Method for measuring at least one physical interfacial property

Abstract

The invention relates to a method for determining (136) a value of a physical interfacial property using a digital model (I), in which: - z is a height relative to the apex of the droplet, - r is the radius of the droplet at the height z, - R0 is the radius of curvature of the droplet at the apex,- V is the known volume of the droplet,- h is the height of the droplet,- r(h) is the radius wetted by the liquid, - g is the standard gravity, - ρ1 and ρ2 are, respectively, the density of the liquid and of the surrounding fluid.

Description

Method for measuring at least one interfacial physical property [1] The invention relates to a method and apparatus for measuring at least one interfacial physical property between a liquid droplet, a solid substrate, and a surrounding fluid. The invention also relates to an information recording medium for implementing the above measurement method. [2] Typically the measured interfacial physical property is one of the following interfacial physical properties: - an interfacial tension between a droplet of liquid and a surrounding fluid, - an interfacial tension between a liquid droplet and a solid substrate, - an interfacial tension between a solid substrate and a surrounding fluid, and - a line voltage at the point of contact between a liquid droplet, a surrounding fluid, and a solid substrate, [3] KRÜSS-SCIENTIFIC® markets devices for measuring such interfacial physical properties. These devices deposit a drop of the liquid onto the substrate face immersed in the surrounding fluid. A camera then generates an image of the drop's contour. An image analysis module then automatically determines the geometric characteristics of the drop's contour based on the image processing. Finally, a numerical model that links the measured geometric characteristics to the values ​​of the interfacial physical properties is used to determine the values ​​of these interfacial physical properties from the measured geometric characteristics. [4] Very often, one of the measured geometric characteristics of the droplet is its contact angle with the substrate. The numerical models used in such devices are well-known models such as the Young-Laplace equation. [5] These devices function correctly. However, in some cases, the value determined for the interfacial physical property is not accurate. For example, this The problem arises in the case of hydrophobic or super-hydrophobic liquids or oleophobic liquids or in other special situations. [6] The state of the art is also known from: - WO2020 / 181932A1, - MEDALE Marc et Al: “Sessile drops in weightlessness: an ideal playround for challenging Youg's equation”, NPJ Microgravity, Vol. 7, n°1, 2021-08-04, - YILDIZ B. et Al: “Shape analysis of a sessile drop on a flat solid surface”, The Journal of Adhesion, vol. 95, n°10, pages 929-942, 2018-04-19. [7] The invention aims to solve this problem by proposing a method and apparatus for measuring a more precise interfacial physical property. [8] It therefore relates to a method for measuring an interfacial physical property in accordance with claim 1. [9] It also has as its object a recording medium for information for the implementation of the above measurement process.

[0010] Finally, it also relates to a measuring device for an interfacial physical property in accordance with claim 11.

[0011] The invention will be better understood upon reading the following description, given solely by way of non-limiting example and made with reference to the drawings in which: - Figure 1 is a schematic illustration of a device for measuring interfacial physical properties, - Figure 2 is a schematic illustration of the right-hand side of the outline of a droplet deposited on a substrate, and - Figure 3 is a flowchart of a method for measuring interfacial physical properties using the apparatus in Figure 1.

[0012] In these figures, the same references are used to designate the same elements. In the remainder of this description, the characteristics and functions well known to a person skilled in the art are not described in detail.

[0013] In this description, a detailed example of an embodiment is first described in Chapter I with reference to the figures. Then, in Chapter II, variations of this embodiment are presented. Finally, the advantages of the different embodiments are presented in Chapter III.

[0014] Chapter I: Example of a method of implementation

[0015] Figure 1 represents a device 2 for measuring interfacial physical properties between a liquid droplet, a solid substrate 4 and a surrounding fluid 6.

[0016] In this embodiment, fluid 6 is a gas. More precisely, fluid 6 is ambient air. The liquid can be any liquid. Similarly, substrate 4 can be any solid substrate. In particular, the substrate can be a hydrophobic or superhydrophobic substrate when the liquid is water, or an oleophobic substrate when the liquid is oil.

[0017] Here, device 2 is placed in a chamber where the internal temperature is maintained at a set temperature and the atmospheric pressure is maintained at a constant value. For example, the set temperature is 20°C and the constant pressure is 1 atm (= 1013.25 hPa). Thus, the ambient temperature and pressure at which the interfacial physical properties are measured are known.

[0018] The substrate 4 is in the form of a plate having a horizontal upper face 8 and, on the opposite side, a lower face 10. Here, the lower face is also a horizontal face. Since faces 8 and 10 are horizontal, they each extend in a plane perpendicular to the gravitational field whose direction and magnitude are represented in Figure 1 by a vector g, hereafter referred to as the "gravity vector".

[0019] Subsequently, terms such as "upper" and "lower" are defined with respect to the direction of the gravity vector g.

[0020] In this embodiment, the substrate 4 also has a hole 12 to receive the end of a needle or nozzle. The hole 12 opens on one side onto face 8 and, on the opposite side, onto face 10. It therefore passes completely through the thickness of the substrate 4. Here, the axis 16 of the hole 12 is vertical.

[0021] In Figure 1, substrate 4 is shown in vertical section passing through axis 16 of hole 12.

