Contact angle prediction method, system, terminal and medium based on multi-fractal theory

Abstract

The application relates to the technical field of contact angle detection of material surfaces, and discloses a contact angle prediction method, system, terminal and medium based on a multi-fractal theory, which introduces the multi-fractal theory to represent the micro-morphology of a material surface, processes a micro-morphology picture to obtain a binary image, and calculates a fractal dimension and a multi-fractal spectrum through the binary image, wherein the fractal dimension is calculated by using a box dimension method, and the multi-fractal spectrum is obtained through nonlinear fitting; compared with a single fractal dimension, the two parameters of a spectrum width Delta alpha and a spectrum difference Delta f of the multi-fractal spectrum can be more comprehensively and meticulously introduced into a prediction model to quantitatively evaluate the roughness of the material surface; the multi-fractal spectrum and the fractal dimension are combined and input into a contact angle prediction model of the multi-fractal theory to obtain an actual contact angle, so that the accuracy of contact angle prediction of a fractal structure surface is improved.

Description

Technical Field

[0001] This invention relates to the field of contact angle detection technology for material surfaces, specifically to a contact angle prediction method, system, terminal, and medium based on multifractal theory. Background Technology

[0002] Wetting is a macroscopic result of the interaction of microscopic properties such as the surface structure of solid materials, liquid properties, and molecular forces at the solid-liquid interface. Research at this stage indicates that the microscopic morphology of solid material surfaces is the main factor affecting the wetting performance of solid-liquid interfaces. Although three classic theoretical models of wettability were proposed early on—the Young model, the Wenzel model, and the Cassie-Baxter model—these models theoretically establish the relationship between the contact angle and its influencing factors. However, the roughness factor, which characterizes the microscopic morphology in these models, is difficult to obtain and apply practically to real solid materials.

[0003] Therefore, researchers introduced fractal theory, using fractal parameters calculated by computer programming software to quantitatively characterize the microstructure of solid material surfaces, finding this method feasible. By combining the scale of the fractal surface microstructure, a contact angle prediction model based on the fractal dimension for fractal surface structures can be obtained, quantitatively characterizing the microstructure of solid surfaces. However, it has been found that the fractal dimension has limitations in describing the local microstructure of surfaces, namely, it is difficult to comprehensively and quantitatively describe the structure, distribution, and other details of the rough microstructure of solid surfaces. Therefore, it is necessary to seek other characterization parameters that can comprehensively and quantitatively characterize the microstructure, in order to obtain new contact angle prediction models based on single fractals and improve the accuracy of contact angle prediction for fractal surface structures. Summary of the Invention

[0004] In order to overcome the shortcomings of the existing technology, the present invention aims to provide a contact angle prediction method, system, terminal and medium based on multifractal theory, so as to solve the technical problem that the fractal dimension cannot fully and quantitatively describe the local micromorphology of the surface and the accuracy of the contact angle prediction of the fractal structure surface is low.

[0005] This invention is achieved through the following technical solution:

[0006] A contact angle prediction method based on multifractal theory includes the following steps:

[0007] Step 1: Collect microscopic images of the surface of the material.

[0008] Step 2: Process the microscopic morphology image to obtain a binarized image;

[0009] Step 3: The fractal dimension and multifractal spectrum are calculated from the binarized image. The fractal dimension is calculated using the box dimension method, and the multifractal spectrum is obtained through nonlinear fitting.

[0010] Step 4: Substitute the multifractal spectrum into the contact angle prediction model based on fractal theory to obtain the contact angle prediction model based on multifractal theory.

[0011] Step 5: Input the multifractal spectrum and fractal dimension into the contact angle prediction model of multifractal theory to obtain the actual contact angle.

[0012] Preferably, in step 2, the specific process of processing the microscopic morphology image to obtain a binarized image is as follows:

[0013] The micro-morphology image is processed in grayscale to obtain the maximum RGB value H1 and the minimum RGB value H2 after grayscale conversion. The first threshold T0 is then calculated using the maximum RGB value H1 and the minimum RGB value H2, where the formula is T0=(H1+H2) / 2.

