A Dynamic Contact Angle Measurement Method Based on the LB Phase Field Model

Abstract

This invention relates to the technical field of fluid interface performance and discloses a dynamic contact angle measurement method based on the Boltzmann phase field model. The method uses a lattice Boltzmann phase field model to simulate the collision process between a dispersed phase fluid in a continuous phase fluid and an obstacle. Within each time step, the current sequence parameters corresponding to each lattice in the phase field model are calculated to determine the region of the dispersed phase fluid within the model, thereby determining the dispersion boundary. A trapezoidal structure is then used to divide the dispersion boundary containing the forward and backward contact angles of the dispersed phase fluid. Finally, the angles between the tangents corresponding to the obstacle boundary and the tangents corresponding to the forward and backward contact angles of the dispersion boundary are calculated, which represent the contact angle between the dispersed phase fluid and the obstacle. This allows for real-time detection of changes in the contact angle of the dispersed phase fluid during the collision process.

Description

Technical Field

[0001] This invention belongs to the technical field of fluid interface performance, specifically relating to a dynamic contact angle measurement method based on the LB phase field model. Background Technology

[0002] The Lattice Boltzmann method (LBM) originated from lattice gas automata (LGA) and has developed into an effective and powerful simulation method applicable to various phenomena and processes, such as single-phase flow, multiphase flow, turbulence, heat transfer, and phase transition. It has gradually become a numerical tool for solving nonlinear partial differential equations. LBM possesses both microscopic and mesoscopic characteristics, making particle interactions easily analytical and simplifying complex macroscopic phenomena in multiphase flow. To date, the Lattice Boltzmann method has been proven and widely used to study droplet behavior, including droplet formation in microchannels, deformation and breakup of droplets exposed to gas flow, and collisions of binary droplets.

[0003] The contact angle is the angle formed at the interface between the solid, liquid, and gas phases on a solid horizontal plane, where a liquid droplet is placed. The liquid phase is sandwiched between the two tangents at the gas-liquid interface and the solid-liquid interface. Contact angle measurement is mainly used to measure the contact angle between a liquid and a solid, i.e., the wettability of a liquid on a solid. It can measure the contact angle of various liquids on various materials. Furthermore, it plays a very important role in scientific research and production in industries such as petroleum, printing and dyeing, pharmaceuticals, spraying, and mineral processing.

[0004] Contact angle is an important indicator for determining the surface properties of solid materials. Currently, different methods are used to measure contact angle depending on the wettability of the material. The mainstream measurement methods include height measurement, angle measurement, circle fitting, and Young-Laplace method. Among them, height measurement, angle measurement, and circle fitting are more suitable for cases where the droplet deformation is small or the droplet is an ideal sphere. However, they are not easy to measure when the droplet deformation is large. Furthermore, they do not tend to calculate dynamic contact angles, so they have significant limitations and are not simple and accurate enough for real-time contact angle measurement. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a dynamic contact angle measurement method based on the LB phase field model, which solves the problems of inaccurate contact angle measurement and the inability to measure contact angle changes in real time and accurately.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A dynamic contact angle measurement method based on the LB phase-field model is proposed. This method uses a lattice Boltzmann phase-field model to simulate the collision process between a dispersed phase fluid in a continuous phase fluid and an obstacle. Based on the lattice Boltzmann method, the current-order parameters corresponding to each lattice in the phase-field model are calculated at each time step. The region where the dispersed phase fluid is located in the phase field model is determined, and then the dispersion boundary corresponding to the dispersed phase fluid is determined. Then, the dispersion boundary where the forward contact angle and the backward contact angle of the dispersed phase fluid are located is divided by a trapezoidal structure. Finally, the angle between the tangent corresponding to the obstacle boundary and the tangent corresponding to the forward contact angle and the backward contact angle of the dispersion boundary is calculated. This is the contact angle between the dispersed phase fluid and the obstacle, so that the change of the contact angle of the dispersed phase fluid during the collision can be detected in real time.

[0008] Furthermore, the phase-field model adopts a cuboid structure, with its width set as the side length of a single cell.