[0022] Figure 1 also shows the cross-section of a droplet 14 of the liquid formed on face 8. The droplet 14 is centered on the vertical axis 16. Axis 16 is an axis of rotational symmetry for the droplet 14, and the droplet 14 exhibits an infinite number of different rotational symmetries about this axis. Such a droplet 14, deposited on a horizontal face of a substrate, is known as a "droplet." sessile. In this case, the vector e z directed vertically from the apex 17 of the drop 14 towards the substrate 4 is parallel and in the same direction as the gravity vector g.

[0023] In this text, "interfacial physical property" refers to one of the interfacial physical properties chosen from the group constituted: - of an interfacial tension Oi2 between the liquid droplet and the fluid 6, - of an interfacial tension o Si between the liquid droplet and the substrate 4, - of an interfacial tension o S 2 between the solid substrate 4 and the fluid 6, and - of a line voltage o S i2 at the level of a contact line between the liquid droplet, the fluid 6 and the substrate 4.

[0024] It is worth recalling that interfacial tension between two bodies characterizes the excess free energy between them. Interfacial tension is expressed in Joules per square meter. It is also known as surface tension or surface energy, and by the English terms surface tension, surface energy, or surface density of free energy.

[0025] The line voltage at the contact line between three bodies—here, the liquid droplet, the substrate 4, and the fluid 6—characterizes the excess free energy at the interface between these three bodies. Line voltage is expressed in joules per meter. In English, line voltage is known as "line tension" or "line density of free energy."

[0026] The contact line between the liquid drop, the substrate 4 and the fluid 6 is represented, in the cross-section of the drop 14, by two points 18 and 20, diametrically opposite with respect to the axis 16.

[0027] Subsequently, device 2 is described in the specific case where it measures the four interfacial physical properties Oi2, o S i, o S 2 and o S i2.

[0028] For this purpose, device 2 includes: - a syringe 30 capable of injecting a known volume of liquid through hole 12 to form droplet 14, - a device 32 for measuring the geometric characteristics of droplet 14, and - an electronic calculator 34 configured to determine the values ​​of the four properties Oi2, o S i, o S 2 and o S i2 from the geometric characteristics measured by device 32.

[0029] Syringe 30 contains: - a reservoir 40 containing the liquid to be ejected to form droplet 14, - a needle or nozzle 42 whose upper end is fluidly connected to the lower end of the hole 12 and whose lower end is fluidly connected to the reservoir 40, - a piston 44 capable of being pushed into the reservoir 40 to eject a predetermined volume of liquid through the hole 12, and - an electrically controllable actuator 46 capable of moving the piston 44.

[0030] Here, the volume of tank 40 is greater than the volume Vma x of the largest drop 14 to be formed on face 8 of the substrate 4.

[0031] The piston 44 is movable in translation along the axis 16. When it moves upwards, liquid is ejected through the hole 12, which increases the volume of the drop 14. Conversely, when the piston 44 moves downwards, liquid is drawn in through the hole 12, which decreases the volume of the drop 14.

[0032] Device 32 allows in particular to measure the radius r of drop 14 at different heights z.

[0033] Figure 2 shows a coordinate system R used here to measure the radius r and the height z of a point M on the contour of droplet 14. In Figure 2, only the right-hand side of droplet 14 is shown. The origin O of the coordinate system R coincides with the apex 17 of droplet 14. The coordinate system R has an axis R z vertical and an axis R rhorizontal lines intersecting at right angles at the origin O. The axis R z is coincident with the axis of revolution symmetry of droplet 14. The R axis z is oriented in the same direction as the vector e z The R axis was defined previously. r is oriented in the same direction as that of a horizontal vector e r The vector e r is directed from the origin O to the right in Figure 2. In this frame R, the coordinates of a point M on the contour of drop 14 are (r; z), where r is the radius of drop 14 at height z and z is the height of point M relative to the origin O.

[0034] Subsequently, the symbol "h" denotes the height of droplet 14 along axis R z and the symbol r(h) denotes the radius of the drop 14 at the level of the face 8 of the substrate 4. Thus the coordinates of the point 20 of contact between the drop 14, the substrate 4 and the fluid 6 are (r(h); h).

[0035] Figure 2 also represents angle 0 m of macroscopic contact. The 9m angle is defined as the angle between: - face 8, and - the vector t m tangent to the contour of drop 14 at point 20.

[0036] Angle 9 m is called "macroscopic" because it is measured on a macroscopic scale.

[0037] To obtain the coordinates in the frame R of several points M on the contour of the droplet 14, the device 32 generates an image of the cross-section of the droplet 14 and then measures the coordinates of several points on the contour of the droplet by image analysis. In this respect, the device 32 is similar, for example, to that described in application EP2899529A1. Thus, only the features of the device 32 necessary to understand the invention are presented hereafter.

[0038] Typically, device 32 includes: - a light source 50 that illuminates the droplet 14 in a direction parallel to the vector e r , - a camera 52 which generates an image of the contour of droplet 14, - an image acquisition module 54 for the image generated by the camera 52 to obtain a digital image, and - a 56 image analysis module that processes the acquired image to extract the desired geometric characteristics of the droplet.

[0039] Here, the light source 50 and the camera 52 are located diametrically opposite each other with respect to axis 16. Thus, the light source 50 casts a shadow on the lens of camera 52 that corresponds to the orthogonal projection of droplet 14 onto this lens. Camera 52 generates an image of this shadow. The contour of this shadow in this image is identical to the contour of droplet 14. The entire contour of the droplet is contained within the generated image.