[0014] The first threshold T0 is compared with all RGB values ​​in the grayscale micro-topography image. When all RGB values ​​in the grayscale micro-topography image are less than the first threshold T0, the grayscale micro-topography image is considered the foreground / background; otherwise, it is considered the background / background. The average RGB value H0 of the foreground / background and the average RGB value H of the background / background of the grayscale micro-topography image are calculated respectively. B The average RGB values ​​H0 of the foreground and background after grayscale conversion of the microscopic morphology image and the average RGB values ​​H of the background after grayscale conversion of the microscopic morphology image are used to determine the relationship between the foreground and background. B The second threshold H is calculated, where the formula is H = (H B +H0) / 2;

[0015] When the second threshold H remains constant, the segmentation threshold h is obtained; otherwise, the segmentation thresholds H0 and H are adjusted again. B The process is iterated and recalculated until the resulting second threshold H remains constant. When the RGB value of the grayscale micro-morphology image is greater than the segmentation threshold h, all pixels in the micro-morphology image are treated as white; otherwise, all pixels in the micro-morphology image are treated as black, thus obtaining a binarized image.

[0016] Furthermore, the formulas for calculating the maximum RGB value H1 and the minimum RGB value H2 after grayscale conversion of the microscopic morphology image are as follows:

[0017] GrayScale(RGB)=max(H1,H2,H3,...)

[0018] GrayScale(RGB)=min(H1,H2,H3,...)

[0019] Where GrayScale represents a grayscale image, RGB represents the grayscale values ​​obtained from processing the image, and max and min represent the maximum and minimum values;

[0020] The average RGB values ​​H0 of the foreground and background and the average RGB value H of the background after grayscale conversion of the microscopic morphology image B The calculation formula is as follows:

[0021] H0 = [RGB] <T0] / N

[0022] H B =[RGB>T0] / N

[0023] Where N represents the number of grids in the image, and T0 represents the first threshold, which is half the sum of H1 and H2.

[0024] Preferably, in step 3, the fractal dimension is calculated using the binarized image. The fractal dimension is calculated using the box dimension method, and the specific process is as follows:

[0025] A MATLAB program is used to load the binarized image processed in step 2 and extract a 2D image. N ×2 N An image of pixels, yielding a 2 N A matrix of order 2, where white pixels are represented as 1 and black pixels as 0; the resulting 2 N The matrix is ​​divided into several blocks, and the number of rows and columns of each block is set to k, where k = 1, 2, 4, ..., 2N-1; when each block contains 1 white pixel, the total number of white pixel grids is counted, thereby obtaining the number of data pairs of grid widths corresponding to the number of white pixel grids;

[0026] Let the region covering the entire black and white pixel grid after binarized image processing be the fractal set A. Then, the number of white pixel grids is represented by N(ε), and the data logarithm of the grid width corresponding to the number of white pixel grids can be represented by lgN(ε). For the fractal set A, N(ε) is the number of sets with diameter ε covering the fractal set A. There is the following mathematical relationship between N(ε) and ε: N(ε)ε^k. In a double logarithmic coordinate system, if a linearly related line can be obtained, then let lgε be the abscissa and lgN(ε) be the ordinate. By fitting the above data, the negative of the slope k of this linearly related line is the value of the box count dimension. The value of the box count dimension is the value of the fractal dimension.

[0027] Preferably, in step 3, the multifractal spectrum is calculated from the binarized image, wherein the multifractal spectrum is obtained through nonlinear fitting, and the specific process is as follows:

[0028] Write a MATLAB program to import the microscopic morphology image obtained in step 1 into a folder in the current MATLAB directory, process it into a binarized image as in step 2, and overlay the target fractal image within a small grid. Let n be the number of pixels in the small grid. ij The total number of pixels in the image is ∑n ij Then the probability measure P ij (δ) is n ij With ∑n ij The ratio;

[0029] The q-order matrix partition function χ(δ) is the sum of the q-order probability measures of all pixels, where q is a weighting factor and represents the probability measure P in the partition function χ(δ). ij The proportion; when q>0, it indicates that a larger weight is in the higher regions of the surface; conversely, q<0 indicates that a larger weight is in the lower regions; the partition function χ(δ) is a power function of δ: X(δ)∝δ -τ(q) , where τ(q) is the quality index;

[0030] Assuming τ(q) and q are convex functions, the graph is a multifractal, which can be obtained by performing the Legendre transformation:

[0031]

[0032] Where f(α) is the multifractal spectrum, which is the fractal dimension of a subset; under the same singularity index α, α is a function of q, then α can be written as α(q);

[0033] The multifractal spectrum is characterized by the spectral width Δα and the spectral difference Δf, and the specific formula is as follows:

[0034] Δα=α max -α min

[0035] Δf=f(α min )-f(α max )

[0036] Where, α max and f(α) max α represents the dimension of the maximum probability subset and the number of dimensions of the maximum probability subset, respectively. min and f(α) min ) represent the dimension of the minimum probability subset and the number of dimensions of the minimum probability subset, respectively.

