WO2023152051A1

WO2023152051A1 - Method for measuring at least one physical interfacial property

Info

Publication number: WO2023152051A1
Application number: PCT/EP2023/052708
Authority: WO
Inventors: Marc MEDALE; David BRUTIN
Original assignee: Universite D'aix Marseille; Centre National De La Recherche Scientifique; Centre National D'etudes Spatiales
Priority date: 2022-02-08
Filing date: 2023-02-03
Publication date: 2023-08-17
Also published as: FR3132572A1; FR3132572B1

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 an apparatus for measuring at least one interfacial physical property between a drop of liquid, 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 interfacial physical property measured is one of the following interfacial physical properties:

- an interfacial tension between a drop of liquid and a surrounding fluid,

- an interfacial tension between a drop of liquid and a solid substrate,

- an interfacial tension between a solid substrate and a surrounding fluid, and

- a line voltage at a line of contact between a drop of liquid, a surrounding fluid and a solid substrate,

[3] The company KRÜSS-SCIENTIFIC® markets devices for measuring such an interfacial physical property. For this, these devices deposit a drop of the liquid on the face of the substrate immersed in the surrounding fluid. Then, a camera generates an image of the outline of this drop. An image analysis module then automatically determines the geometric characteristics of the contour of the drop from the processing of this image. 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 drop is its contact angle with the substrate. The digital models used in such devices are known models such as for example the Young-Laplace equation.

[5] These devices are functioning properly. However, in some cases, the determined value for the interfacial physical property is not accurate. For example, this problem is encountered in the case of hydrophobic or super-hydrophobic liquid or oleophobic liquid or in other particular situations.

[6] 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 an apparatus for measuring a more precise interfacial physical property.

[8] It therefore relates to a method of measuring an interfacial physical property in accordance with claim 1 .

[9] It also relates to an information recording medium for the implementation of the above measurement method.

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

[11] The invention will be better understood on 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 part of the outline of a drop deposited on a substrate, and

- Figure 3 is a flowchart of a method for measuring interfacial physical properties using the apparatus of Figure 1.

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

[13] In this description, a detailed example of an embodiment is first described in a chapter I with reference to the figures. Then, in a chapter II, variants of this embodiment are presented. Finally, the advantages of the different embodiments are presented in a chapter III. [14] Chapter I: Example embodiment

[15] Figure 1 shows an apparatus 2 for measuring interfacial physical properties between a drop of liquid, a solid substrate 4 and a surrounding fluid 6.

[16] In this embodiment, the fluid 6 is a gas. More precisely, the fluid 6 is the 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 super-hydrophobic substrate when the liquid is water or an oleophobic substrate when the liquid is oil.

[17] Here, device 2 is placed in a room whose interior temperature is maintained equal to a set temperature and whose atmospheric pressure is maintained at a constant value. For example, the temperature setpoint is equal to 20°C and the constant pressure is equal to 1 atm (= 1013.25 hPa). Thus, the ambient temperature and the ambient pressure in which the measurements of the interfacial physical properties are carried out are known.

[18] The substrate 4 is in the form of a plate comprising a horizontal upper face 8 and, on the opposite side, a lower face 10. Here, the lower face is also a horizontal face. Since the faces 8 and 10 are horizontal, they each extend in a plane perpendicular to the gravitational field, the direction and amplitude of which are represented in figure 1 by a vector g subsequently called the "gravity vector".

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

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

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

[22] Figure 1 also shows the cross section of a drop 14 of the liquid formed on the face 8. The drop 14 is centered on the vertical axis 16. The axis 16 is an axis of symmetry of revolution for the drop 14 and the drop 14 has an infinity of different symmetries of revolution around this axis. Such a drop 14 which is deposited on a horizontal face of a substrate is known by the term "drop". 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.

[23] In this text, “interfacial physical property” designates one of the interfacial physical properties chosen from the group consisting of:

- an interfacial tension Oi ₂ between the drop of liquid and the fluid 6,

- an interfacial tension o _Si between the drop of liquid and the substrate 4,

- an interfacial tension o _S 2 between the solid substrate 4 and the fluid 6, and

- a line voltage o _S i2 at a line of contact between the drop of liquid, the fluid 6 and the substrate 4.

[24] It is recalled that an interfacial tension between two bodies characterizes the excess of free energy between these two bodies. Interfacial tension is expressed in Joule per square meter. It is also known by the term “surface tension” or “surface tension” and under the English terms “surface tension” or “surface energy” or “surface density of free energy”.