[0040] Module 54 acquires the image generated by camera 52 and provides image analysis module 56 with a digital image of the outline of droplet 14. Typically, in this digital image, droplet 14 is distinguished from the background by its color. For example, in this digital image, pixels corresponding to parts of droplet 14 are dark, such as black or gray, while pixels corresponding to the background are a lighter color, such as white or light gray.

[0041] Module 56 processes the acquired digital image to extract geometric features of droplet 14. Here, module 56 is processing this image The digital process extracts the coordinates, expressed in the coordinate system R, of several points belonging to the contour of droplet 14. In this digital image, the coordinates of these points correspond to the pixels located at the boundary between the dark color of droplet 14 and the light color of the image background. Thus, after this extraction, module 56 has the coordinates, in the coordinate system R, of a list of points on the contour of droplet 14. The number of points in this list is typically greater than three and, preferably, greater than ten, twenty, or fifty.

[0042] In this embodiment, to increase measurement accuracy and facilitate the calculation of first and second derivatives from the coordinates of the points in this list, module 56 establishes the equation of a curve that best approximates the contour of droplet 14. To achieve this, module 56 implements, for example, curve fitting processes. During the implementation of this curve fitting, curve smoothing operations are also performed to reduce or eliminate any singularities or irregularities in the established curve.

[0043] In this embodiment, the image acquisition module 54 and the image analysis module 56 are software modules executed by the electronic computer 34.

[0044] Calculator 34 is designed to fully automate the measurement process shown in Figure 3. To this end, it includes, in particular: - a programmable 60 microprocessor, - a memory 62 which contains the instructions executed by the microprocessor 60, and - a human-machine interface 64.

[0045] Memory 62 contains, in particular, all the instructions necessary to execute the process shown in Figure 3. To this end, it therefore includes, among other things: - instructions for a 70 module for controlling syringe 30, - the instructions for a control module 72 for the measuring device 32, - the instructions of a parameter acquisition module 74, and - instructions for a module 76 for determining the values ​​of interfacial physical properties.

[0046] In addition, here, memory 62 also contains the instructions from modules 54 and 56 described previously.

[0047] The calculator 34 is connected to the syringe 30 and the camera 52. More specifically, the module 70 controls the actuator 46 of the syringe 30 to eject and, alternately, aspirate a predetermined quantity of the liquid.

[0048] Module 72 allows the generation of an image by camera 52, its acquisition by module 54 and then its analysis by module 56.

[0049] Module 74 allows the acquisition, via the human-machine interface 64, of the parameter values ​​necessary for determining the values ​​of interfacial physical properties. Here, module 74 allows the acquisition of: - the density pi of the liquid, - the density p2 of the fluid 6, and - the magnitude of the gravity vector g.

[0050] Furthermore, module 74 allows for the acquisition of the ambient temperature and pressure at which the interfacial physical properties are measured. Indeed, the values ​​of these interfacial physical properties vary with ambient temperature and, to a lesser extent, with ambient pressure. Therefore, when determining the values ​​of these interfacial physical properties, it is also important to specify the temperature and pressure conditions under which these values ​​were identified.

[0051] The human-machine interface 64 is, for example, formed of a screen 80 and a keyboard 82. The screen 80 allows the values ​​determined for the interfacial physical properties to be displayed.

[0052] The method for measuring the properties Oi2, o S i, o S 2 and o S i2 using apparatus 2 will now be described with reference to the process in Figure 3.

[0053] During step 96, module 74 acquires, for example via the human-machine interface 64, the ambient temperature and ambient pressure values ​​in which the measurements of properties Oi2, o S i, o S 2 and o S i2 will be performed. During step 96, the densities pi and p2, respectively, of the liquid and fluid 6 are also acquired. The magnitude of the gravity vector g is also acquired. This latter value corresponds to the magnitude of the vector g at the level of apparatus 2.

[0054] Next, the process continues with a phase 98 of establishing the values ​​of thresholds Sic and Si d For example, in step 100, module 70 commands syringe 30 to form a first series of drops on face 8. increasing volumes from a minimum volume Vmin to the maximum volume V max. Typically, the volume Vmin is less than V ma x / 10 and, preferably, less than V max / 100. Here, the volumes Vmin and V max are the volumes, respectively, of the smallest drop and the largest drop that syringe 30 can form on face 8. Typically, the volume Vmin is less than 10 pL or 5 pL or 1 pL.

[0055] For this, during an operation 102, the syringe 30 is first controlled by the module 70 to form a drop 14 of volume equal to Vmin.

[0056] Then, during an operation 104, the module 72 commands the camera 52 to generate an image of the contour of the drop 14 whose volume is equal to Vmin.

[0057] During operation 106, once the image is generated, it is acquired by the acquisition module 54.

[0058] During operation 110, module 56 processes the image acquired during operation 106. More precisely, as previously stated, module 56 first measures the coordinates of several points belonging to the contour of droplet 14. In particular, and preferably, the coordinates of point 20 are measured. Then, from the measured coordinates of these points, during operation 110, module 56 establishes the equation of a curve that best approximates the contour of this droplet.

[0059] During operation 112, the module 56 determines the value of angle 0 m of macroscopic contact. For example, to do this, from the equation of the curve established during operation 110, the coordinates of the vector t m tangents to this curve at point 20 are calculated. The value of angle 0 m for the volume Vmin, is then calculated from the coordinates of the vectors t m summer r .