[0037] Preferably, in step 4, the contact angle prediction model formula based on multifractal theory is as follows:

[0038] cosθ w = (9Δα^2 + |Δf|) D-2 cosθ

[0039] Where, θ w θ and θ represent the actual contact angle and the intrinsic contact angle, respectively, in °; Δα and Δf represent the spectral width and spectral difference, respectively, and D represents the fractal dimension.

[0040] Preferably, in step 5, the process of prediction based on the contact angle prediction model of multifractal theory is as follows:

[0041] The fractal dimension D, combined with the multifractal spectrum, is substituted into the contact angle prediction model based on multifractal theory. The multifractal spectrum includes the spectral width Δα and the spectral difference Δf. The contact angle cosθ, based on multifractal theory, is then calculated using the known intrinsic contact angle θ. w Then, regarding the contact angle cosθ in multifractal theory... w The inverse calculation formula yields the actual contact angle θ. w The inverse calculation formula is as follows: θ w =arccos(cosθ) w ).

[0042] A contact angle prediction system based on multifractal theory, comprising the aforementioned contact angle prediction method based on multifractal theory, including...

[0043] The image acquisition module is used to acquire the microscopic morphology of the material surface to obtain microscopic morphology images;

[0044] The image processing module is used to process microscopic morphology images to obtain binarized images;

[0045] The first data processing module is used to calculate the fractal dimension and multifractal spectrum from the binarized image. The fractal dimension is calculated using the box dimension method, and the multifractal spectrum is obtained through nonlinear fitting.

[0046] The model creation module is used to substitute the multifractal spectrum into the contact angle prediction model based on fractal theory to obtain the contact angle prediction model based on multifractal theory.

[0047] The second data processing module is used to input the multifractal spectrum and fractal dimension into the contact angle prediction model of multifractal theory to obtain the actual contact angle.

[0048] A mobile terminal includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of a contact angle prediction method based on multifractal theory as described above.

[0049] A computer-readable storage medium storing a computer program, characterized in that, when executed by a processor, the computer program implements the steps of the contact angle prediction method based on multifractal theory as described above.

[0050] Compared with the prior art, the present invention has the following beneficial technical effects:

[0051] This invention provides a contact angle prediction method based on multifractal theory. Multifractal theory is introduced to characterize the microstructure of material surfaces. Microstructure images are processed to obtain binarized images, and the fractal dimension and multifractal spectrum are calculated from these images. The fractal dimension is calculated using the box-count method, and the multifractal spectrum is obtained through nonlinear fitting. Compared to a single fractal dimension, this method provides a more comprehensive and detailed quantitative evaluation of the material surface roughness. Two parameters of the multifractal spectrum, spectral width Δα and spectral difference Δf, are introduced into the prediction model. The multifractal spectrum, combined with the fractal dimension, is input into the multifractal theory-based contact angle prediction model to obtain the actual contact angle, thus improving the accuracy of contact angle prediction for fractal structure surfaces. Attached Figure Description

[0052] Figure 1 This is a flowchart of the contact angle prediction method based on multifractal theory in this invention;

[0053] Figure 2 These are schematic diagrams of the surface micromorphology of PVDF specimens with different numbers in the embodiments of the present invention;

[0054] Figure 3 This is a graph showing the relationship between the fractal dimension of the PVDF and its number in an embodiment of the present invention;

[0055] Figure 4 This is the α-f(α) multifractal spectrum of the PVDF in this embodiment of the invention;

[0056] Figure 5 This is a schematic diagram showing the contact angles between PVDF specimens with distilled water at different serial numbers in an embodiment of the present invention.

[0057] Figure 6 This is a schematic diagram showing the measured and theoretical values ​​of the surface contact angle of the PVDF specimen in distilled water in an embodiment of the present invention. Detailed Implementation

[0058] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0059] The present invention will now be described in further detail with reference to the accompanying drawings:

[0060] The purpose of this invention is to provide a contact angle prediction method, system, terminal, and medium based on multifractal theory, so as to solve the technical problem that the fractal dimension cannot fully and quantitatively describe the local micromorphology of the surface and the accuracy of the contact angle prediction of the fractal structure surface is low in the prior art.

[0061] according to Figure 1 As shown, this invention provides a contact angle prediction method based on multifractal theory, comprising the following steps:

[0062] Step 1: Collect microscopic images of the surface of the material.

[0063] Step 2: Process the microscopic morphology image to obtain a binarized image;

[0064] Specifically, the process of processing microscopic morphology images to obtain binarized images is as follows:

[0065] The micro-morphology image is processed in grayscale to obtain the maximum RGB value H1 and the minimum RGB value H2 after grayscale conversion. The first threshold T0 is then calculated using the maximum RGB value H1 and the minimum RGB value H2, where the formula is T0=(H1+H2) / 2.