[25] The line voltage at the contact line between three bodies, here the drop of liquid, the substrate 4 and the fluid 6, characterizes the excess free energy specific to the interface between these three bodies. Line voltage is expressed in Joule per meter. In English, line voltage is known as “line tension” or “line density of free energy”.

[26] The line of contact between the drop of liquid, 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.

[27] Subsequently, the device 2 is described in the particular case where it measures the four interfacial physical properties Oi ₂ , o _S i , o _S 2 and o _S i2.

[28] For this purpose, device 2 comprises:

- a syringe 30 capable of injecting a known volume of liquid through the hole 12 to form the drop 14,

- a device 32 for measuring the geometric characteristics of the drop 14, and

- an electronic computer 34 configured to determine the values of the four properties Oi ₂ , o _S i , o _S 2 and o _S i2 from the geometric characteristics measured by the device 32.

[29] The syringe 30 comprises: - a reservoir 40 containing the liquid to be ejected to form the drop 14,

- a needle or a nozzle 42 whose upper end is fluidically connected to the lower end of the hole 12 and whose lower end is fluidically connected to the reservoir 40,

- a piston 44 capable of sinking inside the tank 40 to eject a predetermined volume of liquid through the hole 12, and

- a controllable electric actuator 46 able to move the piston 44.

[30] Here, the volume of reservoir 40 is greater than the volume V _max of the largest drop 14 to be formed on face 8 of substrate 4.

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

[32] The device 32 makes it possible in particular to measure the radius r of the drop 14 at different heights z.

[33] Figure 2 shows a reference R used here to measure the radius r and the height z of a point M belonging to the contour of the drop 14. In Figure 2, only the right part of the drop 14 is shown. The origin O of the reference R coincides with the apex 17 of the drop 14. The reference R comprises a vertical axis R _z and a horizontal axis R _r which intersect at right angles at the level of the origin O. axis R _z coincides with the axis of 16 of symmetry of revolution of the drop 14. The axis R _z is oriented in the same direction as the vector e _z previously defined. The axis R _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 FIG. 2. In this frame R, the coordinates of a point M of the outline of the drop 14 are (r; z), where r is the radius of drop 14 at height z and z is the height of point M from origin O.

[34] Subsequently, the symbol “h” designates the height of the drop 14 along the axis R _z and the symbol r(h) designates 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).

[35] Figure 2 also shows the macroscopic contact angle 0 _m . The 9m angle is defined as the angle between: - side 8, and

- the vector t _m tangent to the contour of the drop 14 at the level of the point 20.

[36] The 9 _m angle is called "macroscopic" because it is measured on a macroscopic scale.

[37] To obtain the coordinates in the frame R of several points M of the contour of the drop 14, the device 32 generates an image of the cross section of the drop 14 then measures the coordinates of several points of the contour of the drop by analysis pictures. In this aspect, the device 32 is similar, for example, to that described in application EP2899529A1. Thus, subsequently, only the characteristics of the device 32 necessary to understand the invention are presented.

[38] Typically, device 32 includes:

- a light source 50 which illuminates the drop 14 in a direction parallel to the vector e _r ,

- a camera 52 which generates an image of the contour of the drop 14,

- a module 54 for acquiring the image generated by the camera 52 to obtain a digital image, and

- an image analysis module 56 which processes the acquired image to extract the desired geometric characteristics of the drop.

[39] Here, source 50 and camera 52 are located at diametrically opposite locations with respect to axis 16. Thus, source 50 generates a shadow on the lens of camera 52 which corresponds to the orthogonal projection of drop 14 on this lens. Camera 52 generates an image of this shadow. The outline of this shadow in this image is identical to the outline of drop 14. The entire outline of the drop is contained in the generated image.

[40] The module 54 acquires the image generated by the camera 52 and provides the image analysis module 56 with a digital image of the contour of the drop 14. Typically, in this digital image, the drop 14 is distinguished from the background of the image by its color. For example, in this digital image, the pixels which correspond to parts of the drop 14 are of dark color, for example black or gray, while the pixels which correspond to the background of the image are of another light color, for example white or light grey.

