CN102507391A

CN102507391A - Method for detecting static contact angle of hydrophilic water bead

Info

Publication number: CN102507391A
Application number: CN2011103438283A
Authority: CN
Inventors: 徐志钮; 律方成
Original assignee: North China Electric Power University
Current assignee: North China Electric Power University
Priority date: 2011-11-03
Filing date: 2011-11-03
Publication date: 2012-06-20

Abstract

The invention discloses a method for detecting the static contact angle of a hydrophilic water bead, belonging to the technical field of the detection of the surface energies of materials. The method comprises the following steps of: acquiring an image of the water bead; selecting a circle fitting algorithm or an ellipse fitting algorithm to calculate the estimated value of the static contact angle of the water bead; and selecting the circle fitting algorithm or the ellipse fitting algorithm to calculate the exact value of the static contact angle of the water bead according to the volume of the water bead and the calculated estimated value of the static contact angle of the water bead. According to the method, more accurate contact angles can be obtained through selecting appropriate curve equations for water beads with different contact angles and volumes and carrying out fitting.

Description

Method for detecting static contact angle of water drop in hydrophilic state

Technical Field

The invention belongs to the technical field of material surface energy detection, and particularly relates to a method for detecting a static contact angle of a water droplet in hydrophilic property.

Background

The surface energy is a key property of the material, but the surface energy cannot be directly measured, and the surface energy of the material can be obtained according to the contact angle. How to accurately measure the contact angle has important theoretical significance and practical engineering application value in the fields of relevant subjects such as material science, life science, chemical industry, medical industry, semiconductor industry, ink industry, textile industry, coating industry and the like.

The problem of calculating the contact angle is involved after a liquid drop image is obtained through shooting by a contact angle detection system, the edges of the liquid drop on the image all follow a Young-Laplace equation, but the equations which can be approximately expressed by the edges of the liquid drop are different under different volumes and hydrophobic properties. When the water drop volume is small and the contact angle is not large, the difference between the water drop edge and the circular equation is small. With the increase of the volume of the water drop and the increase of the contact angle, the difference between the edge of the water drop and the equation of a circle is larger and closer to the equation of an ellipse. When the volume of the water drop and the contact angle are further increased, the edge of the water drop is gradually far away from the ellipse equation, and the Young-Laplace equation can be used for well representing the edge of the water drop. When the contact angle is smaller, although the edge of the water drop obeys the ellipse equation, the variable number of the ellipse equation is larger than that of the circle equation, and the calculation accuracy by the circle equation is higher. While for an elliptic curve, the accuracy of fitting with an ellipse is higher if the higher its eccentricity, the larger the contact angle. The water drop obeys the Young-Laplace equation on the solid surface, and obviously has certain deviation from the circle or ellipse equation when the volume and the contact angle of the water drop are both large. When the contact angle is actually measured, the drop volume may vary from a few μ L (microliter) to hundreds of μ L (microliter), and the contact angle of the material to be measured may be large or small. At present, no contact angle algorithm can accurately calculate the contact angle when the material is in a hydrophilic state and at different water drop volumes and contact angles.

Disclosure of Invention

The invention aims to provide a method for detecting a static contact angle of a water drop in hydrophilicity, aiming at solving the problem that the contact angle of the water drop in the hydrophilicity can not be accurately calculated in the prior art.

In order to achieve the above object, the present invention provides a method for detecting a static contact angle of a water droplet in a hydrophilic state, comprising:

step 1: acquiring a water drop image;

step 2: calculating an estimated value of the static contact angle of the water drop according to the volume of the water drop and by selecting a circle fitting algorithm or an ellipse fitting algorithm;

and step 3: and (3) selecting a circle fitting algorithm or an ellipse fitting algorithm to calculate the accurate value of the static contact angle of the water drop according to the volume of the water drop and the estimated value of the static contact angle of the water drop calculated in the step (2).

Specifically, in the step 3, when the estimated value of the static contact angle of the water drop is less than or equal to 15 degrees (angle), a circle fitting algorithm is selected to calculate the accurate value of the static contact angle of the water drop;

when the estimated value of the static contact angle of the water drop is larger than 15 degrees (angle) and smaller than or equal to 70 degrees (angle) and the volume of the water drop is smaller than or equal to 7 mu L, selecting a circle fitting algorithm to calculate the accurate value of the static contact angle of the water drop;

when the estimated value of the static contact angle of the water drop is larger than 15 degrees (angle) and smaller than or equal to 70 degrees (angle) and the volume of the water drop is larger than 7 mu L, selecting an ellipse fitting algorithm to calculate the accurate value of the static contact angle of the water drop;

and when the estimated value of the static contact angle of the water drop is larger than 70 degrees (angle) and smaller than or equal to 90 degrees, selecting an ellipse fitting algorithm to calculate the accurate value of the static contact angle of the water drop.

The selecting a circle fitting algorithm to calculate the estimated value/accurate value of the static contact angle of the water drop specifically comprises the following steps:

step 101: determining the initial value of the circle center and the initial value of the radius of the edge of the water drop, and enabling the iteration number i to be 1;

step 102: calculating the initial value of the contact angle of the water drop by utilizing a triple tangent method, and marking the initial value as A₀；

Step 103: calculating the ith iteration value and the ith iteration value of the radius of the circle center of the edge of the water drop by using a least square model and a Levenberg-Marquardt algorithm;

step 104: calculating the ith iteration value of the water drop contact angle by using a triplet tangent method, and recording the iteration value as A_i；

Step 105: judging whether the ith iteration value of the water droplet contact angle meets | A_i-1-A_i|≤C₁And | A_i-A_i+1|≤C₂If the iteration value of the ith time of the water drop contact angle satisfies | A_i-1-A_i|≤C₁And | A_i-A_i+1|≤C₂If yes, go to step 106; otherwise, let i equal to i +1Step 103 is executed; wherein, C₁Is a first set threshold value, C₂Is a second set critical value;

step 106: the iteration is terminated, A_i+1As an estimate/exact value of the static contact angle of the water droplet.

The method for calculating the initial value/ith iteration value of the water drop contact angle by using the triple tangent method specifically comprises the following steps:

step 201: using formula k₁＝-(x₁-x₀)/y₁-y₀) And k₂＝-(x₂-x₀)/(y₂-y₀) Respectively calculating the slope of a left tangent and the slope of a right tangent on the arc at the triple line;

wherein (x)₀，y₀) Coordinates of initial value of circle center/iteration value of i (x)₁，y₁) And (x)₂，y₂) Respectively the horizontal and vertical coordinates of the intersection point of the left edge of the water drop and the horizontal plane and the horizontal and vertical coordinates of the intersection point of the right edge of the water drop and the horizontal plane;

step 202: using formulas

<math> <mrow> <msub> <mi>θ</mi> <mn>1</mn> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mi>arctan</mi> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>×</mo> <mn>180</mn> <mo>/</mo> <mi>π</mi> <mo>,</mo> </mtd> <mtd> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>&GreaterEqual;</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>180</mn> <mo>+</mo> <mi>arctan</mi> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>×</mo> <mn>180</mn> <mo>/</mo> <mi>π</mi> <mo>,</mo> </mtd> <mtd> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo><</mo> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math>

Calculating a left contact angle on the circular arc at the triple line; using formulas

<math> <mrow> <msub> <mi>θ</mi> <mn>2</mn> </msub> <mo>=</mo> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mn>180</mn> <mo>-</mo> <mi>arctan</mi> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>×</mo> <mn>180</mn> <mo>/</mo> <mi>π</mi> <mo>,</mo> </mtd> <mtd> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>&GreaterEqual;</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mi>arctan</mi> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>×</mo> <mn>180</mn> <mo>/</mo> <mi>π</mi> <mo>,</mo> </mtd> <mtd> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo><</mo> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math>

Calculating a right contact angle on the circular arc at the triple line;

step 203: using the formula theta ═ theta₁+θ₂) And/2, calculating the initial value of the water drop contact angle/the ith iteration value.

The step of calculating the estimated value/accurate value of the static contact angle of the water drop by selecting the ellipse fitting algorithm specifically comprises the following steps:

step 301: using the formula E_min＝min(|Bm|²) Calculating parameters of an elliptic curve equation;

wherein,

B = {[n_{1}^{T}, n_{2}^{T}, . . ., n_{N}^{T}]}^{T},

n_{i} = [x_{i}^{2}, x_{i} y_{i}, y_{i}^{}, x_{i}, y_{i}, 1],

x_iand y_iAre respectively water bead edgesThe abscissa and the ordinate of the selected point on the edge, i is 1, 2, …, and N, N is the number of the selected points on the edge of the water drop;

m＝[a，b，c，d，e，f]^Ta, b, c, d, e and f are elliptic curve equations ax, respectively²+bxy+cy²A parameter of + dx + ey + f ═ 0;

step 302: determining a major semi-axis, a minor semi-axis, a center and an inclination angle of the ellipse according to parameters of an elliptic curve equation;

step 303: and calculating the estimated value/accurate value of the static contact angle of the water drop according to the major semi-axis, the minor semi-axis, the center and the inclination angle of the ellipse.

The step 303 specifically includes:

step 401: using formulas

Respectively calculate (X)_L1，Y_L1) And (X)_R1，Y_R1) (ii) a Wherein (X)_L，X_L) And (X)_R，Y_R) Respectively are the horizontal and vertical coordinates of the lowest points on the left side and the right side of the edge of the water drop, and are also the horizontal and vertical coordinates of corresponding points on the left side and the right side of the triple line of the ellipse; (X)₀，Y₀) Is the abscissa and ordinate of the center of the ellipse, theta₀Is an elliptical inclination angle;

step 402: using formulas

<math> <mrow> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <msub> <mi>θ</mi> <mrow> <mi>L</mi> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mn>180</mn> <mi>π</mi> </mfrac> <mo>[</mo> <mi>a</mi> <mi>tan</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>-</mo> <msub> <mi>L</mi> <mi>S</mi> </msub> </mrow> <mrow> <msub> <mi>L</mi> <mi>L</mi> </msub> <mi>tan</mi> <msub> <mi>θ</mi> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>]</mo> <mo>,</mo> <msub> <mi>Y</mi> <mrow> <mi>L</mi> <mn>1</mn> <mo>&GreaterEqual;</mo> <mn>0</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>θ</mi> <mrow> <mi>L</mi> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mn>180</mn> <mi>π</mi> </mfrac> <mo>[</mo> <mi>π</mi> <mo>+</mo> <mi>a</mi> <mi>tan</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>-</mo> <msub> <mi>L</mi> <mi>S</mi> </msub> </mrow> <mrow> <msub> <mi>L</mi> <mi>L</mi> </msub> <mi>tan</mi> <msub> <mi>θ</mi> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>]</mo> <mo>,</mo> <msub> <mi>Y</mi> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </msub> <mo><</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>θ</mi> <mrow> <mi>R</mi> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mn>180</mn> <mi>π</mi> </mfrac> <mo>[</mo> <mi>a</mi> <mi>tan</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mi>L</mi> <mi>S</mi> </msub> <mrow> <msub> <mi>L</mi> <mi>L</mi> </msub> <mi>tan</mi> <msub> <mi>θ</mi> <mrow> <mi>R</mi> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>]</mo> <mo>,</mo> <msub> <mi>Y</mi> <mrow> <mi>R</mi> <mn>1</mn> </mrow> </msub> <mo>&GreaterEqual;</mo> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>θ</mi> <mrow> <mi>R</mi> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mn>180</mn> <mi>π</mi> </mfrac> <mo>[</mo> <mi>π</mi> <mo>+</mo> <mi>a</mi> <mi>tan</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mi>L</mi> <mi>S</mi> </msub> <mrow> <msub> <mi>L</mi> <mi>L</mi> </msub> <mi>tan</mi> <msub> <mi>θ</mi> <mrow> <mi>R</mi> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>θ</mi> <mn>0</mn> </msub> <mo>]</mo> <mo>,</mo> <msub> <mi>Y</mi> <mrow> <mi>R</mi> <mn>1</mn> </mrow> </msub> <mo><</mo> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math>

Respectively calculating left contact angle reference value theta on the triple line of the ellipse_L2And a reference value theta of right contact angle_R2(ii) a Wherein, theta_L1＝angle(jY_L1/L_S+X_L1/L_L)，θ_R1＝angle(jY_R1/L_S+X_R1/L_L)，L_LIs an ellipse long semi-axis, L_SElliptical minor semi-axis, angle (A) is a function of the phase of the complex A;

step 403: using the formula k ═ Y_L1-Y_R1)/(X_L1-X_R1) Calculating the slope k' of the solid horizontal plane;

step 404: using formulas

Respectively calculating a left contact angle and a right contact angle on the triple line; wherein, theta_LLeft side contact angle on triple line, θ_RRight contact angle on the triple line;

step 405: using the formula theta ═ theta_L+θ_R) And/2 calculating the estimated value/accurate value of the static contact angle of the water drop.

According to the invention, a more accurate contact angle can be obtained by selecting and fitting a proper curve equation for water drops with different contact angles and volumes.

Drawings

FIG. 1 is a flow chart of a method for detecting the static contact angle of a water droplet in a hydrophilic state;

FIG. 2 is a schematic illustration of the effect of noise on the accuracy of a circle fitting algorithm and an ellipse fitting algorithm;

wherein, (a) is a schematic diagram of the influence of noise on the accuracy of a circle fitting algorithm and an ellipse fitting algorithm when the contact angle and the water drop volume are 5 degrees and 1.06 muL respectively;

(b) the schematic diagram is that the noise affects the accuracy of the circle fitting algorithm and the ellipse fitting algorithm when the contact angle and the water drop volume are 70 degrees and 5.05 mu L respectively;

(c) the schematic diagram is that when the contact angle and the water drop volume are respectively 90 degrees and 18.80 mu L, the noise affects the accuracy of the circle fitting algorithm and the ellipse fitting algorithm;

FIG. 3 is a schematic diagram of the edges of a water droplet obtained by fitting a circle fitting algorithm with no noise and with noise to an ellipse fitting algorithm;

wherein, (a) is a schematic diagram of the edge of the water drop obtained by fitting a circle fitting algorithm and an ellipse fitting algorithm when the contact angle and the volume of the water drop are respectively 5 degrees and 1.06 muL and no noise is contained;

(b) the contact angle and the water drop volume are respectively 5 degrees and 1.06 mu L, and the water drop edge is obtained by fitting a circle fitting algorithm and an ellipse fitting algorithm when noise is contained;

(c) the schematic diagram of the water drop edge is obtained by fitting a circle fitting algorithm and an ellipse fitting algorithm when the contact angle and the water drop volume are respectively 50 degrees and 4.95 mu L and no noise exists;

(d) the schematic diagram of the water drop edge is obtained by fitting a circle fitting algorithm and an ellipse fitting algorithm when the contact angle and the water drop volume are respectively 50 degrees and 4.95 mu L and noise is contained;

(e) the schematic diagram of the water drop edge is obtained by fitting a circle fitting algorithm and an ellipse fitting algorithm when the contact angle and the water drop volume are respectively 90 degrees and 18.80 mu L and no noise exists;

(f) the schematic diagram of the water drop edge is obtained by fitting a circle fitting algorithm and an ellipse fitting algorithm when the contact angle and the water drop volume are respectively 90 degrees and 18.80 mu L and noise is contained;

FIG. 4 is a schematic diagram of the effect of drop volume on the accuracy of the fit results of the circle fitting algorithm and the ellipse fitting algorithm at different contact angles;

wherein, (a) is a schematic diagram of the influence of the volume of water drops on the accuracy of the fitting results of the circle fitting algorithm and the ellipse fitting algorithm when the contact angle is 5 degrees;

(b) the method is a schematic diagram of the influence of the volume of water drops on the accuracy of the fitting results of the circle fitting algorithm and the ellipse fitting algorithm when the contact angle is 10 degrees;

(c) the method is a schematic diagram of the influence of the volume of water drops on the accuracy of the fitting results of the circle fitting algorithm and the ellipse fitting algorithm when the contact angle is 15 degrees;

(d) the method is a schematic diagram of the influence of the volume of water drops on the accuracy of the fitting results of the circle fitting algorithm and the ellipse fitting algorithm when the contact angle is 20 degrees;

(e) the schematic diagram is that when the contact angle is 25 degrees, the volume of water drops influences the accuracy of the fitting results of the circle fitting algorithm and the ellipse fitting algorithm;

(f) the method is a schematic diagram of the influence of the volume of water drops on the accuracy of the fitting results of the circle fitting algorithm and the ellipse fitting algorithm when the contact angle is 30 degrees;

(g) the method is a schematic diagram of the influence of the volume of water drops on the accuracy of the fitting results of the circle fitting algorithm and the ellipse fitting algorithm when the contact angle is 35 degrees;

(h) the method is a schematic diagram of the influence of the volume of water drops on the accuracy of the fitting results of the circle fitting algorithm and the ellipse fitting algorithm when the contact angle is 40 degrees;

(i) the method is a schematic diagram of the influence of the volume of water drops on the accuracy of the fitting results of the circle fitting algorithm and the ellipse fitting algorithm when the contact angle is 45 degrees;

(j) the method is a schematic diagram of the influence of the volume of water drops on the accuracy of the fitting results of the circle fitting algorithm and the ellipse fitting algorithm when the contact angle is 50 degrees;

(k) the schematic diagram is that when the contact angle is 55 degrees, the volume of water drops influences the accuracy of the fitting results of the circle fitting algorithm and the ellipse fitting algorithm;

(l) The method is a schematic diagram of the influence of the volume of water drops on the accuracy of the fitting results of the circle fitting algorithm and the ellipse fitting algorithm when the contact angle is 60 degrees;

(m) is a schematic diagram of the influence of the volume of water drops on the accuracy of the fitting results of the circle fitting algorithm and the ellipse fitting algorithm when the contact angle is 65 degrees;

(n) is a schematic diagram of the influence of the volume of water drops on the accuracy of the fitting results of the circle fitting algorithm and the ellipse fitting algorithm when the contact angle is 70 degrees;

(o) is a schematic diagram of the effect of the volume of water droplets on the accuracy of the fitting results of the circle fitting algorithm and the ellipse fitting algorithm when the contact angle is 75 degrees;

(p) is a schematic diagram of the influence of the volume of water drops on the accuracy of the fitting results of the circle fitting algorithm and the ellipse fitting algorithm when the contact angle is 80 degrees;

(q) is a schematic diagram of the influence of the volume of water droplets on the accuracy of the fitting results of the circle fitting algorithm and the ellipse fitting algorithm when the contact angle is 85 degrees;

(r) is a schematic diagram of the influence of the volume of water drops on the accuracy of the fitting results of the circle fitting algorithm and the ellipse fitting algorithm when the contact angle is 90 degrees;

FIG. 5 is a comparison of fitting results of a circle fitting algorithm and an ellipse fitting algorithm;

wherein, (a) is a comparison graph of fitting results of a circle fitting algorithm and an ellipse fitting algorithm when the volume of water droplets and the contact angle are 0.0004 muL and 5 degrees respectively;

(b) is a comparison graph of fitting results of a circle fitting algorithm and an ellipse fitting algorithm when the volume of water drops and the contact angle are respectively 7.6 mu L and 5 degrees;

(c) is a comparison graph of fitting results of a circle fitting algorithm and an ellipse fitting algorithm when the volume of water drops and the contact angle are respectively 0.51 mu L and 90 degrees;

(d) is a comparison graph of fitting results of a circle fitting algorithm and an ellipse fitting algorithm when the volume of water drops and the contact angle are 173.5 mu L and 90 degrees respectively;

FIG. 6 is a comparison graph of fitting results of a circle fitting algorithm and an ellipse fitting algorithm for different water drop volumes with the same contact angle;

wherein, (a) is a comparison graph of fitting results of a circle fitting algorithm and an ellipse fitting algorithm when the volume of water drops is 2 mu L;

(b) is a comparison graph of fitting results of a circle fitting algorithm and an ellipse fitting algorithm when the volume of water drops is 5 mu L;

(c) is a comparison graph of fitting results of a circle fitting algorithm and an ellipse fitting algorithm when the volume of water drops is 10 mu L;

(d) is a comparison graph of fitting results of a circle fitting algorithm and an ellipse fitting algorithm when the volume of water drops is 20 mu L;

FIG. 7 is a graph of bead edge fitting calculations;

wherein, (a) is a calculation result graph of a circle fitting algorithm and an ellipse fitting algorithm when the edge of the water drop is automatically extracted;

(b) a calculation result graph of a circle fitting algorithm after identifying the edge of the water drop by naked eyes;

(c) a calculation result graph of an ellipse fitting algorithm after identifying the edge of the water drop by naked eyes;

FIG. 8 is a comparison graph of fitting results of the circle fitting algorithm and the ellipse fitting algorithm.

Detailed Description

The preferred embodiments will be described in detail below with reference to the accompanying drawings. It should be emphasized that the following description is merely exemplary in nature and is not intended to limit the scope of the invention or its application.

Example 1

FIG. 1 is a flow chart of a method for detecting hydrophilic static contact angle of water drops. In fig. 1, a method for detecting a static contact angle of a water droplet in a hydrophilic state is characterized by comprising:

step 1: and acquiring a water drop image.

The water drop image is shot by a digital camera or a lens, an industrial camera and an image acquisition card, and the plane of the camera is vertical to the plane of the material.

Step 2: and calculating the estimated value of the static contact angle of the water drop according to the volume of the water drop and by selecting a circle fitting algorithm or an ellipse fitting algorithm.

And calculating the estimated value of the static contact angle of the water drop by adopting one of a circle fitting algorithm or an ellipse fitting algorithm.

Wherein, selecting a circle fitting algorithm to calculate the water drop static contact angle estimation value specifically comprises:

step 101: and determining the initial value of the circle center and the initial value of the radius of the edge of the water drop.

Since the difference between the initial solution and the optimal solution will seriously affect the convergence speed and even the calculation accuracy. Setting an array consisting of horizontal and vertical coordinates of the obtained edge points of the water drop as X (N), wherein N is 1, …, 2-1, 2i, … 2N, and X (2i-1) and X (2i) are the horizontal and vertical coordinates of the ith point respectively; the center coordinate of the circle where the edge of the water drop is located is [ X ]₀，Y₀]. The boundary line of gas, liquid and solid states is called triple line, which is the point with the minimum vertical coordinate in the edge of the water drop corresponding to the image, and the left and right side points are respectively provided with serial numbers j and k. Because the contact angle of the water drop on the surface of the material is changed within the range of 0-180 degrees, the contact angles are distributed around 90 degrees under the normal condition, and the initial circle center and the radius used by the algorithm are obtained by the following strategies based on the assumption of a semicircle:

X₀＝(X(2j-1)+X(2k-1))/2；Y₀＝(X(2j)+X(2k))/2 (1)

according to the method, the initial values of the circle center and the radius can be quickly obtained, the deviation of the values from the accurate values is usually not large, and the actual measurement result shows that the method can guarantee the accuracy and the real-time performance of measurement. The number of iterations i is set to 1.

Step 102: calculating the initial value of the water drop contact angle by using a triple tangent method, and marking the initial value as A₀。

The coordinates of the intersection points of the left and right side edges of the water drop and the horizontal plane are respectively (x)₁，y₁)、(x₂，y₂) And the circle center coordinate obtained by fitting is [ X ]₀，Y₀]Then, the left and right slopes are calculated as follows:

k₁＝-(x₁-X₀)/(y₁-Y₀)

k₂＝-(x₂-X₀)/(y₂-Y₀) (3)

in the formula k₁And k₂The slopes of the left and right tangents on the arc at the triple line are respectively. The calculation formula of the contact angles of the left side and the right side is as follows:

θ₁＝atan(k₁)×180/π，k₁≥0；θ₁＝180+atan(k₁)×180/π，k₁＜0；

θ₂＝180-atan(k₂)×180/π，k₂≥0；θ₂＝-atan(k₂)×180/π，k₂＜0； (4)

the contact angle θ of the water drop is calculated as follows:

θ＝(θ₁+θ₂)/2 (5)

in the formula [ theta ]₁And theta₂The contact angles of the left side and the right side are respectively, and the value range of the atan function is

The unit of θ is ° (angle).

Step 103: and calculating the ith iteration value of the circle center of the edge of the water drop and the ith iteration value of the radius by using a least square model and a Levenberg-Marquardt algorithm.

The error defining the nth point is as follows:

e_{n} = \sqrt{{(X (2 n - 1) - X_{0})}^{2} + {(X (2 n) - Y_{0})}^{2}} - R - - - (6)

the total error for all points is:

in the formula X₀、Y₀And R is a variable to be solved. The Levenberg-Marquardt algorithm obtains a calculation speed close to the second-order partial derivative by using the calculation amount of the first-order partial derivative, and is very suitable for the nonlinear least square problem, so the method is selected.

Let e be ═ e₁，e₂，…e_n]^TIs an error column vector; w is a column vector consisting of nonlinear multivariate function variables, W ═ X₀，Y₀，R]^T(ii) a J is a Jacobian matrix and is a Jacobian matrix,

W_jis the jth element in W; and I is a 3-dimensional unit array. The variable parameter iterative formula is as follows:

W(k+1)＝W(k)-(J(k)^TJ(k)+λI)^-1J(k)^Te(k) (8)

wherein k is the number of iterations; lambda is adjusted according to the comparison result of the errors calculated in two times, if the error increases, lambda is equal to lambda multiplied by 10, if the error decreases, lambda is equal to lambda multiplied by 0.1, and the effect of selecting the initial value of lambda is 0.1.

Step 104: calculating the ith iteration value of the water drop contact angle by utilizing a triplet tangent method, and recording the ith iteration value as A_iThe calculation method is the same as that in step 102.

Step 106: the iteration is terminated, A_i+1As an estimate of the static contact angle of the water droplet.

The step of selecting an ellipse fitting algorithm to calculate the estimated value of the static contact angle of the water drop specifically comprises the following steps:

wherein,

B = {[n_{1}^{T}, n_{2}^{T}, . . ., n_{N}^{T}]}^{T},

n_{i} = [x_{i}^{}, x_{i} y_{i}, y_{i}^{2}, x_{i}, y_{i}, 1],

x_iand y_iRespectively the abscissa and the ordinate of the selected point on the edge of the water drop, i is 1, 2, …, and N is the number of the selected points on the edge of the water drop;

m＝[a，b，c，d，e，f]^Ta, b, c, d, e and f are elliptic curve equations ax, respectively²+bxy+cy²+ dx + ey + f is a parameter of 0.

The general equation for an ellipse can be expressed as:

F(m，n)＝n·m＝ax²+bxy+cy²+dx+ey+f＝0 (9)

in the above formula, x and y represent the abscissa and the ordinate, respectively, and m is [ a, b, c, d, e, f ]]^T，n＝[x²，xy，y²，x，y，1]. Is provided with

n_{i} = [x_{i}^{}, x_{i} y_{i}, y_{i}^{2}, x_{i}, y_{i}, 1],

B = {[n_{1}^{T}, n_{2}^{T}, . . ., n_{N}^{T}]}^{T},

F(m，n_i) Referred to as a point on a plane (x)_i，y_i) Algebraic distance to the curve F (m, n) is 0. When the algebraic distance square sum of all the discrete data points is fitted by an ellipse, a corresponding quadratic curve can be solved, the problem of nonlinear least squares is solved, iteration is needed, and the calculated amount and the programmed amount of a conventional least square algorithm such as a Levenberg-Marquardt algorithm are large. For the N-point observations, the fitting criterion was:

b must be defined for formula (10)²4ac < 0 ensures that the result of the fit is elliptical, otherwise the fit could be parabolic or hyperbolic instead of elliptical. Due to b²4ac < 0 is not an equality limiting condition, and a Kuhn-Tucker condition can not guarantee a solution in actual solution, so that a limiting condition b is introduced²-4 ac-1, expressed in matrix form as:

m^TCm＝1 (11)

in the formula

C = [\begin{matrix} 0 & 0 & 2 & 0 & 0 & 0 \\ 0 & - 1 & 0 & 0 & 0 & 0 \\ 2 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \end{matrix}]

Formula (10) is equivalent to:

E_min＝min(|Bm|²) (12)

since B is a known quantity and the quantity to be solved in formula (12) is m, the key to the problem is to optimize m. Introducing Lagrange operator and deriving:

2B^TBm-2λCm＝0 (13)

let S be B^TB, formula (13) is rewritten as:

Sm＝λCm (14)

for equation (14), 6 sets of corresponding eigenvalues λ can be solved by the generalized eigenvalue and generalized eigenvector method_iAnd u_i. For the conditional constraint matrix C, its eigenvalues are [ -2, -1, 2, 0, 0, 0]Only one eigenvalue is positive. Only a unique generalized eigenvalue λ ∈ R and generalized eigenvector u are used as the ellipse fitting solution. For any k ∈ R, (λ, ku) should satisfy formula (11), i.e., k²u^TWhen Cu is 1, then:

k＝[1/(u^TCu)]^1/2＝[1/(u^TSu)]^1/2 (15)

the only solution is:

\hat{m} = ku - - - (16)

step 302: and determining the major semi-axis, the minor semi-axis, the center and the inclination angle of the ellipse according to the parameters of the elliptic curve equation.

The length half axis and the short half axis of the ellipse obtained according to the solved m are respectively L_LAnd L_SCenter is (X)₀，Y₀) The angle of inclination being theta₀In radians; then point (x) on the ellipse₁，y₁) The expression is as follows:

x＝L_Lcosθ；y＝L_Ssinθ

x₁＝xcosθ₀-ysinθ₀+X₀

y₁＝xsinθ₀+ycosθ₀+Y₀ (17)

step 303: and calculating the estimated value of the static contact angle of the water drop according to the major semi-axis, the minor semi-axis, the center and the inclination angle of the ellipse. The process is as follows:

step 401: using formulas

Calculation (X)_L1，Y_L1) And (X)_R1，Y_R1). Wherein (X)_L1，Y_L1) And (X)_R1，Y_R1) Is an intermediate result in the calculation processThe subsequent step 403 is used to calculate the solids level slope. (X)_L，Y_L) And (X)_R，Y_R) Respectively the horizontal and vertical coordinates of the lowest points of the left and right sides on the edge of the water drop (X)₀，Y₀) Is the abscissa and ordinate of the center of the ellipse, theta₀Is an elliptical inclination angle.

Step 402: using formulas

Respectively calculating left contact angle reference value theta on the triple line of the ellipse_L2And a reference value theta of right contact angle_R2(ii) a Wherein, theta_L1＝angle(jY_L1/L_S+X_L1/L_L)，θ_R1＝angle(jY_R1/L_S+X_R1/L_L)，L_LIs an ellipse long semi-axis, L_SThe minor semi-axis of the ellipse, angle (A), is a function of the phase from which the complex number A is obtained.

Step 403: using the formula k ═ Y_L1-Y_R1)/(X_L1-X_R1) The solid level slope k' is calculated.

Step 404: using formulas

Respectively calculating a left contact angle and a right contact angle on the triple line; wherein, theta_LLeft side contact angle on triple line, θ_RThe right contact angle on the triple line.

Step 405: using the formula theta ═ theta_L+θ_R) And/2 calculating the estimated value of the static contact angle of the water drop.

The invention has higher calculation precision when the volume of the water drops is less than 200 mu L and the contact line is not more than 1cm, therefore, in the embodiment, the selected water drops are all less than 200 mu L and the contact line is not more than 1 cm.

When the estimated value of the static contact angle of the water droplet is less than or equal to 15 ° (angle), and the volume of the water droplet is less than 200 μ L and the contact line is not greater than 1cm, the circle fitting algorithm is selected to calculate the accurate value of the static contact angle of the water droplet, and the calculation process is the same as the above step 101-106.

When the estimated value of the static contact angle of the water droplet is greater than 15 ° (angle) and less than or equal to 70 ° (angle), and the volume of the water droplet is less than or equal to 7 μ L and the contact line is not greater than 1cm, the circle fitting algorithm is selected to calculate the precise value of the static contact angle of the water droplet, and the calculation process is the same as the step 101-.

When the estimated value of the static contact angle of the water droplet is greater than 15 DEG (angle) and less than or equal to 70 DEG (angle), the volume of the water droplet is greater than 7 mu L and less than 200 mu L, and the contact line is not greater than 1cm, the ellipse fitting algorithm is selected to calculate the accurate value of the static contact angle of the water droplet, and the calculation process is the same as the step 301 and 303.

When the estimated value of the static contact angle of the water drop is greater than 70 degrees (angle) and not greater than 90 degrees (angle) and the volume of the water drop is less than 200 muL and the contact line is not greater than 1cm, the ellipse fitting algorithm is selected to calculate the accurate value of the static contact angle of the water drop, and the calculation process is the same as the step 301 and 303.

Example 2

Because the image is difficult to avoid some interference and the resolution of the image is limited, noise exists in the method for manually and automatically identifying the edge, and finally, the obtained edge of the water drop has some noise compared with the ideal edge of the water drop, and the signal to noise ratio is different under different conditions, so that the influence of the noise content on the accuracy of contact angle calculation needs to be analyzed. The noise is a random variable obeying normal distribution, and the standard deviation of the noise is aR when the height of the water drop is R. Without loss of generality, the contact angles are typically 5 degrees, 70 degrees and 90 degrees respectively, the water drop volumes are 1.06, 5.05 and 18.80 respectively, a is changed within the range of 0-0.005, noise is randomly generated 1000 times under the condition that each contact angle and the water drop volume are combined, and the average value of the error amplitude of the contact angle obtained by calculating 1000 times is shown in the attached figure 2.

As can be seen from fig. 2, when the contact angle is not very large, the error of the ellipse fitting algorithm tends to increase significantly with the increase of the noise content, while the error of the circle fitting algorithm increases insignificantly with the increase of the noise content within the set noise range, and obviously, the accuracy of the ellipse fitting algorithm is affected by noise more seriously than that of the circle fitting algorithm, which is particularly obvious when the contact angle is small (5 °). Comparing fig. 2(a), (b) and (c), it can be known that the smaller the contact angle, the larger the error caused by the noise to the contact angle calculation, and the larger the contact angle, the 90 ° is in the noise range set by the present invention (see fig. 3 for the specific influence degree), and the influence of the noise on the calculation accuracy of both algorithms is very small and can be ignored. The reason for this rule is that the undetermined variables of the elliptic equation are more, noise easily brings larger error to the elliptic equation, when the contact angle is smaller, the given arc is shorter, the given information is insufficient, and the influence of the noise is large, so the error is larger, and as the contact angle is increased, the arc is longer, and the equation is determined by gradually having enough information, so the influence of the noise is gradually reduced. In the attached fig. 2(b) and (c), the circle fitting algorithm has errors of about 2.5 degrees and about 8 degrees respectively along with the change of the noise content, which is caused by that a certain deviation exists between the circle equation and the edge of the actual water drop along with the increase of the volume and the contact angle of the water drop. The curves obtained by fitting the two algorithms at different noise and contact angles are shown in figure 3.

As can be seen from FIG. 3(a), the edge obtained by fitting the circle and the ellipse fitting algorithm at 5 °, 1.06 μ L and without noise is well matched with the edge of the original bead. As can be seen from fig. 3(b), when the noise is not negligible at 5 °, 1.06 μ L, the effect of the noise on the circle fitting is not greatly affected, but the ellipse fitting result is significantly affected, and the edge of the water bead obtained by fitting has a large difference from the edge of the raw water bead, so that the contact angle calculated by the method has a small error. Although fig. 3(d) and 3(f) contain noise, the result of the bead edge obtained by fitting the two algorithms is obviously closer to the original bead edge than the result of the ellipse fitting algorithm shown in fig. 3(b), and the edge obtained by fitting the circle also has good effect, but obviously has a difference with the original edge curve at the triple line. In the case of fig. 3(c) and 3(e) without noise, the edges obtained by the two algorithms have good effect as a whole, but the circle fitting method also has a certain error in the vicinity of the critical triple line, which directly causes the contact angle obtained by the algorithm to have an error. The above analysis results are consistent with those of FIG. 2, and the two are mutually verified.

The static contact angles are respectively 5n degrees, n is 1, 2, … and 18, and the water drop meets the two conditions that the length of the contact line with the surface of the material is not more than 1cm and the volume is not more than 200 mu L. The noise parameter a is 0.0005, in order to represent the randomness of the noise, the combination of each contact angle and the volume of the water drop is simulated 100 times, and the contact angle mean value obtained by 100 times of calculation is shown in fig. 4. The results of the two algorithm fits at different drop volumes and contact angles are shown in FIG. 5.

As can be seen from the attached figure 4, under the conditions of different hydrophilicities and water drop volumes, the contact angle obtained by the circle fitting algorithm is smaller, the contact angle obtained by the ellipse fitting algorithm is larger, and the contact angles obtained by the ellipse fitting algorithm are larger than those obtained by the circle fitting algorithm. As shown in fig. 5(a) and (b), the edge curve obtained by the circle fitting algorithm with a small contact angle is very close to the edge of the water drop, and the ellipse fitting algorithm has a large error. This is because the arc occupied by the edge of the water drop is short when the contact angle is small, the provided information is less, the variables of the ellipse fitting algorithm are more, and certain errors must exist when the image itself exists or the edge is extracted, and it can be known from fig. 2 that the ellipse fitting algorithm is more easily affected by noise when the contact angle is small than the circle fitting algorithm, so the error is larger than the circle fitting algorithm. As can be seen from the attached FIGS. 5(c) and (d), the difference between the edge obtained by the ellipse fitting algorithm and the real edge is very small when the contact angle is large, while the fitting effect of the circle fitting algorithm is good when the volume of the small water drop is large, and the error is increased when the volume of the large water drop is large. This is because enough information is provided for the fitting algorithm to use when the contact angle is large (90 °), the edge is similar to a circle when the water drop is small in volume, so the fitting effect of both algorithms is good, and when the water drop is large in volume, the edge has a certain difference from the circle equation and is close to the ellipse equation, so the circle fitting error is large and the ellipse fitting error is small.

As can be seen from fig. 4, the error of the circle fitting algorithm gradually increases with the increase of the volume of the water drop under different contact angles, and the error of the circle fitting algorithm is greater than 25 ° when the contact angle is 90 ° and the volume of the water drop is 173.5 μ L. The error of the ellipse fitting algorithm also tends to increase along with the increase of the volume of the water drop, but the increase is not obvious, except that when the contact angle is 5 degrees, the error is approximately 4 degrees, and when other contact angles are in the change range of the volume of the water drop, the calculation errors of the contact angles are all less than 3 degrees. At contact angles of 5 °, 10 ° and 15 °, the maximum value of the circle fitting error is only about 3 °, and the error is close to that of ellipse fitting. It should be noted that, as a result of the analysis shown in fig. 2 and 3, when the contact angle is not very large (not greater than 70 °), the circle fitting algorithm is much less affected by noise than the ellipse fitting algorithm, in some cases when the actually measured contact angle is much more affected by noise than a is 0.0005, and when the volume of the small water drop (not greater than 7 μ L), the error of the circle fitting algorithm is not large (about 3 °), and the circle fitting algorithm should be selected. In addition, the ellipse fitting algorithm has a better effect, especially when the size of the water drop is larger.

From the analysis, when the water-based surface is in a hydrophilic state, if the contact angle is smaller, the circle fitting algorithm has higher accuracy, and the elliptic equation is influenced by interference more and more due to more undetermined variables, so that the error is larger. Therefore, the circle fitting algorithm is selected. With the increase of the volume of the water drop and the contact angle, the edge of the water drop gradually deviates from a circular equation and has small difference with an elliptic equation, the error of the circular fitting algorithm is increased, and the edge obtained by elliptic fitting is closer to the actual edge of the water drop, so that the method has higher accuracy, and the elliptic fitting algorithm is more suitable to be selected. The algorithm selection principle of the invention is consistent with the actual situation, and is expected to obtain better effect. Note that the algorithm of the present invention is based on the volume of the water drop and the real contact angle of the material, the volume of the water drop is a known quantity during actual measurement, but the real contact angle cannot be obtained completely accurately (if the volume is obtained completely accurately before measurement, there is no need for measurement), but the estimated value of the contact angle can be obtained by comparing the calculation result of the actual image circle and ellipse fitting algorithm with that of fig. 4. Because the errors of the two algorithms are similar at the critical point, the accuracy requirement of the algorithm of the invention on the estimation of the contact angle is not high, and the estimation can meet the requirement. And the calculation accuracy can be further improved by selecting a more appropriate algorithm.

Example 3

The silicon rubber samples soaked for different time and after contamination are selected, 2, 5, 10 and 20 mu L of deionized water are dripped on the silicon rubber samples, contact angles are calculated by a circle fitting algorithm and an ellipse fitting algorithm respectively, and the obtained result is shown in figure 6. The invention continuously shoots a plurality of images for one water drop, and the sequence number in the images approximately corresponds to the shooting time. The contact angle gradually decreases with time due to the hysteresis.

As can be seen from the attached figure 6(a), the calculation result of the ellipse fitting algorithm is about 1.6-2.3 degrees larger than that of the circle fitting algorithm, and the real contact angle of the sample is about 85 degrees by combining the attached figure 4 (q). The volume of the water drop is 2 muL, and as can be seen from the attached figure 4(q), the calculation result of the ellipse fitting algorithm is about 1.6 degrees larger than that of the circle fitting algorithm, and the calculation result of the actual water drop in the attached figure 6(a) is very similar to the simulation calculation result. Since the contact angle is larger than 70 degrees, the invention selects the ellipse fitting algorithm, and the ellipse fitting algorithm is slightly more accurate than the circle fitting algorithm as can be seen by combining the attached figure 4 (q). Therefore, the present invention has a good effect.

As can be seen from the attached figure 6(b), the results obtained by the calculation of the circle fitting algorithm and the ellipse fitting algorithm are relatively similar when the volume of the water drop is 5 muL and the contact angle is more than 50 degrees, the calculation result of the ellipse fitting algorithm is-0.7-3.2 degrees greater than that of the circle fitting algorithm, and as can be seen from the attached figures 4(k) -4 (r), when the contact angle is within the range of 50-90 degrees and the volume of the water drop is 5 muL, the calculation result of the ellipse fitting algorithm obtained by simulation is approximately 2 degrees greater than that of the circle fitting algorithm. Therefore, the calculation result of the actual water drop is similar to the simulation calculation result. Because the volume of the water drop is less than 7 mu L, the invention can select an ellipse fitting algorithm when the contact angle is more than 70 degrees, and can select a circle fitting algorithm when the contact angle is less than 70 degrees. As can be seen from fig. 6(b), when the contact angle is greater than 70 °, the calculation result of the ellipse fitting algorithm is very close to that of the circle fitting algorithm, and which algorithm is selected has little influence. When the contact angle is smaller than 70 degrees, the difference between the calculation results becomes larger along with the reduction of the contact angle, and the analysis in combination with the attached figures 2 and 6 shows that the smaller the contact angle is, the larger the error of the ellipse fitting algorithm is caused by the noise, and the influence on the circle fitting algorithm is smaller, so the difference between the calculation results is increased along with the reduction of the contact angle, and at the moment, the selection of the circle fitting algorithm has more accurate calculation results, so the method has good effect.