[0009] The boundary position corresponding to the region where the dispersed phase fluid is located in the phase field model is calculated, which is the dispersion boundary. The collision boundary where the obstacle collides with the dispersed phase fluid is taken as the bottom edge of the trapezoidal structure. The top edge of the trapezoidal structure is determined by extending a predetermined height from the bottom edge of the trapezoidal structure to the dispersion boundary. The dispersion boundary is divided into two parts by the line connecting the midpoints of the bottom and top edges of the trapezoidal structure as the center line. The dispersion boundary where the forward contact angle is located is the dispersion boundary where the backward contact angle is located. Then, the corresponding forward contact angle tangent and backward contact angle tangent are calculated respectively. Finally, the angle between the forward contact angle tangent and backward contact angle tangent and the corresponding tangent of the collision boundary is calculated, which is the forward contact angle and backward contact angle.

[0010] Furthermore, the position data corresponding to the dispersion boundary where the forward contact angle is located and the dispersion boundary where the backward contact angle is located are fitted to obtain the corresponding curves. Then, the tangent line corresponding to the intersection point of the curve and the obstacle is calculated, which is the forward contact angle tangent line or the backward contact angle tangent line.

[0011] Furthermore, based on the lattice Boltzmann phase-field model, the corresponding velocity distribution function, internal energy density distribution function, equilibrium velocity distribution function, and equilibrium internal energy density distribution function are selected to determine the periodic boundary of the phase-field model and the reflection boundary of the obstacle;

[0012] Based on the lattice Boltzmann method, the velocity distribution function, internal energy density distribution function, equilibrium velocity distribution function, and equilibrium internal energy density distribution function of each cell are calculated at each time step. This allows for the calculation of the current macroscopic velocity, density, and current sequence parameters for each cell.

[0013] According to the current order parameter The forward contact angle and backward contact angle are calculated for each time step to obtain the dynamic changes in the contact angle.

[0014] Furthermore, if the current order parameter If the value is greater than zero, the corresponding lattice is determined to belong to the dispersed phase fluid; if the current sequence parameter is greater than zero, the corresponding lattice is determined to belong to the dispersed phase fluid. If the value is less than zero, then the corresponding lattice is determined to be a continuous phase fluid.

[0015] Compared with the prior art, the beneficial effects of the present invention are:

[0016] Using the lattice Boltzmann phase-field model, the collision process between the dispersed phase fluid and the obstacle is evolved according to time steps, and then the order parameters within each time step are combined. The changes in the structure and trapezoidal shape allow for simple, efficient, and accurate calculation of the forward and backward contact angles, even when the dispersed phase droplets undergo significant deformation during collision and movement. This enables real-time monitoring of the contact angle changes during collisions. The solid surface imparting chemical potential can effectively regulate wettability, i.e., the interaction between the fluid and the solid, providing a data foundation for the study of the entire collision process. This allows for a more comprehensive understanding of the physical characteristics of the dispersed phase fluid, the surface properties of the colliding solid, the collision time of the droplets, droplet residue, and the velocity of the droplets after the collision. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the overall process of the present invention;

[0018] Figure 2(a) is a schematic diagram of the periodic boundary of the present invention;

[0019] Figure 2(b) is a schematic diagram of the reflective boundary of the present invention;

[0020] Figure 3 This is a schematic diagram illustrating the collision of oil droplets, such as those from the present invention, with rectangular, triangular, and semi-circular obstacles in water.

[0021] Figure 4(a) shows the current sequence parameter according to the present invention. A schematic diagram of the selected droplet regions;

[0022] Figure 4(b) is a schematic diagram of the boundary of the droplet region of the present invention;

[0023] Figure 5 This is a schematic diagram of the trapezoidal structure of the present invention;

[0024] Figure 6 This is a schematic diagram illustrating the calculation of the forward and backward contact angles of the present invention;

[0025] Figure 7This is a schematic diagram illustrating the contact calculation of a droplet colliding with a planar obstacle according to the present invention;

[0026] Figure 8 This is a schematic diagram illustrating the contact calculation of the droplet colliding with the inclined obstacle according to the present invention.