[41] The module 56 processes the acquired digital image to extract geometric characteristics of the drop 14. Here, the module 56 processes this image digital to extract therefrom the coordinates, expressed in the frame R, of several points belonging to the contour of the drop 14. The coordinates of these points correspond, in this digital image, to the pixels which are at the edge between the dark color of the drop 14 and the light background color of this image. Thus, after this extraction, the module 56 has the coordinates, in the reference R, of a list of points of the contour of the drop 14. The number of points of this list is typically greater than three and, preferably, greater than ten, twenty or fifty.

[42] In this embodiment, to increase the precision of the measurement and facilitate the calculation of first and second derivatives, from the coordinates of the points of this list, the module 56 establishes the equation of a curve which approximates at better the outline of the drop 14. For this, the module 56 implements, for example, curve fitting methods, better known by the English term “curve fitting”. While implementing this curve fitting, curve smoothing operations are also implemented in the end to reduce or eliminate any singularities or irregularities in the established curve.

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

[44] The computer 34 is designed to completely automate the measurement process of Figure 3. To this end, it includes in particular:

- a programmable microprocessor 60,

- a memory 62 which contains the instructions executed by the microprocessor 60, and

- a man-machine interface 64.

[45] The memory 62 includes in particular all the instructions necessary for the execution of the method of Figure 3. To this end, it therefore includes in particular:

- the instructions for a module 70 for controlling the syringe 30,

- the instructions of a module 72 for controlling the measuring device 32,

- the instructions of a parameter acquisition module 74, and

- the instructions of a module 76 for determining the values of the interfacial physical properties.

[46] In addition, here, the memory 62 also includes the instructions of the modules 54 and 56 previously described. [47] The computer 34 is connected to the syringe 30 and to the camera 52. More specifically, the module 70 makes it possible to control the actuator 46 of the syringe 30 to eject and, alternately, suck up a predetermined quantity of the liquid.

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

[49] The module 74 makes it possible to acquire, via the man-machine interface 64, the values of the parameters necessary for determining the values of the interfacial physical properties. Here, module 74 makes it possible to acquire:

- the density pi of the liquid,

- the density p ₂ of the fluid 6, and

- the norm of the gravity vector g.

[50] In addition, module 74 makes it possible to acquire the ambient temperature and the ambient pressure in which the values of the interfacial physical properties are measured. Indeed, the values of these interfacial physical properties vary according to the ambient temperature and also, to a lesser extent, according to the ambient pressure. Therefore, when the values of these interfacial physical properties are determined, it is also important to be able to specify under which temperature and pressure conditions these values were identified.

[51] The man-machine interface 64 is, for example, formed by a screen 80 and a keyboard 82. The screen 80 makes it possible to display the values determined for the interfacial physical properties.

[52] The method for measuring the properties Oi ₂ , o _S i , o _S 2 and o _S i2 using the apparatus 2 will now be described with reference to the method of FIG. 3.

[53] During a step 96, the module 74 acquires, for example via the man-machine interface 64, the values of the ambient temperature and of the ambient pressure in which the measurements of the properties Oi ₂ , o _S i, o _S 2 and o _S i2 will be performed. During step 96, the values of the densities pi and p ₂ , respectively, of the liquid and of the fluid 6 are also acquired. The value of the norm of the gravity vector g is also acquired. This last value corresponds to the norm of the vector g at the level of device 2.

[54] Then, the method continues with a phase 98 of establishing the threshold value Sic and Si _d . For example, for this, during a step 100, the module 70 controls the syringe 30 to form on the face 8, a first series of drops of increasing volumes from a minimum volume Vmin to the maximum volume V _ma x. Typically, the volume Vmin is less than V _ma x/10 and, preferably, less than V _max /100. Here, the volumes Vmin and _Vmax are the volumes, respectively, of the smallest drop and of the largest that the syringe 30 can form on the face 8. Typically, the volume Vmin is less than 10 pL or 5 pL or at 1 µL.

[55] 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.

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

[57] During an operation 106, once the image has been generated, it is acquired by the acquisition module 54.

[58] During an operation 110, the module 56 processes the image acquired during operation 106. More specifically, as previously indicated, the module 56 first measures the coordinates of several points belonging to the outline of the drop 14. In particular, preferably, the coordinates of point 20 are measured. Then, from the measured coordinates of these points, during operation 110, the module 56 establishes the equation of a curve which best approximates the contour of this drop.

