WO2014029191A1

WO2014029191A1 - Method for calculating static contact angle

Info

Publication number: WO2014029191A1
Application number: PCT/CN2013/000093
Authority: WO
Inventors: 徐志钮; 律方成
Original assignee: 华北电力大学（保定）
Priority date: 2012-08-20
Filing date: 2013-01-30
Publication date: 2014-02-27

Abstract

A method for calculating a static contact angle, belonging to the field of material performance tests and comprising: based on the Young-Laplace equation, simulating a liquid drop edge of a certain type of liquid at different volumes and contact angles or a liquid drop edge at different volumes, contact angles and liquid parameters Δρ/γ, wherein Δρ is the difference between liquid density and gas density, and γ is the surface tension of the liquid; calculating a contact angle of the liquid drop edge generated through the simulation, and then obtaining the mapping relationship among the contact angle obtained through the calculation, the liquid drop volume and a true contact angle or the mapping relationship among the contact angle obtained through the calculation, the liquid drop volume, the liquid parameter and the true contact angle; shooting a true liquid drop image and calculating a contact angle of the image; and according to the mapping relationship and the contact angle of the actual image, obtaining an accurate contact angle using an interpolation method. The above-mentioned method can effectively reduce the error of a circle fitting method, an ellipse fitting method and a θ/2 method caused by a large liquid drop volume and contact angle, thereby improving the calculation efficiency and reducing the programming difficulty.

Description

Description of the method for calculating a static contact angle

The invention belongs to the technical field of material property testing, and in particular relates to a method for calculating a static contact angle. Background technique

Hydrophobicity is an important property of the surface of the material and is a key indicator of many materials. Water repellency can be reflected by the contact angle. The contact angle is divided into a static contact angle and a dynamic contact angle. The static contact angle is the corresponding contact angle when the droplet is at rest, which satisfies the Young-Laplace equation.

The method of measuring the static contact angle is mainly the seat drop method. With the development of electronic computer technology, the liquid droplet image is often stored as an electronic image and the static contact angle is calculated by various algorithms. The earliest use is the angle method. This method is used to make the tangent of the droplet at the triple line. The half angle theorem is used to calculate the contact angle. It is easy to implement, but the error is large, and it is greatly affected by the subjective factors of the user. The /2 method obtains the apex of the droplet and the corresponding point of the triplet on the left and right sides. It assumes that the edge of the droplet on the image is part of the circle. Using these 3 points, the bottom and height of the circle inscribed triangle can be determined, based on the bottom and height. The static contact angle is calculated directly. The principle of the round fitting method is similar to the 0/2 method, and the effect of gravity based on the droplet volume is approximately negligible, assuming that the edge of the droplet on the image is part of a circle. As the droplet volume and contact angle increase, the errors of both algorithms increase. The ellipse fitting method is to assume the edge of the droplet on the image as part of the ellipse. The contact angle can be calculated by an algorithm that directly calculates the ellipse parameter. The algorithm is more accurate when the droplet volume is slightly larger and the contact angle is slightly larger. Sexuality, but as the droplet volume and contact angle increase further, the error of the algorithm also increases. Theoretically, regardless of the droplet volume and contact angle, the edge of the droplet on the image satisfies the Young-Laplace equation. The ADSA-P (axisymmetric drop shape analysis-profile) method can optimize the parameters in the equation by Newton's method. Fitting the edge of the droplet, the algorithm has a good effect, especially when the droplet volume is large and the contact angle is large, but the algorithm may have the problem that the iteration does not converge, especially the difference between the initial value and the accurate value. It may occur when it is large, and the algorithm involves three ordinary differential equations in the solution process. Both the amount of calculation and the difficulty of programming are much larger than the other algorithms mentioned above, and the algorithm is greatly affected by noise. Therefore, a considerable part of the existing contact angle measuring instrument supporting software on the market fails to implement the algorithm well, and some software only implements the method.

With the increase of droplet volume and contact angle, the round fitting method, ellipse fitting method and /2 method gradually increase the error, while the circle fitting method, ellipse fitting method and /2 method are difficult to program in these algorithms. The calculation amounts are small, so the present invention analyzes and improves them. Summary of the invention

In order to solve the above problem that the static contact angle cannot be accurately calculated under different water repellency and droplet volume, the present invention provides a method for calculating the static contact angle.