[0060] Next, operations 102 to 112 are repeated for a larger volume drop. Here, during the repetition of operation 102, the actuator 46 is simply commanded to inject an additional quantity Q s a predetermined amount of liquid is added to the previously formed droplet 14 to obtain a new droplet 14 of greater volume. Thus, during this first part of step 100, a first series of drops of increasing volumes is formed on the face 8.

[0061] Here, the quantity Q s The volume injected during each iteration of operation 102 is, for example, the same each time. Thus, the volume of drop 14 is incremented at regular intervals from volume Vmin to volume V max The additional quantity Q s is typically less than (V max - V m in) / 10 and, preferably, less than (V max - V m in) / 100.

[0062] Preferably, once the volume V ma When x is reached, operations 102 to 112 are repeated, this time decrementing the volume of drop 14 at each iteration until a drop 14 with a volume equal to Vmin is returned. Thus, during this second part of step 100, a second sequence of drops with decreasing volumes is formed on face 8. During this second part, the volume of the drop is, for example, decremented with the same regular increment as that used to form the first sequence of drops.

[0063] After the first and second sets of drops have been deposited and their geometric characteristics measured, step 100 is completed and step 120 begins, during which the calculator 34 establishes the threshold values ​​Sic and Sii. d Each of the Sic and Si thresholds d corresponds to the threshold beyond which the angle 9 mThe macroscopic contact distance between droplet 14 and substrate 4 no longer varies with the volume of droplet 14. The Sic threshold is only measured from the sequence of increasing droplets, while the Si threshold d is only measured from the sequence of decreasing drops.

[0064] For example, calculator 34 identifies, in the first series of drops of increasing volumes, the volume Vi m ,c of the drop from which the angle 0 m does not vary with the volume of this drop. Then, calculator 34 records, in the second series of drops of decreasing volumes, the volume Vi m , d from which angle 0 m no longer varies according to the volume of the drop. The volumes Vi m ,c and Vi m , d The readings are generally different due to hysteresis phenomena. However, the volumes Vi m ,c and Vi m , dremain fairly close to each other because the amplitude of these hysteresis phenomena remains small compared to the values ​​of the volumes Vi m ,c and Vi m , d .

[0065] Then, during step 130, module 76 automatically selects four Vi volumes c , V 2c , V 3c and V 4c of drops in the first series of drops of increasing volumes to obtain a first series of four drops of increasing volumes. The volumes Vi c , V 2c , V 3c and V 4c are ranked in ascending order. The Life volume is below the Sic threshold and, preferably, below Sic / 2. The three volumes V 2c , V 3c and V 4c are greater than the Sic threshold and, preferably, greater than 1.5*Si cwhere the symbol "*" denotes the arithmetic multiplication operation. Preferably, there is a ratio greater than or equal to two between any two consecutive volumes of this first series of drops of increasing volumes. Thus, typically, the volume V 2c is at least twice the volume Vi c .

[0066] Next, in step 132, the coordinates of different points on the contour of each of the volume drops Vi c to V 4c are measured. In particular, during this step 132, the radius of each of the drops of volume Vi c to V 4c is measured for the height z=h. Since these measurements were already performed for the same drops during operation 110, step 132 in this case is reduced to selecting the coordinates already measured during operation 110 for each of these drops with volumes Vi c to V 4c .

[0067] During step 134, for each of the drops of volume Vi c to V 4c Module 56 establishes the equation of the curve that best approximates the contour of this droplet. Here, since this has already been done in operation 110 for each of the drops of volume Vi c to V 4c This step involves selecting the four equations of the curves obtained from the volume drops Vi c to V 4c .

[0068] In step 136, module 76 determines the values ​​of the interfacial physical properties from the equations of the curves established in step 134. Thus, the values ​​of the interfacial physical properties are also determined from the coordinates of the points measured in step 132, since the equations of the curves were obtained from these measured coordinates.

[0069] To this end, module 76 uses a numerical model (1) that relates the coordinates (r; z) of a point M on the contour of a drop to the interfacial physical properties O12, Osi, Os2 and o S i2. This numerical model (1) is defined by the following system of equations: Or : - z is the height, relative to the apex 17 of the drop, at which point M of the interface between the drop and the surrounding fluid is located, - r is the radius of the droplet at height z in a plane parallel to the horizontal face 8, - z' is the first derivative of z with respect to r, - z" is the second derivative of z with respect to r, - Ro is the radius of curvature of the droplet at the apex 17 of the droplet, - V is the known volume of the droplet, - h is the height of the droplet along the R axis z , - r(h) is the radius wetted by the liquid, that is to say the radius of the drop at the level of the horizontal face 8, - the symbol "±" means equal to: - to the "+" sign when the drop has been obtained by decreasing its volume to volume V, and - to the sign "-" when the drop has been obtained by increasing its volume up to volume V.

[0070] In this first example, the symbol "±" is equivalent to the sign "-" when the drop is one of the drops in the first series of four drops. Conversely, the symbol "±" is equivalent to the sign "+" when the drop is one of the drops in the second series of four drops.

[0071] The model (1) is parameterized by the following known parameters which were defined previously: - the non-zero magnitude g of the gravitational field acting on the droplet during the execution of step 132, - the density pi of the liquid, - the density p2 of the fluid 6, - the known volume V of the droplet deposited on face 8, and - the wet radius r(h).

[0072] In this embodiment, the wetted radius r(h) is measured during step 132. Therefore, the square of the wetted radius, denoted r 2 (h) in model (1), is also known.