[59] During an operation 112, the module 56 determines the value of the angle 0 _m of macroscopic contact. For example, for this, from the equation of the curve established during operation 110, the coordinates of the vector t _m tangent to this curve at the point 20 are calculated. The value of the angle 0 _m for the volume Vmin is then calculated from the coordinates of the vectors t _m and e _r .

[60] Then, operations 102 to 112 are repeated for a drop of greater volume. Here, during the repetition of operation 102, the actuator 46 is simply controlled to inject a predetermined additional quantity Q _s of liquid into the previously formed drop 14 so as to obtain a new drop 14 of greater volume. Thus, during this first part of step 100, a first series of drops of increasing volume is formed on face 8.

[61] Here, the quantity Q _s injected during each reiteration of operation 102 is for example the same each time. Thus, the volume of the drop 14 is incremented with a regular step from the volume Vmin to the 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. [62] Preferably, once the volume V _ma x has been reached, operations 102 to 112 are repeated, this time decreasing, at each iteration, the volume of the drop 14 until it returns to one drop 14 whose volume is equal to Vmin. Thus, during this second part of step 100, a second series of drops of decreasing volumes is formed on the face 8. During this second part, the volume of the drop is for example decremented with the same regular step as that used to form the first series of drops.

[63] After the deposition of the first and second sequences of drops and the measurements of the geometric characteristics of these drops, step 100 is completed and then begins a step 120 during which the computer 34 establishes the threshold value S ic and Si _d . Each of the thresholds Sic and Si _d corresponds to the threshold beyond which the angle 9 _m of macroscopic contact between the drop 14 and the substrate 4 no longer varies as a function of the volume of the drop 14. The threshold Sic is only measured from of the sequence of increasing drops while the threshold Si _d is only measured from the sequence of decreasing drops.

[64] For example, the computer 34 notes, in the first sequence of drops of increasing volume, the volume Vi _m ,c of the drop from which the angle 0 _m no longer varies according to the volume of this drop. Then, the computer 34 records, in the second sequence of drops of decreasing volume, the volume Vi _m , _d from which the angle 0 _m no longer varies as a function of the volume of the drop. The volumes Vi _m ,c and Vi _m , _d recorded are generally different because of hysteresis phenomena. However, the volumes Vi _m ,c and Vi _m , _d remain fairly close to each other because the amplitude of these hysteresis phenomena remains low compared with the values of the volumes Vi _m ,c and Vi _m , _d .

[65] Then, during a step 130, the module 76 automatically selects four volumes Vi _c , V _2c , V _3c and V _4c of drops in the first sequence of drops of increasing volumes to obtain a first series of four drops of growing volumes. The volumes Vi _c , V _2c , V _3c and V _4c are listed in ascending order. The Life volume is lower than the Sic threshold and, preferably, lower than Sic/2. The three volumes V _2c , V _3c and V _4c are greater than the threshold Sic and preferably greater than 1.5*Si _c , where the symbol "*" designates the arithmetic multiplication operation. Preferably, there is a ratio greater than or equal to two between two consecutive volumes of this first series of drops of increasing volumes. Thus, typically, the volume V _2c is at least twice greater than the volume Vi _c . [66] Then, during a step 132, the coordinates of different points of the outline of each of the drops of volume Vi _c to V _4c are measured. In particular, during this step 132, the radius of each of the drops of volumes Vi _c to V _4c is measured for the height z=h. Given that these measurements have already been carried out for the same drops during operation 110, step 132 is reduced in this case to selecting the coordinates already measured during operation 110 for each of these volume drops Vi _c to V _4c .

[67] During a step 134, for each of the drops with volumes Vi _c to V _4c , the module 56 establishes the equation of the curve which best approximates the contour of this drop. Here, since this has already been done during operation 110 for each of the drops of volumes Vi _c to V _4c , this step boils down to selecting the four equations of the curves obtained from the drops of volumes Vi _c to V _4c .

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

[69] For this, the module 76 uses a numerical model (1) which connects the coordinates (r; z) of a point M of 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 the point M of the interface between the drop and the surrounding fluid is located,

- r is the radius of the drop 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 drop at the level of the apex 17 of the drop,

- V is the known volume of the drop,

- h is the height of the drop along the R _z axis,

- r(h) is the radius wetted by the liquid, i.e. the radius of the drop at the level of the horizontal face 8,

- the symbol "±" is equal:

- to the "+" sign when the drop was obtained by decreasing its volume to volume V, and

- to the "-" sign when the drop was obtained by increasing its volume to volume V.