In order to achieve the above object, the technical solution proposed by the present invention is a method for calculating a static contact angle, characterized in that the method comprises:

Step 1: Based on the Young-Laplace equation, the simulation produces droplet edges at different volume and contact angles or droplets at different volumes, different contact angles, and different liquid parameters;

The liquid parameter is Δρ/;τ, where Δρ is the difference between the liquid and the gas density, : Κ is the surface tension of the liquid; and the liquid is any liquid used in the measurement of the static contact angle;

Step 2: Calculate the contact angle of the edge of the droplet produced by the simulation, and obtain the relationship between the calculated contact angle, the droplet volume and the true contact angle or the calculated contact angle, droplet volume, liquid parameter and true contact angle;

Step 3: Take a real droplet edge image and calculate the contact angle of the actual image;

Step 4: According to the calculated contact angle, the relationship between the droplet volume and the true contact angle, and the contact angle of the actual image or according to the calculated contact angle, the droplet volume, the relationship between the liquid parameter and the true contact angle, and the contact angle of the actual image, Interpolation is used to obtain an accurate contact angle.

The contact angle of the edge of the droplet produced by the calculation simulation is a circle fitting method, an ellipse fitting method or a 0/2 method.

The contact angle of the i-think actual image adopts a circle fitting method, an ellipse fitting method or a /2 method. The interpolation method is a two-point interpolation method, a linear interpolation method, or a cubic spline interpolation method.

The invention is based on the interpolation method can effectively reduce the error caused by the large droplet volume and the contact angle to the circle fitting method, the ellipse fitting method and the /2 method; compared with the ADSA-P method, the computational complexity of the optimization algorithm is avoided, and the time consuming The ADSA-P method can adapt to the calculation of different droplet volume and contact angle conditions, but the programming is difficult. The round fitting method, the ellipse fitting method or the Θ/2 method and the interpolation method of the present invention have no overly complicated iterative process. The programming difficulty is relatively small. DRAWINGS

1 is a flow chart of a method for calculating a static contact angle provided by the present invention;

Figure 2 is a flow chart of the circle fitting method;

Figure 3 is a schematic view of the edge of the droplet;

Fig. 4 is a schematic diagram showing the calculation results of the circle fitting method when the contact angle is 5°; wherein, (a) is a schematic diagram of the calculation result of the circle fitting method when the water droplet volume is 0.01 and the contact angle is 5 °, (b) Is a schematic diagram of the calculation result of the circle fitting method when the water droplet volume is 47.06 and the contact angle is 5°;

Figure 5 is a schematic diagram showing the calculation results of the circle fitting method when the contact angle is 90°; wherein (a) is a schematic diagram of the calculation result of the circle fitting method when the water droplet volume is 0.44 L and the contact angle is 90°, (b) ) is a schematic diagram of the calculation result of the 3⁄4 fitting method when the water droplet volume is 911.70 and the contact angle is 90°;

Fig. 6 is a schematic diagram showing the calculation results of the circle fitting method when the contact angle is 179°; wherein, (a) is a schematic diagram of the calculation result of the circle fitting method when the water droplet volume is 0.86 and the contact angle is 179°, (b) Is a schematic diagram of the calculation result of the circle fitting method when the water droplet volume is 1004. 78 and the contact angle is 179 °;

Fig. 7 is a schematic diagram showing the influence of the droplet volume on the calculation result of the circle fitting method; wherein (a) is the influence of the water droplet volume on the calculation result of the circle fitting method when the contact angle is 5°, and (b) the contact angle is 90°. The effect of the water droplet volume on the calculation result of the circle fitting method, (c) is the influence of the water droplet volume on the calculation result of the circle fitting method when the contact angle is 179 °; Fig. 8 is a schematic diagram of the calculation of the /2 method;

Fig. 9 is a schematic diagram showing the calculation results of the simulated droplet front edge when the contact angle increases with the droplet volume; where (a) is the contact angle r and the corrected front and back circle fitting method is simulated for the water droplet volume Edge of water Schematic of the calculation results, (b) is a schematic diagram of the calculated results of the modified front and rear circle fitting method for the simulated waterdrop edge as the contact angle is 108°, and (c) is the contact angle of 177° and increases with the water droplet volume. A schematic diagram of the calculation results of the modified watermark edge for the modified front and back circle fitting method;

