CN109186500B

CN109186500B - Contact angle acquisition method for liquid-liquid two-phase displacement image in micron capillary

Info

Publication number: CN109186500B
Application number: CN201811132549.0A
Authority: CN
Inventors: 雷达; 李云; 冯静娅; 文孟刚
Original assignee: Xian Jiaotong University
Current assignee: Xian Jiaotong University
Priority date: 2018-09-27
Filing date: 2018-09-27
Publication date: 2020-03-31
Anticipated expiration: 2038-09-27
Also published as: CN109186500A

Abstract

A contact angle acquisition method of a liquid-liquid two-phase displacement image in a micron capillary adopts a cubic polynomial to fit a phase interface and calculate the contact angle, and the method can be suitable for an asymmetric phase interface and is more suitable for a measurement image obtained in an actual experiment; the method is based on the mode of local gray extreme value of the image, realizes the phase interface of the low-contrast image for liquid-liquid displacement in the micro-pipeline, and further obtains the contact angle. The method realizes the identification of the phase interface, the wall surface and the contact point of the low-contrast image of the liquid-liquid displacement in the micro-pipeline based on the mode of the local gray extreme value of the image, has high fault-tolerant rate, can adapt to the image with noise, can accurately and efficiently identify the phase interface, the wall surface and the contact point, and can be used for accurately measuring the contact angle. The method can adapt to fitting of asymmetric phase interfaces, has strong algorithm robustness, and greatly improves the efficiency of data processing and the measurement precision.

Description

Contact angle acquisition method for liquid-liquid two-phase displacement image in micron capillary

Technical Field

The invention relates to a contact angle acquisition method of a liquid-liquid two-phase displacement image in a micron capillary tube, which is suitable for experiments in the fields of micro-scale two-phase flow research and petroleum enhanced exploitation.

Background

The displacement mechanism of two immiscible liquids in a single micron-scale capillary is the basis of two-phase displacement in a natural environment porous medium, which occurs in numerous industrial or natural processes, such as water flooding, polymer flooding, etc. of tight reservoirs, characterized by weak viscosity (the number of capillaries is in the range of 10)^-10<Ca<10^-5) Weak gravity (Bo number of bond less than 10)^-4). These two dimensionless numbers are defined as Ca ═ μ V/γ, μ is the liquid viscosity, V is the phase interface velocity, γ is the interfacial tension; bo ═ ρ gh²And/γ, ρ is the density of the liquid, g is the acceleration of gravity, and h is the characteristic dimension of the flow region. The key factor affecting the displacement process is the capillary force, and the key parameter for calculating the capillary force is the contact angle between the two-phase interface and the wall surface of the pipeline. The calculation of the capillary force is calculated according to a Young-Laplace formula, and is shown as a formula (1). The actual range of the contact angle theta is 0-180 DEG when theta<At 90 DEG time P_cIs a positive value when theta>At 90 deg. P_cNegative values, therefore, the capillary force may be a resistance that impedes displacement and may also be a motive force for propelling displacement. Furthermore, contact Angle evaluationThe error in (2) will cause serious errors in the calculation of the capillary force, resulting in a misevaluation of the displacement process. Therefore, obtaining dynamic contact angle information under the industrial conditions described above is critical to assessing the overall liquid-liquid displacement process within the porous media.

Displacement experiments of two-phase immiscible liquids in micro-scale capillaries are common methods to study dynamic contact angles. Existing experiments often perform manual analysis on microscopic images of phase interfaces and manually measure contact angles. The image processing method adopted by the existing commercial equipment is only limited to analyzing the shape of the liquid drop on the solid surface (the contact angle is measured by the sitting drop method), and the image analysis algorithm of the liquid drop shape comprises a symmetric shape analysis method (ADSA-P), a high aspect ratio method, an ellipse fitting method and the like. However, the above algorithm is proposed for the shape detection of the liquid drop on the plane, is suitable for the image with high contrast, and is not suitable for the phase interface shape with low contrast during the displacement of the liquid in the micro-pipeline. To measure the contact angle of the liquid-liquid displacement phase interface in the microchannel, the phase interface needs to be identified from the image.