[70] In this first embodiment, the symbol "±" is equal to the sign "-" when the drop is one of the drops of the first series of four drops. Conversely, the symbol "±" is equal to the sign "+" when the drop is one of the drops of the second series of four drops.

[71] The model (1) is parameterized by the following known parameters which have been defined previously:

- the non-zero norm g of the gravity field which is exerted on the drop during the execution of step 132,

- the density pi of the liquid,

- the density p ₂ of the fluid 6,

- the known volume V of the drop deposited on face 8, and

- the wet radius r(h).

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

[73] Model (1) includes, 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 translates the fact that the radius of the drop at the height z=0 is zero. The condition z'(0) = 0 translates the fact that the tangent to the apex of the drop is horizontal. There second constraint equation makes it possible to determine the height h of the drop from its volume V. The first constraint equation makes it possible to define the radius of curvature R _o according to the known parameters, the height h and the values of the physical properties interfaces Oi ₂ , Osi, Os2 and o _S i2 to be determined.

[74] In this model (1), when the equation of the contour curve of a drop is known, the integral of the second constraint 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 drop is known. Then, when the height h and the equation of the contour curve of the drop are known, the first constraint equation makes it possible to express the radius R _o as a function of the four interfacial physical properties Oi ₂ , Osi, Os2 and o _S i2. Thus, for each drop whose contour equation is known, the model (1) makes it possible to obtain a system of equations in which the only unknowns are the values of the four interfacial physical properties Oi ₂ , Osi, Os2 and Osi2. Therefore, by selecting four drops whose contour equations are different, we obtain a final system of four systems of equations with four unknowns. This final system is solved automatically by the module 76 in order to obtain, from the contours of four drops, a value for each of the interfacial physical properties Oi ₂ , o _S i , Os2 and o _S i2 .

[75] Here, the module 76 determines the values of the properties Oi ₂ , o _S i , Os2 and o _S i2 from the equations of the curves of the contours of the four volume drops Vi _c to V _4c .

[76] More precisely, since the volumes V _2c to V _4c are greater than the threshold Sic, the last term of the first constraint equation which depends on the line voltage Osi2, can be neglected. Thus, for each of the drops with volumes V _2c to V _4c , a system of equations is obtained in which the three unknowns are only the interfacial physical properties Oi ₂ , o _Si and o _S 2 . The module 76 first solves the intermediate system formed from these three systems of equations for determining first values of the three interfacial physical properties Oi ₂ , o _Si and o _S 2 . The first values determined for each of the properties Oi ₂ , o _Si and o _S 2 from drops of volumes V _2c to V _4c are subsequently denoted Oi ₂ , _c , o _Si , _c , and o _S 2 , _c .

[77] Then, the model (1) and the volume drop contour equation Vi _c are used to obtain a new system of equations. In this new system of equations the unknowns Oi ₂ , o _Si and o _S 2 are replaced by their values, respectively, Oi ₂ , _c , o _Si , _c , and o _S 2, _c . This makes it possible to obtain a system of equations in which the only remaining unknown, at this stage, is the line voltage cr _S i2. Solving this system of equations then makes it possible to obtain the first value o _S i2,c of the line voltage cr _S i2.

[78] Here, during a step 138, steps 130 to 136 are repeated but using the second sequence of drops of decreasing volumes instead of the first sequence of drops of increasing volumes. Thus, during this reiteration of steps 130 to 136, the volumes Vi _c , V _2c , V _3c and V _4c are replaced by volumes, respectively Vi _d , V _2d , V _3d and V _4d . The execution of step 138 makes it possible to determine, for each of the properties Oi ₂ , o _S i , o _S 2 and o _S i2 , second values noted, respectively Oi ₂ , _d , o _S i , _d , o _S 2,d and o _S i2,d. These second values Oi ₂ , _d , o _Si , _d , a _S 2 , _d and o _S i2, _d are not necessarily the same as the first values Oi ₂ , _c , o _Si , _c , Os2,c and o _S i2, _c . For the same interfacial physical property, the difference between these first and second values is representative of the amplitude of the hysteresis phenomenon which exists between a series of drops of increasing volumes and a series of drops of decreasing volumes. Thus, step 138 also makes it possible to calculate the amplitude of the hysteresis on the values of the measured interfacial physical properties.