Figure 10 is a schematic diagram showing the calculation result of the corrected front and rear circle fitting method for the actual droplet image;

Figure 11 is a schematic diagram showing the calculation result of the actual droplet image by the circle fitting method; wherein, (a) is the calculation result of the actual water bead image by the circle fitting method when the water droplet volume is 5 ix l, and (b) is the water droplet volume. Schematic diagram of the calculation result of the actual water bead image by the circle fitting method at 10 L;

12 is a schematic diagram of calculation results of a superhydrophobic image based on a circle fitting method and an ADSA-P method; wherein (a) is a schematic diagram of a superhydrophobic image based on a circle fitting method, and (b) is a superhydrophobic image based on an ADSA-P method. Schematic diagram of the calculation results; Figure 13 is a schematic diagram of the calculation results of the 液滴 / method for the simulated droplet edge before and after the correction of the contact angle with the increase of the droplet volume; wherein, (a) is the contact angle of 7 ° and with the water droplets The calculation results of the simulated waterdrop edge before and after the volume increase, (b) The calculation of the simulated waterdrop edge by the /2 method before and after the correction when the contact angle is 108° and the water droplet volume increases. The result is a schematic diagram, (c) is a schematic diagram of the calculation results of the simulated waterdrop edge before and after the correction of the contact angle of 177° with the increase of the water droplet volume;

Figure 14 is a schematic diagram showing the calculation results of the actual water bead image before and after the correction of the /2 method;

Figure 15 is a schematic diagram showing the calculation results of the superhydrophobic image based on the ADSA-P method. Detailed ways

The preferred embodiments are described in detail below with reference to the accompanying drawings. It is to be understood that the following description is only illustrative, and is not intended to limit the scope of the invention.

1 is a flow chart of a method for calculating a static contact angle provided by the present invention. As shown in FIG. 1, the calculation method of the static contact angle provided by the present invention includes:

Step 1: Based on the Young-Laplace equation, simulate the edge of the water droplets with different volumes and contact angles or the droplet edges of different volumes, contact angles and liquid parameters.

The static contact angle takes a point every 5° from 5° to 179° (the last point is 4° apart), and each contact angle is taken The value-time simulation produces 100 different volumes of water bead edges, requiring a bead volume of less than 1000 μL and a contact line of no more than 2 cm, resulting in a total of 3,600 bead edges, selected for the edge of the water bead volume and contact line length. analysis.

The static contact angle takes one point every 5° from 5° to 179° (the last point is 4° apart), and the droplet parameters are from 10 kg/(mN · m ² ) to 200 kg/(mN · m ² ) A point is taken every 10 kg/(mN · m ² ) in the range, and each contact angle and droplet parameter combination value is simulated to produce 100 different volume droplet edges, and the droplet volume is required to be less than 1000 uL and the contact line No more than 2 cm, a total of 72,000 droplet edges are produced, and the above-mentioned droplet edges are selected for analysis.

Step 2: Calculate the contact angle of the edge of the droplet produced by the simulation, and obtain the relationship between the calculated contact angle, the volume of the water droplet and the true contact angle or the calculated contact angle, droplet volume, liquid parameter and true contact angle.

The contact angle of the edge of the water droplet produced by the simulation is calculated by the circle fitting method or the /2 method. The process of calculating the contact angle using the circle fitting method and method is explained below.

Circle fitting method

Step 201: Obtain an initial value.

Because the difference between the initial solution and the optimal solution will seriously affect the convergence speed and even the calculation accuracy. Let the array of the edge and the ordinate of the droplet edge obtained by the simulation be («), " = 1,2,~, 2 - 1, 2,..., 2 , where (2 - 1), (2) The horizontal and vertical coordinates of the point are respectively; the coordinates of the center of the circle where the edge of the drop is located are [ o, ]. The boundary line between the gas, liquid and solid states is called the triple line, and the image corresponds to the point where the ordinate is the smallest in the edge of the droplet, and the left and right points are respectively set.

