CN112179813A - Liquid contact angle on-line measurement method based on experimental image - Google Patents
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Abstract
An on-line measuring method of liquid contact angle based on experimental image, the method is based on static or quasi-static real-time experimental image directly obtained in experiment, extract the interface outline with Canny method; then, solving a series of predicted contours by changing the predicted contact angle serving as a boundary condition by using a Young-Laplace equation; and comparing the predicted profile with the experimental profile to calculate a norm error so as to determine a contact angle and an error limit. The method converts the measurement of the contact angle into the error contrast of the profile, not only has higher measurement precision, but also can reflect the change of the contact angle in the experiment caused by the instability of the coating. The measuring method can be used for measuring the contact angle on a plane and spherical substrate, does not need a special measuring device, can be applied to common horizontal drop experiments, and can also be applied to the contact angle measurement in liquid bridge, capillary lifting and liquid experiments containing air holes, which cannot be realized by the conventional method.
Description
Technical Field
The invention relates to an on-line measuring method of a liquid contact angle, in particular to an on-line measuring method of a liquid contact angle based on an experimental image, and belongs to the technical field of physical measurement.
Background
The contact angle of solid-liquid-gas or solid-liquid is an important index for measuring the affinity of three phases of solid-liquid-gas/solid-liquid, is closely related to the wetting state of the three phases of solid-liquid-gas/solid-liquid, and is an important characterization index commonly used in the fields of industrial production and scientific research. The current method for measuring the contact angle is mainly the horizontal dropping method, namely, the contact angle is measured by using the contact profile of a liquid drop and a substrate by dropping a small liquid drop on the surface of a solid flat sample. The method needs a special measuring instrument and requires the solid sample to be in a horizontal position, and does not meet special experimental requirements. The method is used for measuring the contact angle of the surface of the material before the experiment begins, and for some surfaces with unstable coatings, the method can not accurately reflect the actual condition of the contact angle at the later stage of the experiment and can not monitor the change condition of the contact angle in real time, so that the effect of the coating in the experiment can not be fed back in time.
Disclosure of Invention
The invention aims to provide an on-line liquid contact angle measuring method based on an experimental image, aiming at the problems that a special measuring instrument is needed in the current liquid contact angle measurement, the contact angle change caused by coating instability in the experimental process cannot be reflected in real time, and a flat substrate needs to be specially processed.
The technical scheme of the invention is as follows:
the measuring process is realized by predicting the contact angle, further predicting the outline and comparing the predicted outline with the experimental outline to calculate the norm error, and the norm error between the predicted outline and the experimental outline is taken as the standard for measuring the measuring effect; finally obtaining a minimum predicted contact angle with norm error meeting the target precision, a maximum predicted contact angle and a predicted contact angle with the minimum norm error, namely an upper limit of a contact angle measurement result, a lower limit of the contact angle measurement result and an optimal value of the contact angle measurement result; the method comprises the following specific steps:
1) selecting a static or quasi-static solid-liquid-gas or solid-liquid three-phase contact area image from a real-time experiment video to obtain an experiment image;
2) selecting the position of the solid substrate: if the substrate is a flat substrate, selecting two points on the substrate, and if the substrate is a spherical substrate, selecting three points on the substrate;
3) after the position of the solid substrate is determined, calculating the gray change gradient of different positions by using a canny algorithm according to the gray distribution of an experimental image, and identifying the interface profile by using a double-threshold method;
4) performing polynomial fitting on the interface profile extracted in the step 3), and performing smoothing treatment on the interface profile;
5) by observing an experimental image, giving a value which is obviously smaller than an actual contact angle as an iteration initial value of a predicted contact angle;
6) using the predicted contact angle as a boundary condition of the predicted interface contour, and solving coordinate increment of any two adjacent interface points by using a difference format of a Young-Laplace equation so as to obtain all points on the predicted contour;
7) comparing the predicted contour obtained in the step 6) with the experimental contour processed in the step 4), calculating a norm error, if the norm error is greater than the target precision, increasing a predicted step length for the predicted contact angle, and repeating the step 6); if the norm error is smaller than the target precision, taking the predicted contact angle as the lower limit of the contact angle measurement result, and returning the lower limit of the contact angle measurement result;
8) predicting the contact angle to increase by a prediction step; using the predicted contact angle as a boundary condition of the predicted interface contour, and solving coordinate increment of any two adjacent interface points by using a difference format of a Young-Laplace equation so as to obtain all points on the predicted contour;
9) comparing the predicted contour obtained in the step 8) with the experimental contour processed in the step 4), calculating a norm error, and repeating the step 8) if the norm error is smaller than the target precision; if the norm error is larger than the target precision, subtracting a step length from the predicted contact angle to serve as the upper limit of the contact angle measurement result, stopping stepping, and returning to the upper limit of the contact angle measurement result;
10) and taking the predicted contact angle with the minimum norm error between the lower limit of the contact angle measurement result and the upper limit of the contact angle measurement result as the optimal value of the contact angle measurement result, returning the optimal value of the contact angle measurement result, and finishing the measurement.