[79] Chapter II: Variants:

[80] Variants of the process:

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

[82] When the value of some of the interfacial physical properties is already known, what was previously described can be implemented to measure the other interfacial physical properties that are not known. The number of interfacial physical properties measured is then less than four. Consequently, during step 136, the values of the interfacial physical properties which are already known are introduced into the model (1) as a known parameter. In this case, the number of drops of the series of drops used to determine the values of the unknown interfacial physical properties can be decreased. In an extreme case, the series of drops used consists of a single drop. This last case is encountered for example, when the only interfacial physical property to be measured is the line voltage o _S i2 while the interfacial tensions O12, Osi and o _S 2 are known.

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

[84] The value of the line voltage o _S i2 can also be determined only from measurements carried out on drops whose volume is greater than the threshold Sic or Sid. In this case, the accuracy of the value of the line voltage o _S i2 determined may be less good. On the other hand, the phase 98 of establishing the values of the thresholds Sic and Sid can be omitted.

[85] In a corresponding way, the values of the interfacial tensions can also be determined only from the geometric characteristics of drops whose volume is lower than the threshold Sic or Si _d . In this case, similarly to what is indicated in the previous paragraph, the precision on the determined values of the interfacial tensions may be less good. However, on the other hand, the phase 98 of establishing the values of the thresholds Sic and Si _d , can be omitted.

[86] If it is not necessary to take into account the influence of hysteresis on the values of interfacial physical properties, then, it is not necessary to use a series of drops of increasing volumes and a series of drops of decreasing volumes. For example, either only the series of drops of increasing volumes, or only the series of drops of decreasing volumes is used to determine the values of the interfacial physical properties. A series of drops formed both by increasing and decreasing their volumes in any temporal order can also be used. [87] When the values of the thresholds Sic and Si _d are known in advance, the phase 98 of establishing the value of these thresholds can be omitted. In this case, during step 132, the series of drops of increasing and decreasing volumes are deposited and their geometric characteristics are measured in a manner similar to what was described with regard to phase 98.

[88] In another simplified embodiment, the Sic and Si _d thresholds 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.

[89] When the apparatus 2 is only designed to be used on the earth's surface and in conditions where it is stationary with respect to the earth's surface, the norm of the vector g of gravity can be considered to be a constant and prerecorded in memory 62.

[90] Device variants:

[91] The device 2 can include several syringes 30 capable of operating in parallel. This makes it possible to form, in parallel, several drops on the face 8. In such a case, the image generated by the camera 52 then also comprises several drops.

[92] Other embodiments of the syringe 30 are possible. For example, the syringe described in application EP2899529A1 can be used instead of syringe 30. In this case, the needle of the syringe is located above face 8 and the drop is deposited on face 8 and not not injected through the substrate 4. In this case, it is not necessary for the substrate 4 to include the hole 12. On the other hand, the energy stored by the drop during its deposit on the face 8 of the substrate 4, can slightly deform the drop 14 and therefore slightly falsify the measurements of the interfacial physical properties.

[93] As a variant, the drop whose geometric characteristics are measured by the device 32 is a pendant drop and not a sessile drop. To obtain a pendant drop, the syringe 30 is, for example, placed above the substrate 4. In this case, the drop 14 is formed on the face 10 and no longer on the face 8 of the substrate. The measurement method previously described in the case of a sessile drop applies identically to the case of a pendent drop. Indeed, model (1) can also be used for a hanging drop. [94] Other embodiments of the computer 34 are also possible. For example, as a variant, the computer 34 does not include the control module 70 of the syringe 30 nor the control module 72 of the camera 52. In this case, these two control modules 70 and 72 are integrated, respectively, in the syringe 30 and in the camera 52. To this end, the syringe 30 and the camera 52 each comprise their own microprocessor and their own memory in order to execute these modules. Consequently, these two modules are directly controlled by the user in order to obtain the different images of the drops. For example, the user supplies directly to the control module 70 of the syringe 30 the different volumes of drops to be formed on the face 8. In response, the module 70 controls the actuator 46 to form, one after the other, these different drops of different volumes. In parallel, each time a new drop is formed on the face 8, the camera 52 generates an image of this drop and records it on a digital medium, for example, removable. Once the various digital images necessary to determine the interfacial physical properties have been generated and recorded on the support, this support is connected to the computer 34. The acquisition module 54 is then configured to acquire the images of the drops from this support. The rest of the process is then identical to what was previously described.

