in the course 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 interfacial area and the change in the interfacial area between the liquid and the solid surface 4 to be tested are determined, and the liquid-solid work of adhesion is calculated based on these. 11. The method according to point 9 or 10, in which the material of the circular solid surface 1 is glass. 12. The method according to point 9 or 10, wherein the material of the circular solid surface 1 is platinum. 13. The method according to point 9 or 10, in which the meniscus of the liquid adheres (pins) to the edge of the circular solid surface 1. 14. The method according to point 9 or 10, wherein the contact angle occurring at the phase boundary of the liquid, the fluid medium 6 and the solid surface 4 to be tested is calculated from the liquid-solid work of adhesion. 15. The method according to point 9 or 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 an image of the capillary bridge 9. 16. The method according to point 10, in which 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 10, in which the circular solid surface 1, the solid surface to be tested 4 and the capillary bridge 9 are arranged 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 vapor space nearly saturated with liquid. 19. The method according to point 17, in which the fluid medium 6 forming the environment of the capillary bridge 9 in the sample chamber 5 is a medium in the liquid state that is immiscible with liquids. 20. The method according to point 19, in which a fluid medium 6 in a liquid state that is immiscible with the liquid is filled into the sample chamber 5 after the capillary bridge 9 has been formed. 21. The method according to point 19, in which the fluid medium 6 in a liquid state that is immiscible with the liquid is filled in the sample chamber 5 in such a state of the capillary bridge 9 that it has a minimum or a maximum volume.

[0141] The present invention is naturally not limited to the preferred embodiments described in detail above, but is capable of further variations, modifications and developments within the scope of protection determined by the claims.

Claims

1. A method for determining the liquid-solid adhesion work, in the course of which, in relation to a liquid cylindrically symmetric capillary bridge (9) formed in a fluid medium (6) between an end with a peripheral circular edge of a measuring element and a surface (4) to be tested of a solid to be tested, the method comprising the steps of: - by performing a cylindrically symmetrical preservation correction on said cylindrically symmetrical capillary bridge (9) starting from an initial state and ending in a final state, determining (S110a) a first interfacial area change of a first interfacial area of ​​the capillary bridge (9) and the fluid medium (6) and a second interfacial area change of a second interfacial area of ​​the capillary bridge (9) and the surface to be tested (4) between the initial state and a final state; and determining (S100) during the cylindrically symmetrical retention correction at least one displacement value of the work-related displacement corresponding to the cylindrically symmetrical retention correction and therefore a respective force value of the capillary force corresponding to the capillary bridge (9), thereby determining (S110b) a total mechanical work corresponding to the capillary force for the cylindrically symmetrical retention correction based on the at least one displacement value determined during the cylindrically symmetrical retention correction and the force value assigned to each of them; for said cylindrical symmetry preservation correction, based on said first interfacial area change, said second interfacial area change, said total mechanical work, and the liquid-fluid interfacial tension of said capillary bridge (9) and said fluid medium (6), the solid-liquid interfacial tension of the surface to be tested (4) and the capillary bridge (9), and the solid-fluid interfacial tension of the surface to be tested (4) and the fluid medium (6) determining a first difference value (S120); - determining (S130) the liquid-solid work of adhesion, which corresponds to the cylindrical symmetry retention correction and is indicative of the capillary bridge (9) and the surface (4) to be tested, by subtracting the first difference value from the liquid-fluid interfacial tension; The method by which this is performed.

2. formula [0010] and calculating the first difference value according to -γ ＳＬ is the solid-liquid interfacial tension, and γ ＳＦ is the solid-fluid interfacial tension, － [0025] is the total mechanical work, -γ ＬＦ is the liquid-fluid interfacial tension, -ΔA is the first interfacial area change and ΔB is the second interfacial area change; The method of claim 1.

3. 3. The method according to claim 1 or 2, characterized in that a measuring element is applied having a capillary conducting channel (14) opening at its end having a peripheral circular edge, the end of the capillary conducting channel (14) opposite the end having a peripheral circular edge is connected to a liquid feeder (12), the cylindrically symmetrical holding correction is performed on the cylindrically symmetrical capillary bridge (9) by passing the liquid through the capillary conducting 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 conducting channel (14).

4. 1. An apparatus for determining liquid-solid work of adhesion, comprising: a measuring element having an end with a peripheral circular edge for placing said end with a peripheral circular edge in a fluid medium (6) together with a solid to be tested having a surface to be tested (4), said measuring element and said surface to be tested (4) being placed relative to each other in such a way that, when using said device, a liquid cylindrically symmetrical capillary bridge (9) can be formed between said end with a peripheral circular edge and said surface to be tested (4), said measuring element having a capillary conducting channel (14) opening into said end with a peripheral circular edge; a liquid feeder (12) connected to said end of said capillary conducting channel (14) opposite said end having a peripheral circular edge; an interfacial area determination device adapted to determine a first interfacial area of ​​said capillary bridge (9) and said fluid medium (6) and a second interfacial area of ​​said capillary bridge (9) and said surface to be tested (4); Equipped with The liquid feeder (12) is adapted to perform a cylindrically symmetrical retention correction on the cylindrically symmetrical capillary bridge (9) by forcing the liquid through the capillary conducting channel (14), the device further comprising: a displacement determination unit adapted to determine, in the course of said cylindrically symmetrical retention correction, at least one displacement value of said work-related displacement of said liquid in said capillary conducting channel (14) which corresponds to said cylindrically symmetrical retention correction; a force measuring device (2) adapted to determine a force value of a capillary force corresponding to said capillary bridge (9) for said at least one displacement value; an integrator unit (10) adapted to determine a total mechanical work corresponding to the capillary forces for the cylindrically symmetrical retention correction based on the at least one displacement value determined by the displacement determination unit in the course of the cylindrically symmetrical retention correction and on the force value assigned to each of them; for said cylindrical symmetry preserving correction, based on a first interfacial area change of the first interfacial area and a second interfacial area change of the second interfacial area determined by the interfacial area determination device between an initial state and a final state of the cylindrically symmetric capillary bridge (9), to the total mechanical work and to the liquid-fluid interfacial tension of the capillary bridge (9) and the fluid medium (6), the solid-liquid interfacial tension of the surface to be tested (4) and the capillary bridge (9), and the solid-fluid interfacial tension of the surface to be tested (4) and the fluid medium (6); determining a first difference value of a work determination unit adapted to determine a liquid-solid adhesion work corresponding to said cylindrically symmetric retention correction and being indicative of said capillary bridge (9) and said surface to be tested (4) by subtracting said first difference value from said liquid-fluid interfacial tension; An apparatus comprising:

5. formula [0030] The first difference value is calculated according to -γ ＳＬ is the solid-liquid interfacial tension, and γ ＳＦ is the solid-fluid interfacial tension, － [0045] is the total mechanical work, -γ ＬＦ is the liquid-fluid interfacial tension, -ΔA is the first interfacial area change and ΔB is the second interfacial area change; 5. The apparatus of claim 4.

6. 6. Apparatus according to claim 4 or 5, characterized in that the force measuring device (2) is a gravimetric scale having a measuring surface arranged opposite the end of the measuring element having a peripheral circular edge, the measuring surface being adapted to position the solid body to be tested such that the surface to be tested (4) faces the end having a peripheral circular edge.

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