[0066] The first threshold T0 is compared with all RGB values ​​in the grayscale micro-topography image. When all RGB values ​​in the grayscale micro-topography image are less than the first threshold T0, the grayscale micro-topography image is considered the foreground / background; otherwise, it is considered the background / background. The average RGB value H0 of the foreground / background and the average RGB value H of the background / background of the grayscale micro-topography image are calculated respectively. B The average RGB values ​​H0 of the foreground and background after grayscale conversion of the microscopic morphology image and the average RGB values ​​H of the background after grayscale conversion of the microscopic morphology image are used to determine the relationship between the foreground and background. B The second threshold H is calculated, where the formula is H = (H B +H0) / 2;

[0067] When the second threshold H remains constant, the segmentation threshold h is obtained; otherwise, the segmentation thresholds H0 and H are adjusted again. BThe process is iterated and recalculated until the resulting second threshold H remains constant. When the RGB value of the grayscale micro-morphology image is greater than the segmentation threshold h, all pixels in the micro-morphology image are treated as white; otherwise, all pixels in the micro-morphology image are treated as black, thus obtaining a binarized image.

[0068] The formulas for calculating the maximum RGB value H1 and the minimum RGB value H2 after grayscale conversion of the microscopic morphology image are as follows:

[0069] GrayScale(RGB)=max(H1,H2,H3,...)

[0070] GrayScale(RGB)=min(H1,H2,H3,...)

[0071] Where GrayScale represents a grayscale image, RGB represents the grayscale values ​​obtained from processing the image, and max and min represent the maximum and minimum values;

[0072] The average RGB values ​​H0 of the foreground and background and the average RGB value H of the background after grayscale conversion of the microscopic morphology image B The calculation formula is as follows:

[0073] H0 = [RGB] <T0] / N

[0074] H B =[RGB>T0] / N

[0075] Where N represents the number of grids in the image, and T0 represents the first threshold, which is half the sum of H1 and H2.

[0076] Step 3: The fractal dimension and multifractal spectrum are calculated from the binarized image. The fractal dimension is calculated using the box dimension method, and the multifractal spectrum is obtained through nonlinear fitting.

[0077] Specifically, the fractal dimension is calculated from the binarized image, where the fractal dimension is calculated using the box dimension method. The specific process is as follows:

[0078] A MATLAB program is used to load the binarized image processed in step 2 and extract a 2D image. N ×2 N An image of pixels, yielding a 2 N A matrix of order 2, where white pixels are represented as 1 and black pixels as 0; the resulting 2 N The matrix is ​​divided into several blocks, and the number of rows and columns of each block is set to k, where k = 1, 2, 4, ..., 2N-1; when each block contains 1 white pixel, the total number of white pixel grids is counted, thereby obtaining the number of data pairs of grid widths corresponding to the number of white pixel grids;

[0079] Let the region covering the entire black and white pixel grid after binarized image processing be the fractal set A. Then, the number of white pixel grids is represented by N(ε), and the data logarithm of the grid width corresponding to the number of white pixel grids can be represented by lgN(ε). For the fractal set A, N(ε) is the number of sets with diameter ε covering the fractal set A. There is the following mathematical relationship between N(ε) and ε: N(ε)ε^k. In a double logarithmic coordinate system, if a linearly related line can be obtained, then let lgε be the abscissa and lgN(ε) be the ordinate. By fitting the above data, the negative of the slope k of this linearly related line is the value of the box count dimension. The value of the box count dimension is the value of the fractal dimension.

[0080] Specifically, the multifractal spectrum is calculated from the binarized image. The multifractal spectrum is obtained through nonlinear fitting, and the specific process is as follows:

[0081] Write a MATLAB program to import the microscopic morphology image obtained in step 1 into a folder in the current MATLAB directory, process it into a binarized image as in step 2, and overlay the target fractal image within a small grid. Let n be the number of pixels in the small grid. ij The total number of pixels in the image is ∑n ij Then the probability measure P ij (δ) is n ij With ∑n ij The ratio;

[0082] The q-order matrix partition function χ(δ) is the sum of the q-order probability measures of all pixels, where q is a weighting factor and represents the probability measure P in the partition function χ(δ). ij The proportion; when q>0, it indicates that a larger weight is in the higher regions of the surface; conversely, q<0 indicates that a larger weight is in the lower regions; the partition function χ(δ) is a power function of δ: X(δ)∝δ -τ(q) , where τ(q) is the quality index;

[0083] Assuming τ(q) and q are convex functions, the graph is a multifractal, which can be obtained by performing the Legendre transformation:

[0084]

[0085] Where f(α) is the multifractal spectrum, which is the fractal dimension of a subset; under the same singularity index α, α is a function of q, then α can be written as α(q);

[0086] The multifractal spectrum is characterized by the spectral width Δα and the spectral difference Δf, and the specific formula is as follows:

[0087] Δα=α max -α min

[0088] Δf=f(α min )-f(α max )

[0089] Where, α max and f(α) max α represents the dimension of the maximum probability subset and the number of dimensions of the maximum probability subset, respectively. min and f(α) min ) represent the dimension of the minimum probability subset and the number of dimensions of the minimum probability subset, respectively.