%j, k. Since the contact angle of the droplets on the surface of the material varies from 0° to 180°, the contact angle is usually distributed around 90°. Based on the hypothesis of the semicircle, the initial center and radius used by the algorithm are obtained using the following strategy:

X ₀ = (X(2j-\) + X(2k-l))/2

Y ₀ = (X(2j) + X(2k))/2 ^Q)

According to the method, the initial values of the center and the radius can be quickly obtained, and the deviation from the accurate value is usually not large. The measured results show that the method can ensure the accuracy and real-time of the measurement. Step 202: Select a least squares model and algorithm

Let the radius of the circle where the edge of the drop is located be A, then define the error of the "point" as follows:

e _n = ^{X(2n -l)-X ₀ ) ² + (X(2n) -Y ₀ ) ² -R (3) Then the total error of all points is:

1 ^N

^E = ∑ ^e (4) where, 7 ₀ , W is the variable to be determined. The Levenberg-Marquardt algorithm uses the calculation of the first-order partial derivative to obtain the calculation speed close to the second-order partial derivative, which is very suitable for the nonlinear least squares problem. Therefore, this method is chosen.

Let = ^, ,..., : J ⁷ " be the error column vector; be a column vector composed of nonlinear multivariate function variables,

W = [X ₀ , Y ₀ , R] ^T . / is the Jacobian matrix, =^~, ^ is the 'th element'; / is the 3-dimensional unit matrix. The variable parameter iteration formula is as follows -

W{k + \) = W{k)- {J{kf J{k) + λΐγ ^λ J{kf e{k) (5)

In the formula, ^: is the number of iterations; it is adjusted according to the comparison result of the two calculation errors before and after. If the error increases, λ = If the error decreases, then 1 = Ax 0.1, and the initial value of 0.1 is good.

Step 203: Calculation of contact angle

Let the coordinates of the intersection point of the left and right sides of the droplet and the horizontal plane be (x _P ), (x ₂ , y ₂ ), and the coordinates of the center of the circle obtained by the fitting are [ o, ], then the slopes of the left and right sides are calculated as follows: -

The sum of the equations is the slope of the left and right tangent lines on the arc at the triple line. The calculation formulas for the contact angles of the left and right sides are as follows: (9, =atan(^ ₁ )xl80/^,A: ₁ >0;>! =180 + atan(^)xl80/^-,^ <0

6> ₂ =180-atan( : ₂ ) l80/^,^ ₂ >0;6> ₂ =180 + atan(A: ₂ )xl80/^, : ₂ <0 (7) Calculation of the contact angle e of the droplet as follows:

Θ = {Θ _Χ +Θ ₂ )Ι2 (8) where ^ and ^ are the contact angles of the left and right sides respectively, and the value of the &^0 function is -"/2~ /2, the unit of S is (angle).

Step 204: Convergence criteria

The Levenberg-Marquardt algorithm improves the accuracy by iteration, and judging the convergence is critical to the accuracy and real-time of the algorithm. The algorithm decides whether to stop the calculation based on the change of the contact angle obtained before and after the iteration. The results of three consecutive calculations in the iterative process of the Levenberg-Marquardt algorithm tend to characterize the convergence well. Therefore, the convergence criteria are as follows: Let the contact angles obtained after the W, N + \. N + 2 iterations be ^^, A _N+1 , A _N+2 , respectively, if

^A N - ₊ ι|≤ 3⁄4 | ₊ ι - ₊₂ | ≤ Q (9) Then the iteration is terminated, where G and G are respectively set threshold values, and the invention selects 0.5° and 0.0Γ, which can be used in specific applications. According to the actual situation, the standard deviation of the contact angle calculated by using the standard under normal conditions is only about 0.5°. The circular fitting method flow chart is shown in Figure 2.

The effect of droplet volume and contact angle on the accuracy of the circle fitting method.

When the droplet volume is small, the effect of gravity can be approximately ignored, and the edge of the droplet is approximately circular on the image, and the contact angle can be obtained by a circle fitting method. As the droplet volume and contact angle increase, the effects of gravity are not negligible, and their effects on the accuracy of the circle fitting method need to be analyzed. At the same time, the calculation results are affected by the two, which is also the premise of the subsequent interpolation correction circle fitting method. The simulated droplet edge in the invention is generated based on the first-order ordinary differential equations of the Young-Laplace equation. When a drop is dropped onto a solid surface, the corresponding drop edge is as shown in Figure 3.