In the above technical solution, the differential format of the Young-Laplace equation includes the following two types:
a) two-dimensional planar conditions:
wherein γ is the surface tension between the liquid-gas or liquid-liquid interfaces;
is the tangential angle differential; ds is the differential of the interface arc length; x is the abscissa; z is the ordinate; dx is the abscissa differential; dz is the ordinate differential; Δ p is the pressure difference at the reference position, which needs to satisfy the condition: Δ p ═ ρ gz0Wherein z is0Is the liquid phase depth at the reference position; rho is the density difference of liquid-gas or liquid-liquid two phases; g is the acceleration of gravity;
b) the case of axial symmetry:
wherein γ is the surface tension between the liquid-gas or liquid-liquid interfaces;
is the tangential angle differential; ds is the differential of the interface arc length; r is the abscissa; z is the ordinate; dr is the abscissa differential; dz is the ordinate differential; Δ p is the pressure difference at the reference position, which needs to satisfy the condition: Δ p ═ ρ gz0Wherein z is0Is the liquid phase depth at the reference position; rho is the density difference of liquid-gas or liquid-liquid two phases; g is the acceleration of gravity.
Compared with the prior art, the invention has the following advantages and prominent technical effects: firstly, a real-time experiment image directly obtained from an experiment is utilized, and a special measuring device is not needed; for the unstable condition of the material surface coating, the change condition of the contact angle in the experimental process can be reflected; the application field is expanded from a conventional horizontal drop experiment to a capillary lifting experiment, a liquid bridge experiment and a liquid experiment containing air holes, and the method is also suitable for measuring the contact angle on the spherical substrate with curvature; and thirdly, the predicted contour is solved by a self-adaptive method, the measurement of the contact angle is converted into the contrast of the contour, and the higher precision is achieved.
Drawings
FIG. 1 is a flow chart of the measurement method of the present invention.
FIG. 2 is a front view of the backlight of the collapse experiment of the air holes in the liquid film.
FIG. 3 is a comparison of the predicted profile and the experimental profile for the example predicted contact angle of 152 degrees.
FIG. 4 is a comparison of the predicted profile and the experimental profile for the example where the predicted contact angle is 154 degrees.
FIG. 5 is a graph comparing the predicted profile and the experimental profile when the predicted contact angle is 156 degrees in the examples.
Fig. 6 is a corresponding relationship between the predicted contact angle and the error norm in the embodiment.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings and examples.