[0027] Figure 9 This is a schematic diagram illustrating the contact calculation of the droplet colliding with a curved obstacle according to the present invention. Detailed Implementation

[0028] To make the technical means, creative features, objectives and effects of this invention easier to understand, the following embodiments are described in detail with reference to the accompanying drawings. It should be noted that the description of these embodiments is for the purpose of helping to understand this invention, but does not constitute a limitation of this invention.

[0029] It should be noted that in the description of this invention, the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. The terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance. Furthermore, unless otherwise explicitly specified and limited, the terms "installed," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication of two elements. When two elements are "fixedly connected" or "rotationally connected," the two elements can be directly connected or there may be an intermediate element. Conversely, when an element is referred to as being "directly on" another element, there is no intermediate element. The fixed or fixed connection method can be screwed, welded, riveted, plugged, or connected through a third component. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0030] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of the invention.

[0031] like Figure 1As shown, this invention provides a dynamic contact angle measurement method based on the Boltzmann phase-field model. It uses a lattice Boltzmann phase-field model to simulate the collision process between a dispersed phase fluid in a continuous phase fluid and an obstacle, calculating the order parameters corresponding to each lattice in the phase-field model at each time step. The region where the dispersed fluid is located in the phase-field model is determined, and then the dispersion boundary corresponding to the dispersed fluid is determined. A trapezoidal structure is then used to divide the dispersion boundary containing the advancing and retreating contact angles of the dispersed fluid. Finally, the angles between the tangents corresponding to the obstacle boundary and the tangents corresponding to the advancing and retreating contact angles of the dispersion boundary are calculated; these are the contact angles between the dispersed fluid and the obstacle. This allows for real-time detection of the changes in the contact angle of the dispersed fluid during the collision process. Thus, using the lattice Boltzmann phase-field model, the collision process between the dispersed fluid and the obstacle is divided according to time steps, and then the order parameters within each time step are considered. The changes in the contact angle and the trapezoidal structure enable simple, efficient, and accurate calculation of the corresponding contact angle, thereby allowing real-time detection of the contact angle changes of the dispersed phase fluid during the collision process. This provides a data foundation for the study of the entire collision process, enabling a more comprehensive understanding of the physical characteristics of the dispersed phase fluid. The solid surface endowed with chemical potential can effectively regulate wettability, i.e., the interaction between the fluid and the solid. This solves the technical problem in existing fluid mechanics where contact angle measurement is too complex and cannot accurately measure contact angle changes in real time.

[0032] The following is a detailed explanation using the example of a dispersed phase fluid, such as oil, moving in a continuous phase fluid, such as water, and colliding with obstacles, such as planar solids or curved solids.

[0033] First, calculate the order parameters.

[0034] Based on the lattice Boltzmann phase-field model, the corresponding velocity distribution function, internal energy density distribution function, and equilibrium velocity distribution function and internal energy density distribution function are selected. The periodic boundary of the phase-field model and the reflection boundary of the obstacle are determined, and the time step and discrete velocity set are set. According to the lattice Boltzmann method, the velocity distribution function, internal energy density distribution function, and equilibrium velocity distribution function and internal energy density distribution function for each cell within the current time step are calculated. Then, the current macroscopic velocity, density, and current sequence parameters for each cell are calculated.

[0035] Specifically as follows:

[0036] Initialize the velocity distribution function f q (r α ,t), internal energy density distribution function g q (rα (t) and equilibrium velocity distribution function Equilibrium internal energy density distribution function

[0037] Discrete velocity set c α Defined as:

[0038]

[0039] Step 1: Calculate the macroscopic density ρ, velocity u, and order parameters of the fluid within the current time step.

[0040]

[0041]

[0042] Where the subscript q indicates the direction of discretization velocity; t is the current time step, and r α The position space (x, y, z) of the fluid particle is represented; c αq The discrete velocity represents the velocity in the q direction; c = Δx / Δt is the lattice velocity; the grid step size is Δx = 1, and the time step size is Δt = 1.