[95] In another variant, the computer 34 comprises only one of the two modules 70, 72 control.

[96] The syringe 30 can comprise several pistons of different sizes so that, for a displacement of the same length, the volume of liquid displaced by one of these pistons is smaller than the volume of liquid displaced by the other pistons. In particular, in this case, the syringe comprises a small piston which displaces a volume of liquid five to ten times less than the volume of liquid displaced by the other pistons for the same length of displacement. The displacement of the small piston in addition to the displacement of the other pistons makes it possible to increase the precision on the volume of liquid ejected by hole 12.

[97] Other embodiments of the device 32 for measuring geometric characteristics of a drop are possible. For example, the light source 50 can be replaced by another light source which generates, in a plane parallel to the vectors _ez and e _r , a comb of laser beams. This laser beam comb has a multitude of laser beams parallel to each other. When each of these laser beams crosses the contour of the drop 14, the direction of propagation of the beam is modified. The 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 outline of the drop 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 one side of the axis 16 diametrically opposite to the lens of the camera 52. For example, the source 50 is located directly above the drop 14 in the vertical plane passing through the apex 17 and parallel to the vector e _r .

[98] Other variants:

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

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

[101] Several of the variants described in this chapter II can be combined together.

[102] Chapter III: Advantages of the Embodiments Described

[103] Model (1) is more accurate than known models currently used to measure interfacial physical properties. In particular, the radius of curvature Ro of the drop at the level of the apex is not a parameter of the model which must be measured as in the case of most known models. Moreover this model takes into account the fact that the liquid of the drop seeks to minimize its interface with the fluid and with the substrate to minimize the total energy of the system. This constraint is defined by the first constraint equation of the model (1). This constraint is not modeled by the other known models. Because of this, the values measured by the methods described above are more accurate than the values measured by implementing other measurement methods. This improvement in precision is in particular particularly perceptible in particular cases such as the case where the substrate is hydrophobic or super-hydrophobic or oleophobic. Thus, the measurement method described here can be used with a much larger number of liquid/substrate/surrounding fluid combinations. In addition, it works for both very small drops and very large drops. big size. The model (1) is also more generic than the known models because it functions just as well in the case of a pendent drop as of a sessile drop. Thus, what has been described here is not limited to the use of sessile drops.

[104] The fact of using measurements obtained from a drop whose volume is lower than the threshold Sic or Si _d , makes it possible to increase the precision and the reliability of the value determined for the line voltage o _S i2 . Indeed, in this context, the line voltage Osi2 has a preponderant effect on the shape of the drop.

[105] The fact of using measurements obtained from a drop whose volume is greater than the Sic or Si _d threshold, makes it possible to increase the precision and the reliability of the values determined for the interfacial tensions. Indeed, it is when the volume of the drop is greater than the Sic or Si _d threshold that the effect of the interfacial tensions on the shape of the drop is preponderant.

[106] The determination of the values of the interfacial physical properties only from a series of drops of increasing volumes, makes it possible to obtain more precise values of the interfacial physical properties for drops whose volume increases over time. Conversely, determining the values of the interfacial physical properties only from a series of drops of decreasing volume, makes it possible to obtain more precise values for the interfacial physical properties for drops whose volume decreases over time.

[107] Determining the value of an interfacial physical property both from measurements made with a series of drops of increasing volume and a series of drops of decreasing volume also makes it possible to measure the amplitude hysteresis on the value of this interfacial physical property.

[108] Determining the wetting radius r(h) from the same measurements and the same model (1) avoids having to measure this wetting radius. In some cases, this provides a more accurate value of the wetting radius.

Claims

1. Method for measuring at least one interfacial physical property between a drop of liquid, a solid substrate and a surrounding fluid, this interfacial physical property belonging to the group consisting of:

- an interfacial tension O12 between the drop of liquid and the surrounding fluid,

- an interfacial tension o _Si between the drop of liquid and the solid substrate,

- an interfacial tension o _S 2 between the solid substrate and the surrounding fluid, and

- a line voltage o _S i2 at a line of contact between the drop of liquid, the surrounding fluid and the solid substrate, this method comprising the following steps: a) for at least one drop of known volume, performing the following operations:

- the formation (102) of the drop of known volume of 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 a electronic calculator, with a value of the interfacial physical property:

- from the measurements obtained at the end of step a), and

- using a numerical model which links the various measurements obtained to the value of this interfacial physical property, characterized in that the numerical model used during step b) is the following numerical model:

Or :

- z is a height, relative to the apex of the drop, at which a point of the interface between the drop and the surrounding fluid is located,

- r is the radius of the drop 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 drop at the level of the apex of the drop,

- V is the known volume of the drop,

- h is the height of the drop along the vertical axis passing through the apex of the drop,

- r(h) is the radius wetted by the liquid, i.e. the radius of the drop at the level of the horizontal face of the substrate,

- g is the non-zero norm of the gravity field exerted on the drop during the execution of step a),

- pi is the predetermined density of the liquid,

- p ₂ is the predetermined density of the surrounding fluid,

- the symbol "±" is equal:

2. Method according to claim 1, in which, when the interfacial physical property to be measured is the line voltage o _S i2:

- step a) comprises the formation of a drop of liquid whose volume is less than a threshold Si, where the threshold Si is the threshold beyond which the contact angle between the drop and the solid substrate does not vary more depending on the volume of the drop, 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. Method according to any one of the preceding claims, in which when the interfacial physical property to be measured is one of the interfacial tensions O12, Osi or Os2:

- step a) comprises the formation of a drop of liquid whose volume is greater than a threshold Si, where the threshold Si is the threshold beyond which the contact angle between the drop and the solid substrate does not vary more depending on the volume of the drop, and

- during step b) (136), the value of the tension of the interfacial tension is determined from the measurements obtained from this drop of liquid whose volume is greater than the threshold Si.

4. Method according to any one of the preceding claims, in which:

- 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 then by forming, in the 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

- During step b) (136), the value of the interfacial physical property is only determined from the measurements carried out on this first series of drops.

5. Method according to any one of the preceding claims, in which:

- during step a) (102), a second series of drops of decreasing volume is formed by forming, on the solid substrate, a drop of initial volume then by forming, in order of decreasing volume, the following drops by sucking a predetermined quantity of liquid into the previous drop already formed on the solid substrate, and

- During step b) (136), the value of the interfacial physical property is only determined from the measurements carried out on this second series of drops.

6. Method according to claims 4 and 5 taken together, in which the method comprises the calculation (138) of a hysteresis amplitude from the difference between:

- the value of the interfacial physical property determined solely from the measurements carried out on the first series of drops, and - the value of the interfacial physical property determined only from the measurements carried out on the second series of drops.

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

8. Method according to any one of the preceding claims, in which:

- 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. Method according to any one of the preceding claims, in which:

- the method comprises the acquisition (106) of an image of a cross section of the drop 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 rays from this drop, in a plane parallel to the horizontal face of the substrate, at different heights by relative to the apex of the drop.

10. Support (62) for recording information comprising instructions executable by an electronic computer for the implementation of a method according to any one of the preceding claims, this support comprising instructions which, when they are 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 method in accordance with any one of the preceding claims, and

- using a numerical model which links the various 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 the first derivative of z with respect to r,

- z" is the second derivative of z with respect to r,

- V is the known volume of the drop,

- pi is the predetermined density of the liquid,

- p ₂ is the predetermined density of the surrounding fluid,

- the symbol "±" is equal:

11. Apparatus for measuring at least one interfacial physical property between a drop of liquid, a solid substrate and a surrounding fluid, this interfacial physical property belonging to the group consisting of:

- a line voltage o _S i2 at a line of contact between the drop of liquid, the surrounding fluid and the solid substrate, this apparatus comprising:

- a syringe (30) capable of forming drops, of different known volumes, of the liquid on 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 computer (34) configured to automatically determine a value of the interfacial physical property:

- from the measurements made by the measuring device, and

- using a digital model which links the various measurements obtained to the value of this interfacial physical property, characterized in that the digital model used by the electronic computer (34) is the following digital model:

- z' is the first derivative of z with respect to r,

- z" is the second derivative of z with respect to r,

- V is the known volume of the drop,

- pi is the predetermined density of the liquid,

- p ₂ is the predetermined density of the surrounding fluid,

- the symbol "±" is equal:

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 drop formed by the syringe on the solid substrate, and

- an image analysis module (56) capable of:

- to acquire the image of the cross section of the drop, then

- automatically analyzing the acquired image to extract rays from this drop, in a plane parallel to the horizontal face of the substrate, at different heights relative to the apex of the drop, then

- to establish the equation of a curve which best approximates the contour of the cross section of the drop.