[0090] Step 4: Substitute the multifractal spectrum into the contact angle prediction model based on fractal theory to obtain the contact angle prediction model based on multifractal theory.

[0091] Specifically, the contact angle prediction model formula based on multifractal theory is as follows:

[0092] cosθ w = (9Δα^2 + |Δf|) D-2 cosθ

[0093] Where, θ w θ and θ represent the actual contact angle and the intrinsic contact angle, respectively, in °; Δα and Δf represent the spectral width and spectral difference, respectively, and D represents the fractal dimension.

[0094] Step 5: Input the multifractal spectrum and fractal dimension into the contact angle prediction model of multifractal theory to obtain the actual contact angle.

[0095] Specifically, the process of predicting contact angles based on the multifractal theory is as follows:

[0096] The fractal dimension D, combined with the multifractal spectrum, is substituted into the contact angle prediction model based on multifractal theory. The multifractal spectrum includes the spectral width Δα and the spectral difference Δf. The contact angle cosθ, based on multifractal theory, is then calculated using the known intrinsic contact angle θ. w Then, regarding the contact angle cosθ in multifractal theory... w The inverse calculation formula yields the actual contact angle θ. w The inverse calculation formula is as follows: θ w =arccos(cosθ) w ).

[0097] Example

[0098] according to Figure 2As shown, this embodiment provides microscopic schematic diagrams of the surface of PVDF specimens under different numbers. PVDF specimens were selected for this embodiment. Since PVDF specimens are non-conductive and their microstructure cannot be directly collected, the PVDF specimens were first sputtered with gold using a fully automated ion sputtering system. Then, conductive adhesive was used to attach the PVDF specimens to the sample stage, and the sample chamber was placed inside. The specimens were then rotated up, down, left, and right. Observation began at a low magnification, gradually increasing the magnification until the surface microstructure was clearly and intuitively observed. Images were then taken and saved for further processing.

[0099] The next step involves using MATLAB software for image preprocessing, such as noise reduction. Then, a MATLAB program is written to perform threshold analysis using an iterative method. This involves binarizing the obtained microscopic morphology diagram and performing grayscale processing to obtain the first threshold T0 and the second threshold H. When the second threshold H remains constant, the segmentation threshold h is obtained; otherwise, H0 and H are recalculated. B The process is iterated and recalculated until the resulting second threshold H remains constant. Pixels whose RGB values ​​after grayscale conversion are greater than the segmentation threshold h are treated as white, and vice versa, the binarization process is completed.

[0100] See Figure 3 This provides a graph showing the relationship between the fractal dimension of PVDF specimens and their serial number. After loading the binarized image, the required order matrix is ​​randomly selected, and the relationship between the matrix and the "grid width" is statistically analyzed to ensure that N(ε) ∝ ε. k The number of white pixel grids is used to calculate the fractal parameters of the image.

[0101] See Figure 4 This provides the α-f(α) multifractal spectrum of PVDF. Import the acquired SEM images into the folder in the current MATLAB directory, process the SEM grayscale images into binarized images, and utilize relevant theories and... The program calculates the singularity index α and the multifractal spectrum f(α), and then uses Δα = α max -α min Δf=f(α) min )-f(α max The multifractal spectrum parameters Δα and Δf of the PVDF specimen were calculated, and the multifractal spectrum of the PVDF specimen was drawn based on the obtained multifractal spectrum parameters Δα and Δf.

[0102] This embodiment validates the model based on the data obtained from the PVDF specimen. (See [link]) Figure 5 In one embodiment of the present invention, a schematic diagram of the contact angle between PVDF specimens with distilled water at different serial numbers is provided; see [link to previous document]. Figure 6In one embodiment of the present invention, a schematic diagram of the measured and theoretical values ​​of the surface contact angle of a PVDF specimen in distilled water is provided. The results show that the error between the theoretical and measured values ​​of the PVDF specimen surface is 14.55%.