[0043] Step 2: Calculate the equilibrium distribution function and

[0044]

[0045]

[0046] In the formula The chemical potential h is defined as the square of the speed of sound in a lattice unit.

[0047]

[0048] In the formula, A = B = -1.316 × 10 -3 κ=0.855×10 -3 A and κ are parameters related to surface tension and interface thickness, ω q Weighting coefficients:

[0049]

[0050] Step 3: Update the velocity distribution function f′ after the collision. q (r α (t) and internal energy density distribution function g′ q (r α ,t);

[0051]

[0052]

[0053] Where, τ f =1,τ g =0.56 dimensionless relaxation parameter, representing the time required to reach equilibrium within the grid point; F q The force is represented by the following equation:

[0054] F q =ω q (c aq ·F)

[0055] Where, F = 1.1 × 10 -6 It is a dimensionless parameter, representing macroscopic forces including gravity and buoyancy.

[0056] Step 4: Transfer the velocity and internal energy density distribution functions of the current grid node to the adjacent grid nodes according to the discrete velocity direction.

[0057] f q (r α +c αq Δt, t+Δt)=f′ q (r α ,t)

[0058] g q (r α +c αq Δt, t+Δt)=g′ q (r α ,t)

[0059] Among them, f q (r α +c αq Δt, t+Δt) and g q (r α +c αq Δt, t+Δt) represents the particle distribution function after the collision, indicating the particle distribution along direction q from the lattice point (r). α ,t) moves to a neighboring grid point (r) α +c αq Δt, t+Δt);

[0060] f q (r α +c αq Δt, t+Δt) and g q (r α +c αq The utilization of Δt, t+Δt) in the next time step, in step one, utilizes f q (r α ,t) and gq (r α ,t) Calculate macroscopic density ρ, velocity u and order parameters value;

[0061] Step 5: Process the boundary conditions to update the distribution function on the boundary.

[0062] As shown in Figure 2(a), periodic boundary conditions are used for open boundaries in the upper and lower, left and right and front and back. For example, the distribution functions of the fluid point A at the rightmost end, in the 1, 5 and 8 directions, which are at the same horizontal position, are used as the distribution functions of the fluid point B at the leftmost end, in the 3, 6 and 7 directions.

[0063] As shown in Figure 2(b), when a particle reaches a solid wall lattice point, it is returned to the fluid along the original path. The direction of motion is opposite to the incident direction. At boundary lattice points, such as lattice point A, no collision step is performed, only the migration step is performed. According to the idea of ​​bounce, the standard bounce scheme stipulates that the distribution function after the collision at the boundary lattice point is given by the distribution function after the collision of the adjacent fluid lattice points (positions B, F, and C at the solid-liquid interface), and the direction is reversed.

[0064] f′2(A,t)=f′4(F,t)

[0065] f′5(A,t)=f′7(C,t)

[0066] f′8(A,t)=f′6(B,t)

[0067] During the migration step, the distribution functions f′2, f′5, and f′8 on the boundary grid points migrate to the adjacent fluid grid points.

[0068] f2(F,t+Δt)=f′2(A,t)

[0069] f5(C,t+Δt)=f′5(A,t)

[0070] f8(B,t+Δt)=f′8(A,t)

[0071] By repeating the above process, the current sequence parameters within each time step can be calculated.

[0072] Secondly, calculate the contact angle.

[0073] Based on the current order parameters of each cell in the phase field model at each time step. The region where the dispersed phase fluid is located in the phase field model is determined, and then the dispersion boundary corresponding to the dispersed phase fluid is determined. Then, the dispersion boundary where the forward contact angle and the backward contact angle of the dispersed phase fluid are located is divided by a trapezoidal structure. Finally, the angle between the tangent corresponding to the obstacle boundary and the tangent corresponding to the forward contact angle and the backward contact angle of the dispersion boundary is calculated. This is the contact angle between the dispersed phase fluid and the obstacle, so that the change of the contact angle of the dispersed phase fluid during the collision can be detected in real time.