According to the liquid contact angle on-line measuring method based on the experimental image, a special measuring device is not needed, the experimental image is directly used for realizing on-line contact angle measurement, and the method is not limited to a horizontal drop experimental image; the change of the contact angle in the experiment can be reflected in the case of unstable coating, and the method can be used for measuring the contact angle of not only a plane substrate but also a spherical substrate. The measuring process is realized by predicting the contact angle to further obtain a predicted contour and comparing the predicted contour with an experimental contour to calculate a norm error, and the norm error between the predicted contour and the experimental contour is used as a standard for measuring the measuring effect; the method finally obtains the minimum predicted contact angle, the maximum predicted contact angle and the predicted contact angle with the minimum norm error, wherein the norm error meets the target precision, namely the optimal values of the upper limit of the contact angle measurement result, the lower limit of the contact angle measurement result and the contact angle measurement result. The method specifically comprises the following steps:
1) selecting a static or quasi-static experimental image of a solid-liquid-gas or solid-liquid three-phase contact area needing to measure a contact angle from a real-time experimental video;
2) sequentially selecting points on the solid substrate, returning the enter key to the positions of the points on the substrate after the selection is finished, and treating the substrate as a flat substrate if two points are selected; if three points are selected, treating the substrate as a spherical substrate;
3) referring to the solid substrate position determined in the step 2), calculating the gray level change gradient of different positions by using a canny algorithm according to the gray level distribution of the experimental image, wherein two adjustable threshold values, namely a high threshold value and a low threshold value, are provided as parameters for controlling the boundary identification continuity: the pixel points with the gray gradient larger than the high threshold are considered as strong boundary points; pixel points with gray gradients smaller than the low threshold are not considered as boundary points; the gray gradient is between two thresholds, and the pixel points near the strong boundary point are considered as weak boundary points; the gray gradient is between two thresholds, but the pixel point which is not near the strong boundary point is not considered as the boundary point;
4) performing polynomial fitting on the interface contour extracted in the step 3) to perform smoothing processing on the boundary, wherein the polynomial fitting is used for extracting boundary points and comparing the boundary points with a predicted contour obtained by subsequent calculation, the order of the polynomial fitting can be adjusted, and the fitting condition is observed in real time;
5) according to the experimental image, giving a value which is obviously smaller than the actual contact angle as an initial predicted contact angle;
6) and (3) taking the predicted contact angle as a boundary condition of the predicted interface profile, and solving the corresponding predicted interface profile by utilizing a differential format of a Young-Laplace equation: the program can calculate the coordinate increment of any two adjacent boundary points according to the difference format, and the coordinate of each point can be calculated by increment accumulation only by knowing the predicted contact angle of the coordinate of the first point;
i. the differential format of the Young-Laplace equation comprises two conditions:
a) two-dimensional case:
wherein γ is the surface tension between the liquid-gas or liquid-liquid interfaces;
is the tangential angle differential; ds is the differential of the interface arc length; x is the abscissa; z is the ordinate; Δ p is the pressure difference at the reference position, which needs to satisfy the condition: Δ p ═ ρ gz0Wherein z is0Is the liquid phase depth at the reference position; rho is the density difference of liquid-gas or liquid-liquid two phases; g is the acceleration of gravity; dx is the abscissa differential; dz is the ordinate differential;
b) the axisymmetric case is:
wherein γ is the surface tension between the liquid-gas or liquid-liquid interfaces;
is the tangential angle differential; ds is the differential of the interface arc length; r is the abscissa; z is the ordinate; Δ p is the pressure difference at the reference position, which needs to satisfy the condition: Δ p ═ ρ gz0Wherein z is0Is the liquid phase depth at the reference position; rho is the density difference of liquid-gas or liquid-liquid two phases; g is the acceleration of gravity; dr is the abscissa differential; dz is the ordinate differential;
using the predicted contact angle as a boundary condition, and solving the predicted profile comprises the following steps:
a) the predicted contact angle is taken as the coordinate s is 0, and x is x1Z is 0 or s is 0 and r is r1The tangent angle coordinate of the point where z is 0, i.e. the tangent angle coordinate of the first point, where x1And r1The abscissa value of the outline contact part identified in the step 4;
b) solving the coordinate increment from the first point to the second point by utilizing a Young-Laplace equation difference format, and summing the coordinate increment with the coordinate of the first point to obtain the coordinate of the second point;