[0103] In summary, this invention provides a contact angle prediction method based on multifractal theory. Multifractal theory is introduced to characterize the microstructure of material surfaces. Microstructure images are processed to obtain binarized images, and the fractal dimension and multifractal spectrum are calculated from these images. The fractal dimension is calculated using the box-count method, and the multifractal spectrum is obtained through nonlinear fitting. Compared to a single fractal dimension, this method provides a more comprehensive and detailed quantitative evaluation of the roughness of the material surface. Two parameters of the multifractal spectrum, spectral width Δα and spectral difference Δf, are introduced into the prediction model. The multifractal spectrum, combined with the fractal dimension, is input into the multifractal theory-based contact angle prediction model to obtain the actual contact angle, thus improving the accuracy of contact angle prediction for fractal structure surfaces.

[0104] The present invention also provides a contact angle prediction system based on multifractal theory, which is based on the contact angle prediction method based on multifractal theory described above, including an image acquisition module, an image processing module, a first data processing module, a model creation module, and a second data processing module.

[0105] The image acquisition module is used to acquire the microscopic morphology of the material surface to obtain microscopic morphology images;

[0106] The image processing module is used to process microscopic morphology images to obtain binarized images;

[0107] The first data processing module is used to substitute the multifractal spectrum into the contact angle prediction model based on fractal theory to obtain the contact angle prediction model based on multifractal theory.

[0108] The model creation module is used to substitute the multifractal spectrum into the contact angle prediction model based on fractal theory to obtain the contact angle prediction model based on multifractal theory.

[0109] The second data processing module is used to input the multifractal spectrum and fractal dimension into the contact angle prediction model of multifractal theory to obtain the actual contact angle.

[0110] The present invention also provides a mobile terminal, including a memory, a processor, and a computer program stored in the memory and executable on the processor, such as a contact angle prediction program based on multifractal theory.

[0111] When the processor executes the computer program, it implements the steps of the contact angle prediction method based on multifractal theory described above. The specific steps are as follows:

[0112] Step 1: Collect microscopic images of the surface of the material.

[0113] Step 2: Process the microscopic morphology image to obtain a binarized image;

[0114] Step 3: The fractal dimension and multifractal spectrum are calculated from the binarized image. The fractal dimension is calculated using the box dimension method, and the multifractal spectrum is obtained through nonlinear fitting.

[0115] Step 4: Substitute the multifractal spectrum into the contact angle prediction model based on fractal theory to obtain the contact angle prediction model based on multifractal theory.

[0116] Step 5: Input the multifractal spectrum and fractal dimension into the contact angle prediction model of multifractal theory to obtain the actual contact angle.

[0117] Alternatively, when the processor executes the computer program, it implements the functions of each module in the above system, for example:

[0118] The image acquisition module is used to acquire the microscopic morphology of the material surface to obtain microscopic morphology images;

[0119] The image processing module is used to process microscopic morphology images to obtain binarized images;

[0120] The first data processing module is used to substitute the multifractal spectrum into the contact angle prediction model based on fractal theory to obtain the contact angle prediction model based on multifractal theory.

[0121] The model creation module is used to substitute the multifractal spectrum into the contact angle prediction model based on fractal theory to obtain the contact angle prediction model based on multifractal theory.

[0122] The second data processing module is used to input the multifractal spectrum and fractal dimension into the contact angle prediction model of multifractal theory to obtain the actual contact angle.

[0123] For example, the computer program can be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules / units can be a series of computer program instruction segments capable of performing specific functions, which describe the execution process of the computer program in the mobile terminal. For example, the computer program can be divided into an image acquisition module, an image processing module, a first data processing module, a model creation module, and a second data processing module; the specific functions of each module are as follows:

[0124] The image acquisition module is used to acquire the microscopic morphology of the material surface to obtain microscopic morphology images;

[0125] The image processing module is used to process microscopic morphology images to obtain binarized images;

[0126] The first data processing module is used to substitute the multifractal spectrum into the contact angle prediction model based on fractal theory to obtain the contact angle prediction model based on multifractal theory.

[0127] The model creation module is used to substitute the multifractal spectrum into the contact angle prediction model based on fractal theory to obtain the contact angle prediction model based on multifractal theory.

[0128] The second data processing module is used to input the multifractal spectrum and fractal dimension into the contact angle prediction model of multifractal theory to obtain the actual contact angle.

[0129] The mobile terminal can be a computing device such as a desktop computer, laptop, handheld computer, or cloud server. The mobile terminal may include, but is not limited to, a processor and a memory.

[0130] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor. This processor is the control center of the mobile terminal, connecting all parts of the mobile terminal via various interfaces and lines.