[0074] Using the current order parameter To distinguish between two different fluids;

[0075]

[0076] In this invention, the simulation region is a cuboid with dimensions L×W×H (two-dimensional simulation L≠1, W=1, H≠1) and L×W×H (three-dimensional simulation, L≠1, W≠1, H≠1).

[0077] When measuring the contact angle, we used a two-dimensional simulation. To obtain the droplet position in the flow field, we used sequence parameters... The set of position parameters D for all oil droplets is selected, and then the set of edges DE is selected from set D.

[0078]

[0079] The edge set DE is used to select the position coordinates of the droplet edge. The threshold is set according to specific needs, taking into account the initial diameter and deformation state of the droplet.

[0080] Then, a trapezoidal structure is used to divide the dispersion boundary where the forward contact angle and the backward contact angle of the dispersed phase fluid are located. The selection principle of the trapezoidal structure is as follows: when the obstacle is a plane or an inclined plane, the collision surface of the obstacle is selected as the bottom edge of the trapezoidal structure; when the obstacle is a curved surface, the line connecting the intersection of the obstacle and the droplet boundary is selected as the bottom edge of the trapezoidal structure.

[0081] In selecting the top edge and height of the trapezoid, the droplet position coordinates closest to the collision surface are chosen. The top edge of the trapezoid is determined by extending a predetermined height from the bottom edge of the trapezoid towards the dispersion boundary. This predetermined height can be 1 / 3 of the total length of the dispersion boundary. The top edge passes through the centerline z of the trapezoid. l The line connecting the midpoints of the bottom and top edges divides the set of forward and backward contact angle droplet positions (DE). front and DE back .

[0082] DE front ={(x,z)|(x,z)∈DE,ax+b <z l}

[0083] DE back ={(x,z)|(x,z)∈DE,ax+b>z l}

[0084] Through set DE front and DE back The obtained position data of the droplet's advancing and retreating contact angles can be used to derive the corresponding curve equations z of the advancing and retreating contact angle dispersion boundaries, respectively. n Then calculate the fitted curve equation z. n The coordinates of the intersection point (x0, z0) with the collision surface of the obstacle.

[0085] When the collision surface of the obstacle is a plane or an inclined plane, the fitted curve z is obtained. n The tangent L1 at the intersection point is the contact angle tangent and the retreating contact angle tangent, respectively. Then, calculate the straight line where the collision surface is located as L2. By finding the angle between lines L1 and L2, the contact angle between the droplet and the obstacle can be obtained. That is, the angle between the forward contact angle tangent, the retreating contact angle tangent and the collision boundary finger is the forward contact angle and the retreating contact angle, respectively.

[0086] Similarly, when the collision surface of the obstacle is a circular curved surface, it is also necessary to find the tangent L2 of the circular curved surface at the coordinate point of the intersection. Then, by finding the angle between lines L1 and L2, the contact angle between the droplet and the curved obstacle can be obtained.

[0087] The fitted curve equation is shown below:

[0088] z n =ax 2 +bx+c

[0089] When the collision surface is a plane or an inclined plane, the equation of the line is as follows:

[0090] z p =a p x p +b p

[0091] When the collision surface is a circular curved surface, let the center O(x) be... c ,z c A circular surface with radius R has a straight line equation that is the tangent line to the circular surface at the intersection point (x0, z0), as shown below:

[0092] Equation of a circular surface: (xx) c ) 2 +(zz c ) 2 =R 2

[0093] Tangent line at (x0, y0):

[0094] The intersection point of the fitted curve equation and the collision surface line equation is (x0, z0). At this intersection point, the tangent line to the fitted curve equation is:

[0095] z q =(2az0+b)x q +z0-(2ax0+b)x0

[0096] The slope k of the tangent line to the fitted curve equation and the straight line equation of the collision surface is obtained by fitting the curve equation. q k p Find the included angle:

[0097] If the two lines are perpendicular, that is, k q k p =1, at which point the included angle θ is 90°;

[0098] If the two lines are not perpendicular, let the angle between them be θ.