[0073] Model (1) comprises, in order: - a second-order differential equation, - two boundary conditions associated with the second-order differential equation, - a first and a second constraint equations in integral form. The condition z(0) = 0 means that the radius of the droplet at height z=0 is zero. The condition z'(0) = 0 means that the tangent to the apex of the droplet is horizontal. The second stress equation allows us to determine the height h of the droplet from its volume V. The first stress equation allows us to define the radius of curvature R. o depending on the known parameters, the height h and the values ​​of the interfacial physical properties Oi2, Osi, Os2 and o S i2 to be determined.

[0074] In this model (1), when the equation of the contour curve of a droplet is known, the integral of the second stress equation can be calculated. Therefore, since the volume V is known, the height h is also known as soon as the equation of the contour curve of the droplet is known. Then, when the height h and the equation of the contour curve of the droplet are known, the first stress equation allows us to express the radius R o based on the four interfacial physical properties Oi2, Osi, Os2 and o Si2. Thus, for each droplet whose contour equation is known, model (1) yields a system of equations in which the only unknowns are the values ​​of the four interfacial physical properties Oi2, Osi, Os2, and Osi2. Therefore, by selecting four dropslet whose contour equations are different, we obtain a final system of four systems of equations with four unknowns. This final system is automatically solved by module 76 to obtain, from the contours of four dropslet, a value for each of the interfacial physical properties Oi2, o S i, Os2 and o S i2.

[0075] Here, module 76 determines the values ​​of the Oi2 properties, o S i, Os2 and o S i2 from the equations of the contour curves of the four drops of volumes Vi c to V 4c .

[0076] More specifically, since volumes V 2c to V 4care greater than the Sic threshold, the last term of the first stress equation, which depends on the line voltage Osi2, can be neglected. Thus, for each of the drops of volume V 2c to V 4c , a system of equations is obtained in which the three unknowns are only the interfacial physical properties Oi2, o Si and o S 2. Module 76 first solves the intermediate system formed by these three systems of equations to determine initial values ​​of the three interfacial physical properties Oi2, o Si and o S 2. The first values ​​determined for each of the properties Oi2, o Si and o S 2 from drops of volume V 2c to V 4c are subsequently denoted Oi2, c , o S i, c , and o S 2, c .

[0077] Next, the model (1) and the equation of the contour of the volume droplet Vi care used to obtain a new system of equations. In this new system of equations, the unknowns Oi2, o Si and o S 2 are replaced by their respective values, Oi2, c , o S i, c , and o S 2, c This allows us to obtain a system of equations in of which the only remaining unknown, at this stage, is the line voltage cr S i2. Solving this system of equations then allows us to obtain the first value o S i2,c of the line voltage cr S i2.

[0078] Here, during step 138, steps 130 to 136 are repeated, but using the second sequence of drops with decreasing volumes instead of the first sequence of drops with increasing volumes. Thus, during this repetition of steps 130 to 136, the volumes Vi c , V 2c , V 3c and V 4c are replaced by volumes, respectively Vi d , V2d , V 3d and V 4d . The execution of step 138 allows us to determine, for each of the properties Oi2, o S i, o S 2 and o S i2, of the second values ​​denoted, respectively Oi2, d , o S i, d , o S 2,d and o S i2,d. These second values ​​Oi2, d , o S i, d , has S 2, d and o S i2, d are not necessarily the same as the first Oi2 values, c , o Si , c , Os2,c and o S i2, cFor a given interfacial physical property, the difference between these first and second values ​​represents the amplitude of the hysteresis phenomenon that exists between a series of drops of increasing volumes and a series of drops of decreasing volumes. Thus, step 138 also allows for the calculation of the hysteresis amplitude on the measured interfacial physical property values.

[0079] Chapter II: Variants:

[0080] Variations of the process:

[0081] The number of drops used to determine the values ​​of the interfacial physical properties Oi2, o Si , Os2 and o S i2, can be greater than four. For example, eight drops are used. In this case, for example, initial intermediate values ​​are determined for the properties Oi2, o Si , Os2 and o Si2 using the first four drops. Then, intermediate values ​​are determined for these same properties using the last four drops. Finally, the values ​​determined for the properties Oi2, o S i, o S 2 and o S i2 are the result of an arithmetic mean of the first and second intermediate values.

[0082] When the value of some of the interfacial physical properties is already known, the previously described method can be used to measure the other, unknown interfacial physical properties. The number of interfacial physical properties measured is then less than four. Therefore, in step 136, the values ​​of the interfacial physical properties that are already known are introduced into model (1) as known parameters. In this case, the The number of drops in the drop series used to determine the values ​​of unknown interfacial physical properties can be reduced. In an extreme case, the drop series used consists of only one drop. This latter case occurs, for example, when the only interfacial physical property to be measured is line voltage. S i2 while the interfacial tensions O12, Osi and o S Two are known.

[0083] Instead of being provided or measured, some of the parameters of model (1) can be considered unknowns, and their values ​​are then determined, along with the values ​​of the interfacial physical properties, in step 136. In this case, the greater the number of parameters of model (1) to be determined, the greater the number of drops to be used in order to have a number of droplet contour equations at least equal to the number of unknowns. This variant is advantageously used to determine the value of certain parameters that are more difficult to measure precisely, such as the parameter r(h).

[0084] The value of the line voltage o S i2 can also be determined solely from measurements taken on drops whose volume exceeds the threshold Sic or Sid. In this case, the accuracy of the line voltage value o SThe determined i2 value may be less accurate. Conversely, phase 98, which establishes the values ​​of the Sic and Sid thresholds, can be omitted.