The Young-Laplace equation with the relationship between the radius of curvature and the pressure difference at any point on the liquid surface is as follows

Where is the internal pressure of the P point liquid and the external pressure; the interfacial tension between the liquid and the gas; R, R2 are the first and second radii of curvature of the P point, respectively.

Assume

x = x _x l R^, z = zl R^, s = s _x l (11) where x is shown in Figure 3; the length of the arc from the origin to the point; the radius of curvature at the origin .

The derived waterbead edge satisfies the following ordinary differential equations

Dx/ds = cose , dz/ds = s' 0 , άθ I ds = 2 + βζ- e I x (12) where β = ί γ ; is the angle of rotation between the tangent and the horizontal plane; g is the gravitational acceleration ; Δ _ρ is the difference in density between the liquid phase and the gas phase.

The method for solving this system of equations is the 4th-order Runge-Kutta method. Deionized water is commonly used for the measurement of static contact angle of materials. The analysis of water is taken as an example. The choice of water droplet volume varies from person to person and experimental conditions, generally not more than 1 mL, even for samples with poor hydrophobicity. Selecting a large volume of water droplets makes the water droplets too large. Therefore, the analysis selects the case where the water droplet volume is less than 1000 and the contact line is not more than 2 cm. The contact angle is very small. It is very difficult to accurately detect the contact angle. The setting is changed within the range of 5~179°, and the contact angle is taken every 5° (the last point is 4° apart). When each contact angle is taken, the simulation produces 100 different volumes of waterdrop images, which produces a total of 3600. Zhang Shuizhu image, select the image that meets the above water bead volume and contact line length for analysis. Figure 4 shows the edge of the water droplet obtained by the simulation with the static contact angle of 5 ° and the water droplet volume of 0.01 and 47.06 respectively. Figure 5 shows the static contact angle of 90 ° and the water droplet volume of 0.44 respectively. And the water droplet edge obtained by the circle fitting method generated by simulation at 911.70 μL; Figure 6 shows the water obtained by the simulation with the circle fitting method when the static contact angle is 179° and the water droplet volume is 0.86 and 1004.78 μL respectively. Bead edge. The error of the circle fitting method with increasing water droplet volume at different contact angles is critical for the modified circle fitting method. Without loss of generality, the present invention selects the case where the contact angles are 5°, 90°, and 179°, respectively. Fig. 7 shows the change of the contact angle calculated by the round fitting method as the contact angle is constant.

It can be seen from Fig. 4 that when the contact angle is small, such as 5°, the round fitting method can well fit the water bead regardless of whether the water droplet volume is small (0.01 μίί) or large (47. 06 UL). edge. 5之间。 Although the absolute value is not large, the error of the circle fitting method is approximately 0° when the water droplet volume is 0.01, and the error is about 2. 5° when the water droplet volume is 47. 06. However, the relative error is up to 50%. At this time, the good edge fitting effect does not necessarily correspond to the accurate contact angle calculation result, and it is easy to mislead the user in actual use. Therefore, the result needs further correction. It can be seen from Fig. 5 that when the contact angle is not small, such as 90°, but the volume of the water droplet is small, such as 0. 44 M l, the circle fitting method can well fit the edge of the water droplet, as can be seen from Fig. 7b. The accuracy of the contact angle calculation is also high, but if the water droplet volume is large, such as 911. 70 UL, the edge of the water droplet obtained by the circle fitting method has a large gap with the edge generated by the simulation, and the calculation error of the contact angle exceeds 50°. It can be seen from Fig. 6 that when the contact angle is 179° and the water droplet volume is 0.86, the circle fitting method has a good fitting effect, and the fitted edge is closer to the edge of the water droplet, only in the critical triple line. There is a slight deviation in the position. In actual use, it is easy to mistakenly think that the fitting effect is very good at this time. However, it can be seen from Fig. 7c that the calculation error of the contact angle is about 10° at this time, and it is easy to give the user a better round fitting method. , Calculate the illusion that the accuracy of the contact angle is high. When the volume of the water droplets increased to 1004. 78 P L, the circle fitting method obtained a large gap between the edge and the edge of the water droplet, and the calculation error of the contact angle even exceeded 115°. If the actual contact angle calculation software does not draw the edge of the fit, even if there is a certain error in the calculation result, as long as it is not too large, the user (especially the new user) may believe the calculation result of the algorithm and thus affect the contact angle measurement. The accuracy.