Disclosure of Invention

The invention aims to provide a contact angle acquisition method for a liquid-liquid two-phase displacement image in a micron capillary, which can identify a wall surface, a phase interface and a contact point from the image and measure the contact angle and the position of the contact point.

In order to achieve the purpose, the invention adopts the following technical scheme:

a contact angle acquisition method for a liquid-liquid two-phase displacement image in a micron capillary tube divides an obtained microscopic image into coordinates, and sets the pixel size width of the image as L_xAnd length L_y(ii) a Then the following steps are carried out:

firstly, searching two points A and B at the leftmost ends of two wall surfaces along the y direction by a multi-extremum searching technology to obtain coordinates (0, y)_A) And (0, y)_B)；

Step two, along A-E (0, y) of the midpoint of line B_E) X in the horizontal direction_ESearching a single local minimum value to obtain a certain point F on the phase interface, wherein the coordinate point is (x)_F,y_F)；

Step three, adopting a sorting algorithm to search a single extreme value along the y direction, further searching partial wall surfaces, setting a range to avoid the phase interface in order to avoid the search of the phase interface to the wall surfaces, and enabling 0<x_D1＝x_C1<x_FX is more than or equal to 0 and less than or equal to x_D1And y is not less than 0 and not more than y_EThe search within the range yields a wall A-D1, where the coordinates of D1 are (x)_D1,y_D1) (ii) a At 0<x_f<x_C1And y_E≤y≤L_ySearching in the range to obtain a wall B-C1, wherein the coordinate of C1 is (x)_C1,y_C1)；

Step four, adopting a sorting algorithm to search a single extreme value along the x direction, further searching a part of phase interfaces, setting a range to avoid the two walls in order to avoid the search of the two walls to the phase interfaces, and enabling 0<y_D2<y_F<y_C2<L_yX is more than or equal to 0 and less than or equal to L_xAnd y_D2≤y≤y_C2The search in the range obtains a partial phase interface C2-D2, and the coordinates of the two points are (x)_D2,y_D2)、(x_C2,y_C2)；

Step five, respectively fitting all coordinate points in the line segments of A-D1 and B-C1 by adopting a linear function to obtain a linear function f_ADAnd f_BCFitting a cubic function to all points in the C2-D2 curve to obtain a cubic function f_CD(ii) a Solving for f_ADAnd f_CDThe intersection point of (A) and (B) is obtained as the coordinate (x) of the contact point D_D,y_D) Solving for f_ADAnd f_CDTo obtain the coordinates (x) of the contact point C_C,y_C) (ii) a The line segments B-C and A-D are wall surfaces, and the curve C-D is a phase interface;

step six, according to the fitting function x ═ f of the phase interface obtained in the step five_CD(y) coordinate (x) of C_C,y_C) And coordinates (x) of D_D,y_D) Respectively substitute for f_CDIn the first derivative of (3), the contact angle theta of the phase boundary at the points C and D is determined_CAnd theta_D；f_CDOf primary derivative f'_CDIs composed of

f′_CD＝3a_CDy²+2b_CDy+c_CD(13)

Will ordinate y_CAnd y_DIn the formula (13), the slope is obtained, and the slope is converted into an angle to obtain the contact angle theta_CAnd theta_D；

The invention is further improved in that the specific process of the step one is as follows:

the point A and the point B are gray minimum value points on a straight line with x being 0 and are also two points with the gray gradient having the maximum value along the y direction, so that the coordinates of the two points with the gray gradient maximum value are found and distinguished, and the coordinates of the point A and the point B are determined;

let the gray-scale value of any coordinate point (x, y) be I (x, y), then the following steps are performed:

(1) forward difference is carried out on the gray value of the coordinate point on the straight line with x being 0 to represent that the change gradient dI exists, and two maximum value points exist in the dI;

(2) the y coordinates of all points on the straight line with x equal to 0 are arranged in descending order according to the gray gradient value I (0, y), and a coordinate sequence (y) is obtained₁,y₂,...y_n) Coordinate y₁Is the position of one maximum value point, searching the coordinate sequence in sequence, and searching the first coordinate point y satisfying the formula (3)_kIn which 1 is<k is less than or equal to n, α is a coefficient less than 1 in formula (3), and h is the vertical distance h between the point A and the point B_B-y_A；

|y_k-y₁|>αh (3)