[0099] The contact angle between the droplet and the obstacle can be calculated as 180°-θ using θ.

[0100] To verify the feasibility of the dynamic contact angle measurement method of the present invention, we conducted the following experiments:

[0101] A lattice Boltzmann phase-field model is adopted, and a flow field with nx = 240 and ny = 1260 is established based on the discrete velocity model D2Q9. Solid models are placed in the field as obstacles to simulate the collision process of droplets during their ascent. The solid models can be cuboid planar models, triangular inclined plane models, and semi-circular curved boundary models, such as... Figure 3 As shown, a collision simulation is performed by a droplet, such as oil, rising in another liquid, such as water, and colliding with a solid model. During the collision, the dynamic contact angle is measured, and the forward and backward contact angles are distinguished and measured by a trapezoidal structure.

[0102] Cuboid planar model:

[0103] S={(x,y)|115 <x<125,1180<y<1205}

[0104] Triangular inclined plane model:

[0105]

[0106] Semicircular curved boundary model:

[0107] S = {(x,y)|(x-120)} 2 +(x-1200) 2=15 2 ,y<1200}

[0108] As shown in Figure 4, the order parameters obtained through the phase-field model The coordinates of a droplet during its motion can be filtered to identify the state of the substance. The A fluid is identified as the oil phase region. The region identified as fluid B, i.e., the aqueous liquid phase, is located within the diffusion interface layer. It changes continuously from 0 to 1.

[0109]

[0110] When obtaining the droplet position in the flow field, the order parameter is used. The set of position parameters D for all droplets is filtered out, and then the coordinates are judged to determine whether it is an edge position, and the edge set DE is filtered out.

[0111]

[0112] like Figure 5 As shown, the edge position data coordinates of some droplets are selected through the DE set. The selection principle is as follows: using a trapezoidal structure, the collision surface of the solid obstacle is selected as the base of the trapezoidal structure. In the selection of the top and height of the trapezoid, the droplet position coordinates close to the collision surface are selected. The forward and backward contact angle droplet position sets DE are divided by the centerline of the trapezoidal structure. front and DE back .

[0113] By finding the base and top of the trapezoidal structure, we can obtain the median of the trapezoid. Let the median l of the trapezoid be y = ax + b, then...

[0114] DE front ={(x,y)|(x,y)∈DE,ax+b <y}

[0115] DE back ={(x,y)|(x,y)∈DE,ax+b>y}

[0116] like Figure 6 As shown, through set DE front and DE backThe obtained droplet edge position data can be fitted to derive curve equations. The intersection point coordinates (yp0, y0) are obtained at the boundary with the solid obstacle. When the collision surface of the solid obstacle is a plane or an inclined plane, the tangent line L1 of the fitted curve is obtained at the intersection point, and the collision surface is L2. By obtaining the angle between lines L1 and L2, the contact angle between the droplet and the solid obstacle can be obtained. When the collision surface of the solid obstacle is a circular curved surface, the tangent line L2 of the circular curved surface at that point can be obtained using the intersection point coordinates. Then, by obtaining the angle between lines L1 and L2, the contact angle between the droplet and the curved obstacle can be obtained.

[0117] The fitted curve equation is shown below:

[0118] y = ax 2 +bx+c

[0119] When the collision surface is a plane or an inclined plane, the equation of the line is as follows:

[0120] y p =a p x p +b p

[0121] When the collision surface is a circular curved surface, let the center O(x) be... c ,y c A circular surface with radius R has a straight line equation that is the tangent line to the circular surface at the intersection point (x0, y0), as shown below:

[0122] Equation of a circular surface: (xx) c ) 2 +(yy c ) 2 =R 2

[0123] Tangent line at (x0, y0):

[0124] If the intersection point of the fitted curve equation and the collision surface line equation is (x0, y0), then at the intersection point, the tangent line to the fitted curve equation is:

[0125] y q =(2ax0+b)x q +y0-(2ax0+b)x0

[0126] The slope k of the tangent line to the fitted curve equation and the straight line equation of the collision surface is obtained by fitting the curve equation. q k p Find the included angle:

[0127] If the two lines are perpendicular, that is, k q k p =1, at which point the included angle θ is 90°;

[0128] If the two lines are not perpendicular, let the angle between them be θ.