For the round fitting method, when the droplet volume is small, the effect of gravity can be almost ignored, and the edge of the droplet is approximately circular on the image, and the contact angle can be obtained by a circle fitting method. As the droplet volume and contact angle increase, the error of the circle fitting method increases. 2 method

When a drop is dropped onto a solid surface, the corresponding drop edge is as shown in Figure 3.

The relationship between the radius of curvature and the pressure difference at any point on the liquid surface is as follows: Young- Laplace equation (is)

Where A is the internal pressure of the liquid at point P and the external pressure; is the interfacial tension between the liquid and the gas; and ^ are the first and second radii of curvature of point p, respectively.

Assume

= X, / Ro , z = z _x l R^ , s = s _x f (14) where, as shown in Figure 3; the length of the arc from the origin to the point; the curvature at the origin half

Cbc/ds = cosO , dz I ds = smG , άθ I ds = 2 +

I x (15) where β = gp / γ is the angle of rotation between the tangential line of point P and the horizontal plane; is the acceleration of gravity; Δ _ρ is the density difference between the liquid phase and the gas phase.

To solve this equation, the fourth-order Runge-Kutta method is used.

The effect of gravity is ignored when the droplet volume is small, which is a part of the circle at the upper edge of the image, and the schematic diagram of the calculation is shown in Fig. 8. Let the droplet have a height of Λ on the solid surface and the diameter of the contact surface with the solid is c/, then the contact angle is calculated as:

6> = 2atan(2/z/<a?) l80/^ (16) where the value of the atari function is -π /2~ π /2.

Current contact angle measurements often store droplet images in an electronic format. Let the coordinates of points C and C in Fig. 8 be (x), (x ₂ , _ ₂ ) and (x ₃ , _ ₃ ), respectively, then the formula for the sum is calculated as follows: a = -( iy ₂ ) ^/ (xi -x ₂ ) (17)

b = \ (18)

c = -{ax _x + y _x ) (19)

(ax ₃ + y ₃ + c) /(a ² +b ^z ) (20) d = {{x _x - x ₂ f + {y _x - y ₂ ) ² r (21) For the method, when the droplet volume is small, the effect of gravity can be approximately ignored, and the edge of the droplet is approximately circular on the image. , The contact angle can be obtained by the 0 /2 method. As the droplet volume and contact angle increase, the error increases gradually. It is necessary to correct the calculation results of the /2 method.

Step 3: Take the actual image of the real droplet and calculate the contact angle of the actual image.

When calculating the contact angle of the actual image, the circle fitting method or method is employed as described above.

Step 4: According to the calculated contact angle, the relationship between the droplet volume and the true contact angle, and the contact angle of the actual image or according to the calculated contact angle, the droplet volume, the relationship between the liquid parameter and the true contact angle, and the contact angle of the actual image, Interpolation is used to obtain an accurate contact angle. The interpolation method can use two-point interpolation, linear interpolation or cubic spline interpolation.

Circle fitting method embodiment

Embodiment 1

In order to make the experimental results more convincing, the static contact angles were chosen to be 7°, 108° and 177°, respectively, and the water droplet volume was also different from the calculated one. The calculation results of the original circle fitting method and the modified circle fitting method proposed by the present invention are shown in Fig. 9.

It can be seen from Fig. 9 that when the original circle fitting method is adopted, the algorithm error gradually increases with the increase of the water droplet volume, and the water droplet volume is less than 1000 UL and the contact line length is not more than 2 cm, when the actual contact angle is 7 respectively. The maximum error of the original circle fitting method at °, 108° and 177° is 3.52°, a 64.54° and a 115.66°. After the correction by the algorithm of the present invention, even the calculation result of the volume increase algorithm maintains a good stability, and the maximum values of the calculated error amplitudes are 0. 12°, 0. 90°, and 0.67°, respectively. ; Standard deviations are 0. 03°, 0. 23° and 0. 26°. It can be seen that the modified circle fitting method proposed by the invention can accurately calculate the static contact angle under the variation of the contact angle and the large volume of the water droplet volume, and greatly improves the accuracy of the static contact angle measurement.