[0131] The memory can be used to store the computer program and / or module. The processor implements various functions of the mobile terminal by running or executing the computer program and / or module stored in the memory and calling the data stored in the memory.

[0132] The memory may primarily include a program storage area and a data storage area. The program storage area may store the operating system and at least one application program required for a given function (such as sound playback or image playback). The data storage area may store data created based on the use of the phone (such as audio data or a phonebook). Furthermore, the memory may include high-speed random access memory (RAM) and non-volatile memory, such as hard disks, RAM, plug-in hard disks, SmartMediaCards (SMC), Secure Digital (SD) cards, flash cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0133] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the contact angle prediction method based on multifractal theory.

[0134] If the modules / units integrated in the mobile terminal are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0135] Based on this understanding, all or part of the processes in the above method can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium. When executed by a processor, the computer program can implement the steps of the contact angle prediction method based on multifractal theory. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or some intermediate form.

[0136] The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signal, telecommunication signal, and software distribution medium, etc.

[0137] It should be noted that the content contained in the computer-readable medium may be appropriately added to or subtracted from the content as required by the legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, the computer-readable medium may not include electrical carrier signals and telecommunication signals.

[0138] The above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. A contact angle prediction method based on a multifractal theory, characterized by, It comprises the following steps: Step 1, collecting the micro morphology of the surface of the substance to obtain a micro morphology picture; Step 2, processing the micro morphology picture to obtain a binary image; Step 3, calculating the fractal dimension and multifractal spectrum from the binary image, wherein the fractal dimension is calculated by using the box dimension method, and the multifractal spectrum is obtained by nonlinear fitting; Wherein, the multifractal spectrum is calculated from the binary image, and the multifractal spectrum is obtained by nonlinear fitting, and the specific process is as follows: The micro-morphology picture obtained in step 1 is imported into a folder in a current path of MATLAB by using a program, is processed into a binary picture according to step 2, the target fractal image is covered in a small square, and the pixel point of the small square is denoted as n ij , the total pixel point of the image is ∑n ij , and the probability measure P ij (δ) is a ratio of n ij to ∑n ij ; The q-th order matrix partition function χ(δ) is the sum of the q-th order probability measures of all pixel points, where q is a weight factor, indicating the probability measure P ij The size of the proportion; when q>0 indicates that the larger weight is in the higher area of the surface; on the contrary, q<0 indicates that the lower area has a larger weight; the partition function χ(δ) is the power function of δ: Wherein, τ(q) is a quality index; It is provided that τ(q) and q are convex function relationship, then the graph is multifractal, and Legendre transformation can be obtained: Wherein, f(alpha) is the multifractal spectrum, and is the fractal dimension of a subset; under the same singularity index alpha, alpha is a function of q, so alpha can be written as alpha(q); It is provided that the multifractal spectrum is characterized by the spectrum width value Delta alpha and the spectrum difference value Delta f, and the specific formula is as follows: where α max and f(α max ) represent the maximum probability subset dimension and the number of maximum probability subset dimensions, respectively, and α min and f(α min ) represent the minimum probability subset dimension and the number of minimum probability subset dimensions, respectively; Step 4, substituting the multifractal spectrum into the contact angle prediction model based on fractal theory to obtain the contact angle prediction model based on multifractal theory; Wherein, the multifractal theory contact angle prediction model formula is as follows: wherein and respectively represent the actual contact angle and the intrinsic contact angle, in °; Δα and Δf respectively represent the spectral width value and the spectral difference value, D represents the value of the fractal dimension; Step 5, inputting the multifractal spectrum and fractal dimension into the multifractal theory contact angle prediction model to obtain the actual contact angle.

2. The contact angle prediction method based on the multi-fractal theory according to claim 1, characterized in that, In step 2, the specific process of processing the micro morphology image to obtain a binary image is as follows: The micro morphology picture is subjected to gray scale processing to obtain the maximum RGB value H1 and the minimum RGB value H2 of the micro morphology picture after gray scale processing, and then the first threshold T0 is calculated by using the maximum RGB value H1 and the minimum RGB value H2, wherein the formula is T0=(H1+H2) / 2; The first threshold value T0 is compared with all RGB values on the gray-scale micro-morphology picture, when all RGB values on the gray-scale micro-morphology picture are less than the first threshold value T0, the gray-scale micro-morphology picture is the front background, otherwise, it is the back background, the average RGB value H0 of the front background after the micro-morphology picture is gray-scaled and the average RGB value H of the back background after the micro-morphology picture is gray-scaled are respectively obtained B The second threshold value H is calculated by the average RGB value H0 of the front background after the micro-morphology picture is gray-scaled and the average RGB value H of the back background after the micro-morphology picture is gray-scaled B , wherein the formula is H=(H B + H0) / 2; When the second threshold H remains constant, the segmentation threshold h is obtained; otherwise, the iteration is performed again on H0 and H B When the second threshold H remains constant, the segmentation threshold h is obtained; otherwise, the iteration is performed again on H0 and H When the RGB value of the grayed microtopography picture is greater than the segmentation threshold h, the pixel points of the microtopography picture are processed in white, otherwise, the pixel points of the microtopography picture are processed in black, and a binary image is obtained.