[0085] Correspondingly, the values ​​of interfacial tensions can also be determined solely from the geometric characteristics of drops whose volume is less than the Sic or Si threshold d In this case, similarly to what was indicated in the previous paragraph, the accuracy of the determined interfacial tension values ​​may be lower. However, in return, phase 98 of establishing the Sic and Si threshold values d , can be omitted.

[0086] If it is not necessary to consider the influence of hysteresis on the values ​​of interfacial physical properties, then it is not necessary to use a series of drops with increasing volumes and a series of drops with decreasing volumes. For example, either only the series of drops with increasing volumes or only the series of drops with decreasing volumes is used to determine the values ​​of the interfacial physical properties. A series of drops formed by both increasing and decreasing their volumes in any temporal order can also be used.

[0087] When the values ​​of the thresholds Sic and Si dSince the values ​​of these thresholds are known in advance, step 98, which establishes their values, can be omitted. In this case, during step 132, series of drops of increasing and decreasing volumes are deposited, and their geometric characteristics are measured in a manner similar to that described in relation to step 98.

[0088] In another simplified embodiment, the thresholds Sic and Si d are considered to be equal. In this case, during phase 98, only the value of one of the thresholds Sic and Si d is established.

[0089] When device 2 is designed only for use on the Earth's surface and under conditions where it is stationary relative to the Earth's surface, the magnitude of the gravity vector g can be considered as a constant and pre-recorded in memory 62.

[0090] Device variants:

[0091] The device 2 can include several syringes 30 capable of operating in parallel. This allows for the formation of several drops on the face 8 in parallel. In such a case, the image generated by the camera 52 also contains several drops.

[0092] Other embodiments of the syringe 30 are possible. For example, the syringe described in application EP2899529A1 can be used instead of the syringe 30. In this case, the syringe needle is positioned above face 8, and the drop is deposited on face 8 rather than injected through substrate 4. In this case, substrate 4 does not need to have hole 12. However, the energy stored by the drop during its deposition on face 8 of substrate 4 may slightly deform drop 14 and thus slightly distort the measurements of the interfacial physical properties.

[0093] Alternatively, the droplet whose geometric characteristics are measured by device 32 is a pendant droplet, not a sessile droplet. To obtain a pendant droplet, the syringe 30 is, for example, positioned above the substrate 4. In this case, the droplet 14 is formed on face 10, rather than on face 8, of the substrate. The measurement procedure previously described for a sessile droplet applies identically to the case of a pendant droplet. Indeed, model (1) can also be used for a pendant droplet.

[0094] Other embodiments of the computer 34 are also possible. For example, alternatively, the computer 34 does not include the syringe 30 control module 70 or the camera 52 control module 72. In this case, these two control modules 70 and 72 are integrated, respectively, into the syringe 30 and the camera 52. To this end, the syringe 30 and the camera 52 each have their own microprocessor and memory to execute these modules. Therefore, these two modules are directly controlled by the user to obtain the different images of the drops. For example, the user directly provides the syringe 30 control module 70 with the different volumes of the drops to be formed on face 8. In response, module 70 commands the actuator 46 to form these different drops of varying volumes, one after the other.In parallel, each time a new droplet forms on face 8, camera 52 generates an image of that droplet and records it onto a digital storage medium, for example, a removable one. Once the various digital images needed to determine the interfacial physical properties have been generated and recorded on the storage medium, this medium is connected to the computer 34. The acquisition module 54 is then configured to acquire images of the droplets from this storage medium. The rest of the process is then identical to that described previously.

[0095] In another variant, the calculator 34 includes only one of the two control modules 70, 72.

[0096] Syringe 30 can have several pistons of different sizes so that, for a given stroke length, the volume of liquid displaced by one of these pistons is less than the volume of liquid displaced by the other pistons. Specifically, in this case, the syringe has a small piston that displaces a volume of liquid five to ten times smaller than the volume of liquid displaced by the other pistons for the same stroke length. The movement of this small piston, in addition to the movement of the other pistons, increases the accuracy of the volume of liquid ejected from hole 12.

[0097] Other embodiments of the device 32 for measuring the geometric characteristics of a droplet are possible. For example, the light source 50 can be replaced by another light source that generates, in a plane parallel to the vectors e z summer r, a laser beam comb. This laser beam comb contains a multitude of laser beams parallel to each other. When each of these As laser beams pass through the contour of droplet 14, the beam propagation direction is changed. Camera 52 generates an image containing the laser beams. In this image, each point where a laser beam changes direction corresponds to a point on the contour of droplet 14. The coordinates of these points are measured in the digital image by the image analysis module 56. In this case, the source 50 is not located on a side of axis 16 diametrically opposite the lens of camera 52. For example, the source 50 is located directly above droplet 14 in the vertical plane passing through apex 17 and parallel to the vector e r .

[0098] Other variations:

[0099] Fluid 6 may be a liquid immiscible with the liquid of drop 14.

[0100] The temperature and pressure conditions under which the interfacial physical properties are measured can be measured directly instead of being controlled by setpoints. In this case, the ambient temperature and pressure are acquired during step 96.

[0101] Several of the variants described in this Chapter II can be combined together.