Embodiment 2

Deionized water of 5, 10, 20, 50, 100, 200, 500 and 1000 was dropped on the silicone rubber sample. Round The results of the legal calculation and the corrected round fitting method proposed by the present invention are shown in Fig. 10. The edges and contact angles obtained by the round fitting method for the true water bead image when the water droplet volume is 5 and 100 PL, respectively, are shown in Fig. 11.

It can be seen from Fig. 10 that for the real water bead image, the round fitting method error increases with the increase of the water droplet volume, and the specific values agree well with the simulation results of Fig. 7b. The modified circle fitting method proposed by the present invention varies the contact angle calculated under different water bead volumes around 109°, the maximum deviation is 4.14°, and the standard deviation is 2.63°. Obviously, the calculated results of the modified algorithm are consistent with the same hydrophobicity of the same silicone rubber sample, so it has higher accuracy. The fluctuation of the contact angle obtained by the modified circle fitting method under different water droplet volumes is caused by the following reasons: 1) There is a certain hysteresis in the contact angle measurement, which causes some fluctuations between the different measurement results; 2) due to manual Determining the edge point of the water droplet causes the calculation result of the circle fitting method to have a certain error; 3) The correction algorithm itself also has a certain error. It can be seen from Fig. 11a that the edge of the water droplet on the image has little difference from the circular equation when the size of the small water droplet is small, and the circle fitting method has a small error, and the fitting edge is very close to the edge of the real water bead. It can be seen from Fig. 1 ib that the edge of the water droplet on the image has a large difference between the edge of the water droplet and the circular equation, and the circle fitting method has a large error, and the edge of the fitting has a large gap with the edge of the real water bead. This is in agreement with the results of Figures 5 and 6 of the simulation, and also supports the rule that the round fitting method increases with the increase of the water droplet volume.

Embodiment 3

There is a super-hydrophobic sample, about 9 drops of deionized water on it, and the obtained image is calculated by the circle fitting method and the ADSA-Ρ method as shown in Fig. 12.

It can be seen from Fig. 12 that when the static contact angle is large, there is still a small error in the round fitting method when the water droplet volume is not too large, and there is a significant difference between the obtained waterdrop edge and the real waterdrop edge, especially in the In the vicinity of the key triple line, it is known from the subsequent analysis that the error is about 18.62°. The ADSA-Ρ method can well fit the edge of the water droplet, and the contact angle is 166. 24°. The accuracy is guaranteed, and it can easily calculate the interfacial tension. However, the principle is more complicated, the programming is difficult, and the calculation time is longer. For example, Figure 12 uses the circle fitting method, the modified circle fitting method, and the ADSA-P method (using a fast algorithm to obtain the initial value, and the water is not considered. The calculation time for the bead tilt and vertex coordinates is 14.6 ms, 97. 3 111 ₅ and 241.4 ms, respectively. The ADSA-P method is more conscientious in calculating the time difference when calculating the contact angle for a large number of images. Obviously, the modified circle fitting method proposed by the present invention is slower than the uncorrected algorithm, but faster than the ADSA-P method. For the image, the contact angle calculated by the modified circle fitting method is 166.41 °, which is 166. 24 ° difference from the ADSA-P method. It is roughly 0.17°, which is much smaller than the error of the original circle fitting method, and its accuracy is guaranteed. The above calculation results show that the modified circle fitting method can also obtain more accurate calculation results when calculating the contact angle in the case of super-hydrophobicity where the algorithm such as circle fitting is prone to large errors.

Embodiment 4

In this case, it is not necessary to fix the liquid type to water, and it is necessary to know the volume of the droplet, the calculated contact angle and the liquid parameters. The true contact angle of the droplet is 100. 21 °, the volume is 266. 08 L, and the droplet parameter is 13745. 70 kg / (mN ' m ² ).

When the original circle fitting method is used, the calculation result is 62.88°, and the error is 37.33°. After the correction by the algorithm of the present invention, the calculation result is 100.96°, and the error is only 0.75°. It can be seen that the present invention can accurately calculate the static contact angle for droplet images produced by different liquids.

/2 method embodiment

Embodiment 1

In order to make the experimental results more convincing, the static contact angles were chosen to be 7°, 108° and 177°, respectively, and the water droplet volume was also different from the above calculated conditions. The calculation results of the original method and the correction method proposed by the present invention are shown in Fig. 13.