c) solving the coordinate increment from the second point to the third point by utilizing a Young-Laplace equation difference format, and summing the coordinate increment with the coordinate of the second point to obtain the coordinate of the third point; repeating the steps until the tangent angle is larger than 180 degrees or smaller than minus 180 degrees, and obtaining a series of points as points on the predicted contour;
when the predicted contour is solved in the step 6, the parameters of the Young-Laplace equation, namely the reference point pressure difference delta p corresponding to the predicted contact angle, need to be targeted, and the step is as follows:
a) giving an initial estimated upper limit and a lower limit of the pressure difference of the reference point;
b) respectively taking the estimated upper limit and the estimated lower limit as Young-Laplace equation parameters, calculating two groups of points on the predicted contour, wherein the tangent angle coordinates of the two groups of contour termination points meet a positive-negative condition;
c) gradually reducing the difference between the estimated upper limit and the estimated lower limit of the pressure difference by utilizing a dichotomy method, and stopping iteration until the difference between the estimated upper limit and the estimated lower limit is smaller than the target precision;
d) taking the average value of the pressure difference estimation upper limit and the estimation lower limit as the reference point pressure difference corresponding to the predicted contact angle, and taking the pressure difference as a Young-Laplace equation parameter to obtain a predicted profile, namely the predicted profile corresponding to the predicted contact angle;
7) comparing the predicted contour obtained in the step 6 with the experimental contour processed in the step 4, calculating a norm error, if the norm error is greater than the target precision, increasing a predicted step length for the predicted contact angle, and repeating the step 6; if the norm error is smaller than the target precision, taking the value as the lower limit of the contact angle measurement result, and returning the lower limit of the contact angle measurement result;
i. step 11, calculating the norm of the norm error includes the following steps:
a) 1-norm:
b) 2-norm:
c) p-norm:
wherein E represents a norm, x1，x2，...，xnTo be the radial coordinate of the point on the experimental profile,
predicting the radial coordinate of a point on the contour, wherein p is any positive integer;
8) predicting the contact angle to increase by a prediction step; solving the predicted interface contour by taking the predicted contact angle as a boundary condition of the predicted interface contour and utilizing a difference format of a Young-Laplace equation, wherein the process is similar to the step 6;
9) comparing the predicted contour obtained in the step 8 with the experimental contour processed in the step 4, calculating a norm error, and repeating the step 8 if the norm error is smaller than the target precision; if the norm error is larger than the target precision, subtracting one step length from the predicted contact angle to serve as the upper limit of the contact angle measurement result, stopping stepping, and returning to the upper limit of the contact angle measurement result;
10) and taking the predicted contact angle with the minimum norm error between the lower limit of the contact angle measurement result and the upper limit of the contact angle measurement result as the optimal value of the contact angle measurement result, returning the optimal value of the contact angle measurement result, and finishing the measurement.
Example (b):
taking the collapse experiment of the air holes in the liquid film as an example, the measurement process is as follows:
1) selecting an experimental image in the quasi-static shrinkage process of the air hole boundary before the liquid film is collapsed as an experimental image of a contact angle to be detected, as shown in fig. 2, wherein a black area is an air hole, and a white area is a liquid film;
2) selecting two points on a substrate, and determining a solid flat substrate;
3) setting the high and low threshold values of the identification image as 120 and 40 respectively;
4) the fitting order of the interface profile is set to 9
5) The contact angle in the experimental image is obviously larger than 150 degrees, 150 degrees are selected as initial prediction contact angles, and the prediction step length is 0.1 degree;
6) selecting an axisymmetric format by a Young-Laplace equation;
7) setting the estimated upper limit of the pressure difference of the reference point to be 60 Pa, the estimated lower limit to be 40 Pa and the target precision of the pressure difference to be 0.001;
8) setting a contact angle norm error to adopt a 2-norm, wherein the target precision is 10;
9) the program sequentially displays a contact angle measurement result lower limit profile comparison graph 3, a contact angle measurement result optimal value profile comparison graph 4, a contact angle measurement result upper limit profile comparison graph 5 and a norm error and predicted contact angle corresponding relation graph 6, wherein the upper limit of the contact angle measurement result, the optimal value of the contact angle measurement result and the position where the iteration of the predicted contact angle is stopped (the predicted contact angle is larger than the upper limit of the contact angle measurement result by one predicted step length) are marked in the graph 6;
10) the program returns the measurement results: the lower limit of the contact angle measurement result is 151.9 degrees, the optimal value of the contact angle measurement result is 154.4 degrees, and the upper limit of the contact angle measurement result is 156.7 degrees.