[0102] Chapter III: Advantages of the described embodiments

[0103] Model (1) is more accurate than known and currently used models for measuring interfacial physical properties. In particular, the radius of curvature Ro of the droplet at the apex is not a parameter of the model that must be measured, as is the case with most known models. Furthermore, this model takes into account the fact that the droplet liquid seeks to minimize its interface with the fluid and the substrate to minimize the total energy of the system. This constraint is defined by the first constraint equation of model (1). This constraint is not modeled by other known models. Because of this, the values ​​measured by the methods described above are more accurate than the values ​​measured using other measurement methods. This improvement in accuracy is particularly noticeable in specific cases, such as when the substrate is hydrophobic, superhydrophobic, or oleophobic.Thus, the measurement method described here is usable with a much larger number of liquid / substrate / surrounding fluid combinations. Furthermore, it works equally well for very small droplets as for very large ones. Large size. Model (1) is also more generic than known models because it works equally well with a pendant droplet and a sessile droplet. Thus, what has been described here is not limited to the use of sessile drops.

[0104] Using measurements obtained from a drop whose volume is less than the Sic or Si threshold d This allows for increased accuracy and reliability of the determined value for the line voltage. S i2. Indeed, in this context, the line voltage Osi2 has a predominant effect on the shape of the droplet.

[0105] Using measurements obtained from a drop whose volume exceeds the Sic or Si threshold d This allows for increased accuracy and reliability of the values ​​determined for interfacial tensions. Indeed, it is when the droplet volume exceeds the Sic or Si threshold. d that the effect of interfacial tensions on the shape of the drop is predominant.

[0106] Determining the values ​​of interfacial physical properties using only a series of droplets of increasing volume allows for more accurate values ​​of these properties for droplets whose volume increases over time. Conversely, determining the values ​​of interfacial physical properties using only a series of droplets of decreasing volume allows for more accurate values ​​of these properties for droplets whose volume decreases over time.

[0107] Determining the value of an interfacial physical property from measurements made with a series of drops of increasing volumes and a series of drops of decreasing volumes also allows us to measure the amplitude of the hysteresis on the value of this interfacial physical property.

[0108] Determining the mooring radius r(h) from the same measurements and the same model (1) avoids the need to measure this mooring radius. In some cases, this allows for a more precise value of the mooring radius.

Claims

Demands 1. A method for measuring at least one interfacial physical property between a liquid droplet, a solid substrate, and a surrounding fluid, this interfacial physical property belonging to the group consisting of: - of an interfacial tension O12 between the liquid droplet and the surrounding fluid, - of an interfacial tension o Si between the liquid droplet and the solid substrate, - of an interfacial tension o S 2 between the solid substrate and the surrounding fluid, and - of a line voltage o S i2 at the level of a contact line between the liquid droplet, the surrounding fluid and the solid substrate, this process comprising the following steps: a) for at least one droplet of known volume, the execution of the following operations: - the formation (102) of the droplet of known volume of the liquid on a horizontal face of the substrate immersed in the surrounding fluid, then - the measurement (110, 132) of the radius of this drop, in a plane parallel to the horizontal face of the substrate, at different heights relative to the apex of the drop, then b) the automatic determination (136), by an electronic computer, of a value of the interfacial physical property: - based on the measurements obtained at the end of step a), and - using a numerical model that links the different measurements obtained to the value of this interfacial physical property, characterized in that the numerical model used in step b) is the following numerical model: Or : - z is a height, relative to the apex of the droplet, at which a point of the interface between the droplet and the surrounding fluid is located. - r is the radius of the droplet at height z in a plane parallel to the horizontal face of the substrate, - z' is the first derivative of z with respect to r, - z" is the second derivative of z with respect to r, - Ro is the radius of curvature of the droplet at the apex of the droplet, - V is the known volume of the droplet, - h is the height of the droplet along the vertical axis passing through the apex of the droplet, - r(h) is the radius wetted by the liquid, that is, the radius of the droplet at the horizontal face of the substrate, - g is the non-zero magnitude of the gravitational field acting on the droplet during the execution of step a), - pi is the predetermined density of the liquid, - p2 is the predetermined density of the surrounding fluid, - the symbol "±" means equal to: - to the "+" sign when the drop has been obtained by decreasing its volume to volume V, and - to the sign "-" when the drop has been obtained by increasing its volume up to volume V.

2. A method according to claim 1, wherein, when the interfacial physical property to be measured is the line voltage o S i2: - step a) involves the formation of a liquid droplet whose volume is less than a threshold Si, where the threshold Si is the threshold beyond which the contact angle between the droplet and the solid substrate no longer varies with the volume of the droplet, and - during step b) (136), the value of the line voltage o S i2 is determined from the measurements obtained from this drop of liquid whose volume is less than the threshold Si.

3. A method according to any one of the preceding claims, wherein the interfacial physical property to be measured is one of the interfacial tensions O12, Osi or Os2: - step a) involves the formation of a liquid droplet whose volume is greater than a threshold Si, where the threshold Si is the threshold beyond which the contact angle between the droplet and the solid substrate no longer varies with the volume of the droplet, and - during step b) (136), the value of the interfacial tension is determined from the measurements obtained from this drop of liquid whose volume is greater than the threshold Si.

4. A method according to any one of the preceding claims, wherein: - during step a) (102), a first series of drops of increasing volumes is formed by forming, on the solid substrate, a drop of initial volume and then forming, in order of increasing volumes, the following drops by injecting an additional quantity of liquid into the previous drop already formed on the solid substrate, and - in step b) (136), the value of the interfacial physical property is determined only from measurements made on this first series of drops.