It can be seen from Fig. 13 that when the original /2 method is adopted, the algorithm error gradually increases with the increase of the water droplet volume, and the water droplet volume is less than 1000 and the contact line length is not more than 2 cm, when the actual contact angle is 7°. The maximum error of the original/2 method at 108° and 177° is 3.07°, a 56.92° and a 103.18°, respectively. After the correction by the algorithm of the present invention, the calculation result of the volume increase algorithm maintains a good stability, and the maximum values of the calculated error amplitudes are 0. 09°, 0. 60° and 0.55°, respectively. ; The standard deviation is 0.03. , 0. 18° and 0. 23°. It can be seen that the correction /2 method proposed by the invention can accurately calculate the static contact angle under the variation of the contact angle and the large volume of the water droplet, and greatly improves the accuracy of the static contact angle measurement.

Embodiment 2

Deionized water of 5, 10, 20, 50, 100, 200, 500 and 1000 was dropped on the silicone rubber sample. The calculation result of the θ 1 method and the calculation result of the modified 0 /2 method proposed by the present invention are as shown in Fig. 14.

As can be seen from Fig. 14, for the real water bead image, the S/2 method error gradually increases as the water droplet volume increases. Ben The singularity of the difference is 7. 03 °, the standard deviation is 4.2. Obviously, the calculated result of the modified algorithm is consistent with the same hydrophobicity of the same silicone rubber sample, so it has higher accuracy. The fluctuation of the contact angle obtained by the correction method under different water droplet volume is mainly due to the following reasons: 1) There is a certain hysteresis in the contact angle measurement, which leads to certain fluctuations between different measurement results; 2) due to manual determination The edge point of the water droplet causes the calculation result of the S /2 method to have a certain error; 3) The correction algorithm itself also has a certain error.

Embodiment 3

There is a superhydrophobic sample, and about 9 deionized water is dropped thereon, and the obtained image is calculated by the ADSA-P method as shown in Fig. 15.

As can be seen from Fig. 15, the ADSA-P rule can well fit the edge of the water bead, and the contact angle is 166. 24°. The accuracy is guaranteed. At the same time, it can conveniently calculate the interfacial tension, and the static contact angle is calculated. 148. 31 ° , from the subsequent analysis, its error is about 17.93 °, the error is large. The ADSA-P method is more complicated, difficult to program, and has a longer calculation time, such as Figure 15, Usage, Correction, and ADSA-P (using a fast algorithm to obtain initial values, without considering waterdrop tilt and vertices). The calculation time for the coordinates is 0. 14 ms, 76. 2 ms and 244.1 ms, and the ADSA-P method is more obvious when calculating the contact angle for a large number of images. Obviously, the modified 0/2 method proposed by the present invention is slower than the uncorrected algorithm, but much faster than the ADSA-P method. For the image, the contact angle calculated by the modified θ I method is 167.59°, which is about 166.24° from the ADSA-P method, which is about 1.35°, which is much smaller than the original 2 method error. Sex is guaranteed. The above calculation results show that the correction ΘΙ method can also obtain more accurate calculation results when the contact angle is calculated in the superhydrophobic case where the /2 method is prone to large errors.

The above is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily think of changes or within the technical scope disclosed by the present invention. Alternatives are intended to be covered by the scope of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

Claim

A method for calculating a static contact angle, characterized in that the method comprises:

Step 1: Based on the Young-Laplace equation, the simulation produces droplet edges of liquids at different volumes and contact angles or droplets of different volumes, different contact angles and different liquid parameters; the liquid parameter is Δ ? /; κ Where Δρ is the difference between the liquid and the gas density; Τ is the surface tension of the liquid; the liquid is any liquid used in the measurement of the static contact angle;

The method for calculating a static contact angle according to claim 1, wherein the contact angle of the edge of the droplet generated by the calculation simulation is a circle fitting method, an ellipse fitting method or a method.

The method of calculating a static contact angle according to claim 1, wherein the calculating the contact angle of the actual image is a circle fitting method, an ellipse fitting method or a method.

4. The method of calculating a static contact angle according to claim 1, wherein the interpolation method is a two-point interpolation method, a linear interpolation method, or a cubic spline interpolation method.