(3) Comparison of y₁And y_kLet the smaller of the two be y_minLarger value is y_maxThe ordinate of point A and point BIs determined as y_A＝y_min，y_B＝y_max。

The invention has the further improvement that the specific process of the step two is as follows:

(1) the ordinate y of the midpoint E of the line A-B is determined_E；

(2) Let line y equal to y_EGray value I (x, y) of all the above coordinate points_E) Gradient of gray scale is obtained according to formula (5), where x ∈ [0, L ]_X](ii) a Get the straight line y ═ y_EGray scale gradients dI (x, y) of all the above coordinate points_E)；

(3) Due to dI (x, y)_E) Search for dI (x, y) with only one maximum_E) Maximum point in the sequence, determining the abscissa x of point F on the phase boundary_FAnd the ordinate x of the point F_F＝x_E。

The invention has the further improvement that the specific process of the step three is as follows:

(1) in order to search the wall surface along the y direction without being influenced by the phase boundary, the x range of the search is limited to 0 ≦ x_D1Or x is more than or equal to 0 and less than or equal to x_C1Wherein x is_D1＝x_C1＝βx_Fβ is a factor less than 1;

(2) to search the wall A-D1, the abscissa x_iTraverse 0 to x_D1For each abscissa x_iCalculating a straight line x ═ x_iUpper gray level I (x)_iY) gradient in the y direction, as shown in equation (6); searching for dI (x)_iY) to obtain a vertical coordinate y corresponding to the wall coordinate point_iA series of coordinate points (x)_i,y_i) Wall A-D1;

(3) to search the wall B-C1, the abscissa x_jTraverse 0 to x_C1For each abscissa x_jCalculating a straight line x ═ x_jUpper gray level I (x)_jY) gradient in the y-direction, formula (6) x_iBy substitution of x_jCalculating dI (x)_jY), search for dI (x)_jY) to obtain a vertical coordinate y corresponding to the wall coordinate point_jA series of coordinate points (x)_j,y_j) Forming wall B-C1.

The invention has the further improvement that the specific process of the step four is as follows:

(1) searching the minimum value of the gray level along the x direction to determine a phase interface, avoiding two wall surfaces, and setting the search range of the y direction as y_D2<y<y_C2Wherein y is_D2And y_C2Are respectively as

In formula (7), h is the distance from point a to point B, i.e., h is y_B-y_AAnd ε is a coefficient whose value ranges from 0<ε<0.5；

(2) To search for a phase interface, y_iCoordinate traversal y_D2To y_C2For each ordinate y_iCalculating the linear y ═ y_iUpper gray level I (x, y)_i) Gradient dI (x, y) in the x-direction_i) As shown in formula (8); searching for dI (x, y)_i) The maximum value of the wall surface coordinate point is obtained to obtain the vertical coordinate y of the corresponding wall surface coordinate point_iA series of coordinate points (x)_i,y_i) Wall C2-D2;

the invention has the further improvement that the concrete process of the step five is as follows:

(1) fitting all points in the A-D1 line segment by adopting a linear function, and obtaining a linear function f by taking the x coordinate as an independent variable and the y as a dependent variable_ADAs shown in formula (9), a_ADAnd b_ADIs a coefficient of a function of one degree,

y＝f_AD(x)＝a_ADx+b_AD(9)

fitting all points in the B-C1 line segment by adopting a linear function, and obtaining a linear function f by taking the x coordinate as an independent variable and the y as a dependent variable_BCAs shown in formula (10), a_BCAnd b_BCAs coefficients of a linear function

y＝f_BC(x)＝a_BCx+b_BC(10)

Fitting a phase interface C2-D2 by using a cubic function, and obtaining a cubic function f by taking a y coordinate as an independent variable and x as a dependent variable_CDAs shown in formula (11);

x＝f_BC(y)＝a_CDy³+b_CDy²+c_CDy+d_CD(11)

(2) the contact points C and D are the intersection points of the two walls and the phase boundary, respectively, and are therefore solved for f_CDAnd f_ADA point of intersection of, and f_CDAnd f_BCIntersection point, obtaining coordinates (x) of contact points C and D_C,y_C) And (x)_D,y_D) Solving the equation set shown in the formula (12);