[0129]

[0130] The contact angle between the droplet and the solid can be calculated from θ as 180° - θ.

[0131] like Figure 7-9 As shown, the trapezoidal structure is selected in the process of calculating the contact angle of droplet collision with a plane, inclined plane and curved solid. The trapezoidal structure can be used to handle the dynamic measurement of contact angle of droplet collision under complex conditions. The forward contact angle and the backward contact angle are measured through the center line of the trapezoid.

[0132] The above embodiments are preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Various modifications or variations that can be made by those skilled in the art without creative effort within the scope of the appended claims are still within the scope of protection of this patent.

Claims

1. A dynamic contact angle measurement method based on the LB phase field model, characterized in that: The collision process between a dispersed phase fluid and an obstacle in a continuous phase fluid is simulated using a lattice Boltzmann phase-field model. Based on the lattice Boltzmann method, the current order parameters corresponding to each lattice in the phase-field model are calculated at each time step. The process involves determining the region of the dispersed fluid in the phase field model, then determining the dispersion boundary corresponding to the dispersed fluid, and then using a trapezoidal structure to divide the dispersion boundary where the forward contact angle and the backward contact angle of the dispersed fluid are located. Finally, the angle between the tangent corresponding to the obstacle boundary and the tangent corresponding to the forward contact angle and the backward contact angle of the dispersion boundary is calculated, which is the contact angle between the dispersed fluid and the obstacle. This allows for real-time detection of the change in the contact angle of the dispersed fluid during the collision process. The phase-field model adopts a cuboid structure, with its width set as the side length of a single cell. The boundary position corresponding to the region where the dispersed phase fluid is located in the phase field model is calculated, which is the dispersion boundary. The collision boundary where the obstacle collides with the dispersed phase fluid is taken as the bottom edge of the trapezoidal structure. The top edge of the trapezoidal structure is determined by extending a predetermined height from the bottom edge of the trapezoidal structure to the dispersion boundary. The dispersion boundary is divided into two parts by the line connecting the midpoints of the bottom and top edges of the trapezoidal structure as the center line. The dispersion boundary where the forward contact angle is located is the dispersion boundary where the backward contact angle is located. Then, the corresponding forward contact angle tangent and backward contact angle tangent are calculated respectively. Finally, the angle between the forward contact angle tangent and backward contact angle tangent and the corresponding tangent of the collision boundary is calculated, which is the forward contact angle and backward contact angle.

2. The dynamic contact angle measurement method based on the LB phase field model according to claim 1, characterized in that: The corresponding curves are obtained by fitting the position data of the dispersion boundary where the forward contact angle is located and the dispersion boundary where the backward contact angle is located. Then, the tangent line corresponding to the intersection of the curve and the obstacle is calculated, which is the forward contact angle tangent line or the backward contact angle tangent line.

3. The dynamic contact angle measurement method based on the LB phase field model according to claim 1, characterized in that: Based on the lattice Boltzmann phase field model, select the corresponding velocity distribution function, internal energy density distribution function, equilibrium velocity distribution function, and equilibrium internal energy density distribution function to determine the periodic boundary of the phase field model and the reflection boundary of the obstacle; Based on the lattice Boltzmann method, the velocity distribution function, internal energy density distribution function, equilibrium velocity distribution function, and equilibrium internal energy density distribution function of each cell are calculated at each time step. This allows for the calculation of the current macroscopic velocity, density, and current sequence parameters for each cell. ; According to the current order parameter It calculates the forward contact angle and backward contact angle within each time step, thereby obtaining the dynamic changes of the contact angle.

4. The dynamic contact angle measurement method based on the LB phase field model according to claim 3, characterized in that: If the current order parameter If the value is greater than zero, then the corresponding lattice is determined to belong to the dispersed phase fluid; If the current order parameter If the value is less than zero, then the corresponding lattice is determined to be a continuous phase fluid.

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