3. The method of predicting contact angle based on multi-fractal theory according to claim 2, characterized in that, The calculation formula of the maximum RGB value H1 and the minimum RGB value H2 of the micro morphology picture after gray scale processing is as follows: GrayScale (RGB) max(H1, H2, H3,.., H n ) GrayScale(RGB)=min(H1,H2,H3,...,Hn) Wherein, GrayScale represents the gray scale, RGB represents the gray value obtained by processing the picture, max and min represent the maximum value and the minimum value; The average RGB value H0 of the front background and the average RGB value H of the back background after the micro-morphology picture is grayed B The calculation formula is: H0=[RGB<T0] / N H B =[RGB>T0] / N Wherein, N represents the number of grids divided by the image, and T0 represents the first threshold, that is, half of the sum of H1 and H2.

4. The contact angle prediction method based on the multi-fractal theory according to claim 1, wherein, In step 3, the fractal dimension is calculated from the binary image, wherein the fractal dimension is calculated by using the box dimension method, and the specific process is as follows: MATLAB program is written, load the binary image after processing in step 2, intercept a 2 N ×2 N pixel image, get a 2 N order matrix, wherein white pixel is represented as 1, black pixel is 0; the obtained 2 N order matrix is divided into several blocks, and the number of rows and columns of each block is set as k, wherein k=1, 2, 4, …, 2N-1; when each block contains one white pixel, the total number of white pixel grids is counted, so that the data logarithm of the grid width corresponding to the number of white pixel grids is obtained. Set the area covering the entire binarization image processing black and white pixel grid as a fractal set A, the white pixel grid number is represented as N(ε), the data logarithm of the grid width corresponding to the white pixel grid number can be represented as lgN(ε); for the fractal set A, N(ε) is the number of sets with a diameter of ε covered in the fractal set A, and there is a mathematical relationship between N(ε) and ε as follows: In the double logarithmic coordinates, if a linearly related straight line can be obtained, set the lgε as the horizontal coordinate and the lgN(ε) as the vertical coordinate, and fit the above data, the negative of the slope k of the linearly related straight line is the value of the box counting dimension, and the value of the box counting dimension is the value of the fractal dimension.

5. The method of claim 1, wherein the method is based on a multi-fractal theory. In step 5, the process of prediction according to the contact angle prediction model based on multifractal theory is as follows: The fractal dimension D is incorporated into a contact angle prediction model based on multifractal theory, wherein the multifractal spectrum includes a spectral width value Δα and a spectral difference value Δf, and the contact angle of the multifractal theory is calculated using a known intrinsic contact angle θ The contact angle of the multifractal theory is further calculated The actual contact angle θ is obtained by an inverse calculation formula w wherein the inverse calculation formula is as follows: θ w =arccos(cosθ w ).

6. A contact angle prediction system based on multifractal theory according to any one of claims 1 to 5, characterized in that, It comprises An image acquisition module for acquiring the micro morphology of the surface of the substance to obtain a micro morphology picture; An image processing module for processing the micro morphology picture to obtain a binary image; A first data processing module for calculating the fractal dimension and multifractal spectrum from the binary image, wherein the fractal dimension is calculated by using the box dimension method, and the multifractal spectrum is obtained by nonlinear fitting; A model creation module for substituting the multifractal spectrum into the contact angle prediction model based on fractal theory to obtain the contact angle prediction model based on multifractal theory; A second data processing module for inputting the multifractal spectrum and fractal dimension into the multifractal theory contact angle prediction model to obtain the actual contact angle.

7. A mobile terminal comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, The computer program is executed by the processor to implement the steps of the contact angle prediction method based on the multi-fractal theory according to any one of claims 1 to 5.

8. A computer-readable storage medium storing a computer program, the computer-readable storage medium comprising instructions that, when executed by a computer, cause the computer to perform the method of any one of claims 1 to 7. The computer program is executed by the processor to implement the steps of the contact angle prediction method based on the multi-fractal theory according to any one of claims 1 to 5.

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