(3) determining all coordinate points on the phase interface and the wall surface: all coordinate points on the wall A-D are required to be taken, and each coordinate point satisfies x_A≤x≤x_DThe x of the abscissa is taken into the formula (9) to be calculated to obtain a corresponding y coordinate, so that coordinates of all points on the wall surface A-D are obtained; all coordinate points on the wall B-C are required to be taken, and each coordinate point satisfies x_B≤x≤x_CThe x of the abscissa is taken into the formula (10) to be calculated to obtain a corresponding y coordinate, so that coordinates of all points on the wall surface B-C are obtained; for all coordinate points on the phase boundary C-D, each will satisfy y_C≤y≤y_DThe ordinate y of (2) is taken into formula (11) to be calculated to obtain the corresponding x coordinate, so that the coordinates of all points on the phase interface C-D are obtained.

The invention further providesThe improvement of the step is that the method also comprises a step seven: when the actually obtained wall surface is not horizontal, the contact angle obtained by equation (14) is corrected as follows: the inclination angle of the wall is the average of the inclination angles of the walls A-D1 and B-C1, i.e., (arctan a)_AD+arctan a_BC) And/2, the final value of the contact angle is:

compared with the prior art, the invention has the following beneficial effects:

the invention adopts cubic polynomial fitting phase interface and calculates the contact angle, overcomes the limitation that ADSA-P of the traditional algorithm can only fit the symmetrical phase interface, can be suitable for the asymmetrical phase interface, and is more suitable for measuring images obtained in practical experiments; the method is based on the mode of local gray extreme value of the image, realizes the phase interface of the low-contrast image for liquid-liquid displacement in the micro-pipeline, and further obtains the contact angle. The method realizes the identification of the phase interface, the wall surface and the contact point of the low-contrast image of the liquid-liquid displacement in the micro-pipeline based on the mode of the local gray extreme value of the image, has high algorithm fault tolerance rate, can adapt to the image with noise, can accurately and efficiently identify the phase interface, the wall surface and the contact point, and can be used for accurately measuring the contact angle. The invention realizes the measurement of the liquid-liquid displacement dynamic contact angle under the conditions of low capillary number and low bond number. The method can adapt to the fitting of the asymmetric phase interface, has strong algorithm robustness, and greatly improves the efficiency of data processing and the measurement precision.

Drawings

Fig. 1 is a microscopic image of liquid-liquid displacement.

Fig. 2 is a gray scale distribution map in a gray scale image of liquid-liquid displacement.

Fig. 3 is a coordinate setting of the liquid-fluid displacement image.

Fig. 4 shows the positions of key points in image processing.

Fig. 5 shows a distribution of the gradation and the gradation gradient in which two minimum points exist on a straight line where x is 0.

Fig. 6 shows that the distribution of the gradation and the gradation gradient has two maximum points on the straight line where x is 0.

Fig. 7 shows two contact angles formed by the interface and the wall surface at two contact points.

FIG. 8 is a graph of the relationship between the derivative of the cubic polynomial and the contact angle.

Detailed Description

The present invention will be described in detail with reference to the accompanying drawings.

The invention provides a method for searching a local extremum in an image, which determines boundary points and then identifies a wall surface, a phase interface and a contact point from the boundary points.

The liquid-liquid displacement image features are as follows:

the microscopic image of the liquid-liquid displacement process adopts an incident light (bottom light source irradiation of a microscope) observation mode, so that an image that the wall surface, the phase interface and the bulk liquid are obviously distinguished can be obtained. The microscopic images of the liquid-liquid displacement belong to the low contrast images, as shown in fig. 1 and 2. The histogram distribution of the image with low contrast is characterized in that the gray distribution is concentrated in a certain area, and the number of pixels in the high gray area and the low gray area is small. In FIG. 2, two straight lines are the walls of the microchannels, and the curve is the phase interface. By utilizing the characteristic, other parameters such as phase interfaces, measured contact angles, phase interface displacement and the like are identified from a series of microscopic images through calculation. The method can efficiently and accurately process a large amount of image data, and greatly improves the research efficiency of the dynamic contact angle in the microcapillary.