Claims (2)
1. An on-line measuring method for liquid contact angle based on experimental image is characterized in that the method comprises the following steps:
1) selecting a static or quasi-static solid-liquid-gas or solid-liquid three-phase contact area image from a real-time experiment video to obtain an experiment image;
2) selecting the position of the solid substrate: if the substrate is a flat substrate, selecting two points on the substrate, and if the substrate is a spherical substrate, selecting three points on the substrate;
3) after the position of the solid substrate is determined, calculating the gray change gradient of different positions by using a canny algorithm according to the gray distribution of an experimental image, and identifying the interface profile by using a double-threshold method;
4) performing polynomial fitting on the interface profile extracted in the step 3), and performing smoothing treatment on the interface profile;
5) by observing an experimental image, giving a value which is obviously smaller than an actual contact angle as an iteration initial value of a predicted contact angle;
6) using the predicted contact angle as a boundary condition of the predicted interface contour, and solving coordinate increment of any two adjacent interface points by using a difference format of a Young-Laplace equation so as to obtain all points on the predicted contour;
7) comparing the predicted contour obtained in the step 6) with the experimental contour processed in the step 4), calculating a norm error, if the norm error is greater than the target precision, increasing a predicted step length for the predicted contact angle, and repeating the step 6); if the norm error is smaller than the target precision, taking the predicted contact angle as the lower limit of the contact angle measurement result, and returning the lower limit of the contact angle measurement result;
8) predicting the contact angle to increase by a prediction step; using the predicted contact angle as a boundary condition of the predicted interface contour, and solving coordinate increment of any two adjacent interface points by using a difference format of a Young-Laplace equation so as to obtain all points on the predicted contour;
9) comparing the predicted contour obtained in the step 8) with the experimental contour processed in the step 4), calculating a norm error, and repeating the step 8) if the norm error is smaller than the target precision; if the norm error is larger than the target precision, subtracting a step length from the predicted contact angle to serve as the upper limit of the contact angle measurement result, stopping stepping, and returning to the upper limit of the contact angle measurement result;
10) and taking the predicted contact angle with the minimum norm error between the lower limit of the contact angle measurement result and the upper limit of the contact angle measurement result as the optimal value of the contact angle measurement result.
2. The method according to claim 1, wherein the differential format of the Young-Laplace equation comprises the following two cases:
a) two-dimensional planar conditions:
wherein γ is the surface tension between the liquid-gas or liquid-liquid interfaces;
is the tangential angle differential; ds is the differential of the interface arc length; x is the abscissa; z is the ordinate; dx is the abscissa differential; dz is the ordinate differential; Δ p is the pressure difference at the reference position, which needs to satisfy the condition: Δ p ═ ρ gz0Wherein z is0Is the liquid phase depth at the reference position; rho is the density difference of liquid-gas or liquid-liquid two phases; g is the acceleration of gravity;
b) the case of axial symmetry:
wherein γ is the surface tension between the liquid-gas or liquid-liquid interfaces;
is the tangential angle differential; ds is the differential of the interface arc length; r is the abscissa; z is the ordinate; dr is the abscissa differential; dz is the ordinate differential; Δ p is the pressure difference at the reference position, which needs to satisfy the condition: Δ p ═ ρ gz0Wherein z is0Is the liquid phase depth at the reference position; rho is the density difference of liquid-gas or liquid-liquid two phases; g is the acceleration of gravity.
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| CN113029870A (en) * | 2021-03-31 | 2021-06-25 | 华中科技大学 | Three-phase contact angle measuring method of partial phase solution liquid system and application thereof |
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