5. A method according to any one of the preceding claims, wherein: - during step a) (102), a second series of drops of decreasing volumes is formed by forming, on the solid substrate, a drop of initial volume and then forming, in order of decreasing volumes, the following drops by drawing a predetermined quantity of liquid from the previous drop already formed on the solid substrate, and - in step b) (136), the value of the interfacial physical property is determined only from measurements made on this second series of drops.

6. A method according to claims 4 and 5 taken together, wherein the method comprises calculating (138) a hysteresis amplitude from the difference between: - the value of the interfacial physical property determined solely from measurements taken on the first series of drops, and - the value of the interfacial physical property determined only from measurements carried out on the second series of drops.

7. A method according to any one of the preceding claims, wherein, in step b), the wetted radius r(h) is also determined from the same measurements obtained at the end of step a) and using the same numerical model.

8. A method according to any one of the preceding claims, wherein: - step a) is repeated at least four times for at least four different volumes of drops, and - during step b), the value of the line voltage o S i2 and the values ​​of the three interfacial tensions O12, Osi and o S 2 are determined using the numerical model.

9. A method according to any one of the preceding claims, wherein: - the method comprises the acquisition (106) of an image of a cross-section of the droplet formed on the horizontal face of the substrate immersed in the surrounding fluid, and - the measurement (110, 132) of the radius of this drop at different heights includes the automatic analysis of the acquired image to extract the radii of this drop, in a plane parallel to the horizontal face of the substrate, at different heights relative to the apex of the drop.

10. Information storage medium (62) comprising instructions executable by an electronic computer for implementing a method according to any one of the preceding claims, this medium comprising instructions which, when executed by the electronic computer, automatically determine a value of the interfacial physical property: - from the measurements obtained at the end of step a) of the process according to any one of the preceding claims, and - using a numerical model that links the different measurements obtained to the value of this interfacial physical property, characterized in that the numerical model used is the following numerical model: Or : - z is a height, relative to the apex of the droplet, at which a point of the interface between the droplet and the surrounding fluid is located. - r is the radius of the droplet at height z in a plane parallel to the horizontal face of the substrate, - z' is the first derivative of z with respect to r, - z" is the second derivative of z with respect to r, - Ro is the radius of curvature of the droplet at the apex of the droplet, - V is the known volume of the droplet, - h is the height of the droplet along the vertical axis passing through the apex of the droplet, - r(h) is the radius wetted by the liquid, that is, the radius of the droplet at the horizontal face of the substrate, - g is the non-zero magnitude of the gravitational field acting on the droplet during the execution of step a), - pi is the predetermined density of the liquid, - p2 is the predetermined density of the surrounding fluid, - the symbol "±" means equal to: - to the "+" sign when the drop has been obtained by decreasing its volume to volume V, and - to the sign "-" when the drop has been obtained by increasing its volume up to volume V.

11. Apparatus for measuring at least one interfacial physical property between a liquid droplet, a solid substrate and a surrounding fluid, this interfacial physical property belonging to the group consisting of: - of an interfacial tension O12 between the liquid droplet and the surrounding fluid, - of an interfacial tension o Si between the liquid droplet and the solid substrate, - of an interfacial tension o S 2 between the solid substrate and the surrounding fluid, and - of a line voltage o S i2 at the level of a contact line between the liquid droplet, the surrounding fluid, and the solid substrate, this device comprising: - a syringe (30) capable of forming drops of various known volumes of liquid onto a horizontal face of the substrate immersed in the surrounding fluid, - a measuring device (32) capable, for each of the drops of different known volumes formed by the syringe, of measuring the radius of this drop, in a plane parallel to the horizontal face of the substrate, at different heights relative to the apex of the drop, and - an electronic calculator (34) configured to automatically determine a value for the interfacial physical property: - based on the measurements taken by the measuring device, and - using a numerical model that links the different measurements obtained to the value of this interfacial physical property, characterized in that the numerical model used by the electronic computer (34) is the following numerical model: - z is a height, relative to the apex of the droplet, at which a point of the interface between the droplet and the surrounding fluid is located. - r is the radius of the droplet at height z in a plane parallel to the horizontal face of the substrate, - z' is the first derivative of z with respect to r, - z" is the second derivative of z with respect to r, - Ro is the radius of curvature of the droplet at the apex of the droplet, - V is the known volume of the droplet, - h is the height of the droplet along the vertical axis passing through the apex of the droplet, - r(h) is the radius wetted by the liquid, that is, the radius of the droplet at the horizontal face of the substrate, - g is the non-zero magnitude of the gravitational field acting on the droplet during the execution of step a), - pi is the predetermined density of the liquid, - p2 is the predetermined density of the surrounding fluid, - the symbol "±" means equal to: - to the "+" sign when the drop has been obtained by decreasing its volume to volume V, and - to the sign "-" when the drop has been obtained by increasing its volume up to volume V.

12. Apparatus according to claim 11, wherein the measuring device (32) comprises: - a camera (52) capable of generating an image of a cross-section of the droplet formed by the syringe on the solid substrate, and - a suitable image analysis module (56): - to acquire the image of the cross-section of the droplet, then - to automatically analyze the acquired image to extract rays from this droplet, in a plane parallel to the horizontal face of the substrate, at different heights relative to the apex of the droplet, then - to establish the equation of a curve that best approximates the contour of the cross-section of the drop.

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