The histogram distribution of an image with low contrast is characterized in that the gray scale distribution is concentrated in a certain area. In the liquid-liquid displacement image, two straight lines are the wall surfaces of the microchannels, and a curve is a phase interface.

Identification of microchannel walls and phase interfaces

The boundary here means the wall surface of the microchannel in the microscopic image and the phase interface between the immiscible liquid phases. The obtained image is divided into coordinates according to the method shown in fig. 3. Let the pixel size width of the image be L_xAnd length L_y。

On the image, the wall surface is two approximate straight lines formed by a series of pixel points with lower gray values. These two lines extend substantially horizontally (x-direction) and therefore require searching for local minima of the gray scale along the vertical direction (y-direction) to determine the wall. The algorithm for searching a single extreme value and the position thereof in an array sequence is mature, but the algorithm for searching a plurality of extreme values and a plurality of positions simultaneously is not mature. The identification of the wall and phase interfaces will be explained separately below.

Identification of part of a wall

Firstly, two points A and B at the leftmost ends (x is 0) of two wall surfaces are searched along the y direction by a multi-extremum searching technology to obtain coordinates (0, y)_A) And (0, y)_B) The approximate positions of the two wall surfaces are obtained;

the specific process of the step one is as follows:

the point a and the point B are gray minimum points on a straight line where x is 0, that is, two points where the gray gradient has a maximum value along the y direction, and therefore, the coordinates of the two points where the gray gradient has a maximum value are found and distinguished, and the coordinates of the point a and the point B can be determined. As shown in fig. 5 and 6;

(1) the gray values of the coordinate points on the straight line where x is 0 are differentiated forward to indicate that there are two maximum points of the variation gradient dI, as shown in fig. 6.

(2) The y coordinates of all points on the straight line with x equal to 0 are arranged in descending order according to the gray gradient value I (0, y), and a coordinate sequence (y) is obtained₁,y₂,...y_n) Coordinate y₁Is the position of one maximum value point, searching the coordinate sequence in sequence, and searching the first coordinate point y satisfying the formula (3)_kIn which 1 is<k is less than or equal to n, α is a coefficient less than 1 in formula (3), and h is the vertical distance h between the point A and the point B_B-y_A。

|y_k-y₁|>αh (3)

(3) Comparison of y₁And y_kLet the smaller of the two be y_minLarger value is y_maxThen the ordinate of point A and point B can be determined as y_A＝y_min，y_B＝y_max。

Step two, E (0, y) along the midpoint of the A-B line_E) X in the horizontal direction_ESearching a single local minimum value to obtain a certain point F on the phase interface, wherein the coordinate point is (x)_F,y_F)；

The specific process of the second step is as follows:

(1) the ordinate y of the midpoint E of the line A-B is determined_E(x is known on the abscissa)_E＝0)，

(2) Let line y equal to y_EGray value I (x, y) of all the above coordinate points_E) Gradient of gray scale is obtained according to formula (5), where x ∈ [0, L ]_X]. Get the straight line y ═ y_EGray scale gradients dI (x, y) of all the above coordinate points_E)；

(3) Due to dI (x, y)_E) Search for dI (x, y) with only one maximum_E) The maximum point in the sequence can determine the abscissa x of the point F on the phase boundary_FAnd the ordinate x of the point F_F＝x_E。

Step three, searching a single extreme value by adopting the existing sorting algorithm along the y direction, further searching partial wall surfaces, setting a range to avoid the phase interface in order to avoid the search of the phase interface on the wall surfaces, and enabling 0<x_D1＝x_C1<x_F. X is more than or equal to 0 and less than or equal to x_D1And y is not less than 0 and not more than y_EThe search within the range yields a wall A-D1, where the coordinates of D1 are (x)_D1,y_D1) (ii) a At 0<x_f<x_C1And y_E≤y≤L_ySearching in the range to obtain a wall B-C1, wherein the coordinate of C1 is (x)_C1,y_C1) See, fig. 4;

the concrete process of the third step is as follows:

(2) to search the wall A-D1, the abscissa x_iTraverse 0 to x_D1For each abscissa x_iCalculating a straight line x ═ x_iUpper gray level I (x)_iY) gradient in the y direction, as shown in equation (6); searching for dI (x)_iY) of the wall surface coordinate points, the vertical coordinate y of the corresponding wall surface coordinate point can be obtained_iAnd a series of coordinate points (x)_i,y_i) Wall a-D1 is formed;

(3) to search the wall B-C1, the abscissa x_jTraverse 0 to x_C1For each abscissa x_jCalculating a straight line x ═ x_jUpper gray level I (x)_jY) gradient in the y-direction, formula (6) x_iBy substitution of x_jCalculating dI (x)_jY), search for dI (x)_jY) of the wall surface coordinate points, the vertical coordinate y of the corresponding wall surface coordinate point can be obtained_jAnd a series of coordinate points (x)_j,y_j) The wall B-C1 is formed.

Determination of phase boundary and contact point:

from the results obtained in the above steps, the phase interface and the contact point can be further determined. The following step three:

step four, searching a single extreme value by adopting the existing sorting algorithm along the x direction, further searching a part of phase interfaces, setting a range to avoid the two walls in order to avoid the search of the two walls to the phase interfaces, and enabling 0<y_D2<y_F<y_C2<L_y. X is more than or equal to 0≤L_xAnd y_D2≤y≤y_C2The search in the range obtains a partial phase interface C2-D2, and the coordinates of the two points are (x)_D2,y_D2)、(x_C2,y_C2)。

The concrete process of the step four is as follows:

In formula (7), h is the distance from point a to point B, i.e., h is y_B-y_AAnd ε is a coefficient whose value ranges from 0<ε<0.5。

(2) To search for a phase interface, y_iCoordinate traversal y_D2To y_C2For each ordinate y_iCalculating the linear y ═ y_iUpper gray level I (x, y)_i) Gradient dI (x, y) in the x-direction_i) As shown in formula (8); searching for dI (x, y)_i) The maximum value can obtain the vertical coordinate y of the corresponding wall coordinate point_iAnd a series of coordinate points (x)_i,y_i) The wall C2-D2 is formed.

Step five, respectively fitting all coordinate points in the line segments of A-D1 and B-C1 by adopting a linear function to obtain a linear function f_ADAnd f_BCFitting a cubic function to all points in the C2-D2 curve to obtain a cubic function f_CD. Solving for f_ADAnd f_CDThe coordinate (x) of the contact point D can be obtained_D,y_D) Solving for f_ADAnd f_CDThe coordinate (x) of the contact point C can be obtained_C,y_C). The line segments B-C and A-D are wall surfaces, and the curve C-D is a phase interface.

The concrete process of the step five is as follows:

y＝f_AD(x)＝a_ADx+b_AD(9)

y＝f_BC(x)＝a_BCx+b_BC(10)

Fitting a phase interface C2-D2 by using a cubic function, and obtaining a cubic function f by taking a y coordinate as an independent variable and x as a dependent variable_CDAs shown in formula (11).

x＝f_BC(y)＝a_CDy³+b_CDy²+c_CDy+d_CD(11)

(2) The contact points C and D are the intersection points of the two walls and the phase boundary, respectively, and are therefore solved for f_CDAnd f_ADA point of intersection of, and f_CDAnd f_BCThe intersection point, the coordinates (x) of the contact points C and D can be obtained_C,y_C) And (x)_D,y_D) The above process is to solve the equation set shown in equation (12).

(3) And determining all coordinate points on the phase interface and the wall surface. All coordinate points on the wall A-D are required to be taken, and each coordinate point satisfies x_A≤x≤x_DThe x of the abscissa is taken into the formula (9) to be calculated to obtain the corresponding y coordinate, so that the coordinates of all points on the wall surface A-D can be obtained; all coordinate points on the wall B-C are required to be taken, and each coordinate point satisfies x_B≤x≤x_CThe x of the abscissa is taken into the formula (10) to be calculated to obtain the corresponding y coordinate, so that the coordinates of all points on the wall surface B-C can be obtained; for all coordinates on the phase boundary C-DPoint, will each satisfy y_C≤y≤y_DThe ordinate y of (a) is taken into the formula (11) to be calculated so as to obtain the corresponding x coordinate, thereby obtaining the coordinates of all points on the phase interface C-D.