Fig. 6(c) shows the case of a 10 μ L drop volume, and it can be seen from fig. 4(n) that the actual contact angle is about 70 °, and the ellipse fitting algorithm is about 2.5 ° to 3.3 ° larger than the circle fitting algorithm, and it can be seen from fig. 4(n) that the ellipse fitting algorithm is about 4 ° larger than the calculation result of the circle fitting algorithm when the contact angle is 70 ° and the drop volume is 10 μ L, and the actual calculation result and the simulation calculation result can be better matched. The ellipse fitting algorithm should have higher accuracy. According to the invention, an ellipse fitting algorithm can be selected, and the accuracy is higher.

FIG. 6(d) shows the case where the volume of the water drop is 20. mu.L, and the contact angle calculated by the ellipse fitting algorithm is about 7.2-7.9 degrees larger than that of the circle fitting algorithm. As can be seen by combining the attached figure 4(o), the contact angle of the sample is about 75 degrees, and as can be seen from the attached figure 4(o), the calculation result of the ellipse fitting algorithm is about 7 degrees larger than that of the circle fitting algorithm, and the actual calculation result can be well matched with the simulation calculation result. The main reason for the difference between the two is that the water drop volume is large, the difference between the circular equation and the water drop edge causes errors in the circular fitting algorithm, obviously, the accuracy of the elliptical fitting algorithm is guaranteed at the moment, and the method also selects the elliptical fitting algorithm, so that the accuracy is high.

Example 4

The volume of the water drop is about 1-2 mu L, the sample is a silicon rubber sample after corona at different time, and the calculation results of the circle and ellipse fitting algorithm are shown in attached figures 7 and 8.

In fig. 7, interference exists at the triple lines because the sample plane is not perpendicular to the lens plane. As can be seen from fig. 7(a), after the edge is automatically identified, the contact angles calculated by the two algorithms are 42.4 ° and 59.0 °, respectively, and the calculation result of the ellipse fitting algorithm is 16.6 ° greater than that of the circle fitting algorithm. This is because the interference near the triple line is large, and the error caused by the interference to the ellipse fitting algorithm is much larger than that of the circle fitting algorithm, which is similar to the rule of fig. 2. As can be seen from fig. 7(b) and fig. 7 (c), the calculation results of the two algorithms after the edge is recognized by naked eyes are respectively 40.5 ° and 43.5 °, the edge can be recognized by naked eyes to better eliminate the oblique interference, the contact angle is not very small, and other interferences are not very large, so that the accuracy of the obtained result is guaranteed, which further verifies that the result obtained by the circle fitting algorithm in fig. 7(a) is more accurate. When the contact angle is less than 70 degrees and the volume of the water drop is less than 7 mu L, the invention can automatically select the circle fitting algorithm, thereby having higher accuracy.

Fig. 8 shows the case of a smaller contact angle, and also shows a certain interference around the triple line, the calculation results of the circle and ellipse fitting algorithms are 14.6 ° and 37.4 °, respectively, and the calculation result of the ellipse fitting algorithm is 22.8 ° greater than that of the circle fitting algorithm. The reason is that the inclination causes certain interference on the obtained water drop image at the triple line of the water drop, and the error of the ellipse fitting algorithm is far larger than that of the circle fitting algorithm when the interference causes a small contact angle, so that the difference between the contact angles obtained by the two is larger, and the circle fitting algorithm has higher accuracy. According to the invention, when the volume of the water drop is less than 7 mu L and the contact angle is less than 70 degrees, a circle fitting algorithm is selected, so that the accuracy is higher. Because the contact angle is small, the difference of the calculation results of the two algorithms is large when the edge of the water drop is identified by naked eyes, and the calculation results are not given in the invention.

The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A method for detecting a static contact angle of a water drop in hydrophilic property is characterized by comprising the following steps:

step 1: acquiring a water drop image;

2. The method according to claim 1, wherein in step 3, when the estimated value of the static contact angle of the water droplet is less than or equal to 15 ° (angle), a circle fitting algorithm is selected to calculate the precise value of the static contact angle of the water droplet;

3. The method of claim 1, wherein the selecting the circle fitting algorithm to calculate the estimated value/the accurate value of the static contact angle of the water droplet specifically comprises:

4. The detection method according to claim 3, wherein the initial value/ith iteration value of the water drop contact angle is calculated by using a triple tangent method, specifically:

step 201: using formula k₁＝-(x₁-x₀)/(y₁-y₀) And k₂＝-(x₂-x₀)/(y₂-y₀) Respectively calculating the slope of a left tangent and the slope of a right tangent on the arc at the triple line;

step 202: using formulas

Calculating a right contact angle on the circular arc at the triple line;

5. The method of claim 1, wherein the selecting an ellipse fitting algorithm to calculate the estimated/accurate value of the static contact angle of the water droplet specifically comprises:

wherein,

B = {[n_{1}^{T}, n_{2}^{T}, . . ., n_{N}^{T}]}^{T},

n_{i} = [x_{i}^{2}, x_{i} y_{i}, y_{i}^{2}, x_{i}, y_{i}, 1],

6. The method as claimed in claim 5, wherein said step 303 comprises:

step 401: using formulas

Respectively calculate (X)_L1，Y_L1) And (X)_R1，Y_R1) (ii) a Wherein (X)_L，Y_L) And (X)_R，Y_R) Respectively are the horizontal and vertical coordinates of the lowest points on the left side and the right side of the edge of the water drop, and are also the horizontal and vertical coordinates of corresponding points on the left side and the right side of the triple line of the ellipse; (X)₀，Y₀) Is the abscissa and ordinate of the center of the ellipse, theta₀Is an elliptical inclination angle;

step 402: using formulas

step 404: using formulas