Measurement of contact Angle:

the contact angle is defined as the angle formed by the phase interface with the wall surface at the location of the point of contact. The contact angle of the phase interface at the contact point position is solved, and the fitting function x ═ f of the phase interface obtained in the previous step is obtained_CD(y) coordinate (x) of C_C,y_C) And coordinates (x) of D_D,y_D) Respectively substitute for f_CDThe contact angle theta of the phase boundary at points C and D can be determined from the first derivative of (2)_CAnd theta_D。f_CDOf primary derivative f'_CDIn order to realize the purpose,

f′_CD＝3a_CDy²+2b_CDy+c_CD(13)

will ordinate y_CAnd y_DIn the formula (13), a slope can be obtained, and the contact angle θ shown in FIG. 6 can be obtained by converting the slope into an angle_CAnd theta_D。

In addition, considering that the actually obtained wall surface is not necessarily horizontal and may have a certain inclination angle, the contact angle obtained by equation (14) is corrected. The inclination angle of the wall is the average of the inclination angles of the walls A-D1 and B-C1, i.e., (arctan a)_AD+arctan a_BC)/2. The final value of the contact angle is then,

the results of the present invention are compared with the results of the contact angle measurement of Kr ü ss DSA100 contact angle instrument, which is a commercial device, and are shown in Table 1 below.

TABLE 1 comparison of the test results of the method of the present invention with the existing commercial equipment Kr ü ss DSA100 contact angle instrument

As can be seen from Table 1, the measurement deviation of the contact angle in the range of 40 to 120 is less than 0.5, indicating that the method of the present invention is accurate in measurement.

Claims

1. A contact angle acquisition method for a liquid-liquid two-phase displacement image in a micron capillary tube is characterized in that an obtained microscopic image is subjected to coordinate division, and the pixel size width of the image is set to be L_xAnd length L_y(ii) a Then the following steps are carried out:

Step four, adopting a sorting algorithm to search a single extreme value along the x direction, further searching a part of phase interfaces, setting a range to avoid the two walls in order to avoid the search of the two walls to the phase interfaces, and enabling 0<y_D2<y_F<y_C2<L_yX is more than or equal to 0 and less than or equal to L_xAnd y_D2≤y≤y_C2Searching in the range to obtain a partial phase interface C2-D2 and coordinate points of two pointsOther than (x)_D2,y_D2)、(x_C2,y_C2)；

f′_CD＝3a_CDy²+2b_CDy+c_CD(13)

2. The method for acquiring the contact angle of the liquid-liquid two-phase displacement image in the microcapillary according to claim 1, wherein the specific process of the step one is as follows:

|y_k-y₁|＞αh (3)

(3) Comparison of y₁And y_kLet the smaller of the two be y_minLarger value is y_maxThen the ordinate of point A and point B is determined as y_A＝y_min，y_B＝y_max。

3. The method for acquiring the contact angle of the liquid-liquid two-phase displacement image in the microcapillary according to claim 1, wherein the specific process of the second step is as follows:

(1) the ordinate y of the midpoint E of the line A-B is determined_E；

4. The method for acquiring the contact angle of the liquid-liquid two-phase displacement image in the microcapillary according to claim 1, wherein the specific process of the step three is as follows:

5. The method for acquiring the contact angle of the liquid-liquid two-phase displacement image in the microcapillary according to claim 1, wherein the specific process of the step four is as follows:

6. the method for acquiring the contact angle of the liquid-liquid two-phase displacement image in the microcapillary according to claim 1, wherein the specific process of the step five is as follows:

y＝f_AD(x)＝a_ADx+b_AD(9)

y＝f_BC(x)＝a_BCx+b_BC(10)

x＝f_BC(y)＝a_CDy³+b_CDy²+c_CDy+d_CD(11)

7. The method for acquiring the contact angle of the liquid-liquid two-phase displacement image in the microcapillary according to claim 1, further comprising the following steps: when the actually obtained wall surface is not horizontal, the contact angle obtained by equation (14) is corrected as follows: the inclination angle of the wall is the average of the inclination angles of the walls A-D1 and B-C1, i.e., (arctan a)_AD+arctan a_BC) /2, then connectThe final value of the antenna is: