A method for obtaining droplet contact angle based on multi-body dissipative particle dynamics simulation

Abstract

The present invention discloses a method for obtaining the contact angle of a droplet based on multi-body dissipative particle dynamics simulation, belonging to the field of droplet molecular simulation. The method comprises: establishing an initial model system, model calculation, obtaining the droplet contour coordinates at the three-phase contact line, fitting a circular curve to obtain the contact angle, and obtaining the tilt angle of each substrate and the corresponding static or dynamic contact angle. The present invention achieves the acquisition of the contact angle corresponding to the current substrate tilt angle of the droplet based on the long-distance and long-term migration process of the droplet on the solid substrate. This method improves the problem of low droplet contact angle measurement accuracy in multi-body dissipative particle dynamics due to short simulation time and the influence of gravity.

Description

Technical Field

[0001] The present invention belongs to the field of droplet molecular simulation, and in particular, relates to a method for obtaining a droplet contact angle based on multi-body dissipative particle dynamics simulation. Background Art

[0002] Droplets are the most common form of microfluidics. As our understanding of droplets grows, the droplet volumes used in microfluidics are shrinking. Currently, the droplets widely used in microfluidics are often smaller than 1 μL. The motion characteristics of such microvolume droplets are often difficult to observe experimentally, so computer simulation has become one of the primary methods for studying droplets. Multibody dissipative particle dynamics (MDPD), as a coarse-grained particle simulation method, has the advantage of being able to simulate micron-sized droplets on large time scales, and is therefore widely used for droplet simulation.

[0003] The static contact angle of a droplet on a solid surface is an important parameter that describes the wettability of the liquid on the solid surface, while the dynamic contact angle is an important parameter for studying the movement of a droplet on a hydrophobic surface. Contact angle measurement technology has important applications in microfluidic chips, hydrophobic surface manufacturing, droplet collection, antifreeze and anti-frost, and other fields. In experimental studies, a contact angle meter can be used to measure the contact angle, but there is no standard procedure to measure the contact angle of a droplet in particle simulation. A commonly used method is to treat the droplet as a perfect hemisphere for contact angle measurement. However, when gravity is introduced, the assumption that the droplet is a perfect hemisphere fails, resulting in low accuracy in contact angle measurements. When measuring the dynamic contact angle of a droplet during migration on an inclined surface, if the solid substrate model is too large, the computer will have insufficient computing power. However, reducing the size of the droplet in the solid substrate model will cause the droplet to quickly detach from the inclined substrate, resulting in too little data collection. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for obtaining the contact angle of a droplet based on multi-body dissipative particle dynamics simulation. This method for obtaining the wettability of a droplet based on multi-body dissipative particle dynamics provides a method for predicting the static and dynamic contact angles of a droplet on a solid substrate at different inclination angles based on the wetting process and migration process of the droplet on the solid substrate.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a method for obtaining the contact angle of a droplet based on multi-body dissipative particle dynamics simulation, comprising the following steps:

[0006] a) Establish an initial model system, including:

[0007] Establish a periodic simulation region in LAMMPS software;

[0008] Construct a coarse-grained droplet numerical model of multi-body dissipative particle dynamics (MDPD) of droplets and solid substrates;

[0009] Set the interaction force between droplet particles and solid particles;

[0010] Apply acceleration g in different directions to the droplet to simulate the acceleration of gravity;

[0011] Obtain models of solid substrates at different tilt angles α;

[0012] b) Model calculation, including:

[0013] For each tilt angle basis, perform:

[0014] Update the position and velocity of each particle using the modified Velocity-Verlet algorithm;

[0015] Relax the model to reach equilibrium;

[0016] Output the information of the position change of each particle in the droplet model over time to the .lammpstrj file;

[0017] c) Obtaining the droplet contour coordinate points at the three contact lines, including:

[0018] For each tilt angle basis, perform:

[0019] Use Ovito software to read the .lammpstrj file described in step b), visualize the numerical model, and obtain the motion animation of the droplet at different solid substrate tilt angles α;

[0020] Mark a set of arc-shaped droplet particle subsets A and B at the three contact lines on the left and right sides of the droplet at n moments in the motion animation;

[0021] Obtain subset A and subset B at each moment and execute: Save the coordinate information of the droplet particles in subsets A and B in the Cartesian coordinate system in two TXT files respectively;

[0022] d) Fitting a circular curve to obtain the contact angle, including:

[0023] Get subset A and subset B at each moment and execute:

[0024] Use MATLAB software to read the TXT text containing the coordinate information of subset A and the TXT text containing the coordinate information of subset B in step c) respectively;

[0025] The first circular curve is fitted using the least squares method and the particle coordinate information in subset A, and the second circular curve is fitted using the least squares method and the particle coordinate information in subset B;

[0026] Let the coordinate point of the particle at the three-term contact line in subset A be point a, draw a horizontal straight line P1 through point a, draw a tangent line L1 through the intersection of P1 and the first circle curve, and the angle formed by L1 and P1 is the contact angle θ1;

[0027] Let the coordinate point of the particle at the three-term contact line in subset B be point b, draw a horizontal straight line P2 through point b, draw a tangent line L2 through the intersection of P2 and the first circle curve, and the angle formed by L2 and P2 is the contact angle θ2;

[0028] e) obtaining a graph of each substrate tilt angle and the corresponding static or dynamic contact angle, including:

[0029] For each tilt angle basis, perform:

[0030] Get θ1 and θ2 at n moments and calculate the average value to get θ1 * θ2 * ;

[0031] θ1 obtained using each tilt angle basis * θ2 * Draw a line graph to obtain each substrate tilt angle and the corresponding static or dynamic contact angle line graph.

[0032] The magnitude of the acceleration g applied in step a) is always 0.000845 DPD units; the direction of the acceleration g can be modified by the spatial vector of g, the position of the substrate remains unchanged, and different inclination angles α of the substrate are calculated and simulated by forming different angles between the acceleration direction and the substrate;

[0033] The periodic simulation area in step a) cooperates with the acceleration g with adjustable direction to ensure that when the droplet slides out of the simulation area on one side, it can return to the solid substrate from the other side without being separated from the solid substrate, thereby ensuring the continuity of the simulation.

[0034] In step c), the height of the arc-shaped subsets A and B is about 15% of the total height h of the droplet; the particles in the subset are selected by sequentially selecting upwards along the droplet contour from the intersection of the three contact lines;

[0035] The solid substrate tilt angle α is characterized in that when α is 0°, the measured θ1 and θ2 are both static contact angles; when α is greater than 0°, the droplet begins to slide to one side, and the measured θ1 and θ2 are both dynamic contact angles; the dynamic contact angles include: advancing contact angle and receding contact angle; θ on the advancing side of the droplet is the advancing contact angle, and θ on the receding side of the droplet is the receding contact angle;

[0036] The beneficial effects of the present invention are:

[0037] 1. This method can effectively obtain the dynamic contact angle of a droplet during motion in multi-body dissipative force dynamics simulations, while improving the accuracy of measuring the static contact angle of a droplet under gravity.

[0038] 2. This method can utilize periodic boundaries in conjunction with acceleration that can change direction to obtain the dynamic contact angle of droplets during long-distance and long-term migration, thereby improving the accuracy of dynamic contact angle measurements. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is the overall flow chart of the present invention;

[0040] Figure 2 Schematic diagram of different angular accelerations g and different base tilt angles α;

[0041] Figure 3 A comparison diagram of the simulation method of the present invention and a conventional simulation method;

[0042] Figure 4 Schematic diagram of the positions of arc subsets A and B;

[0043] Figure 5 is a schematic diagram of the first circular curve;

[0044] Figure 6 is a schematic diagram of the second circular curve;

[0045] Figure 7 A line graph showing each substrate tilt angle and the corresponding static or dynamic contact angle. DETAILED DESCRIPTION

[0046] The present invention is described below by means of specific embodiments in conjunction with the accompanying drawings, but the present invention is not limited thereto. Unless otherwise specified, the simulation methods used in the following embodiments are conventional methods that can be obtained by consulting relevant materials.

[0047] Example 1: Figure 1-7 As shown,

[0048] Taking an 80w / w% glycerol / water mixed droplet as an example, the above method for determining the static and dynamic contact angles of the droplet based on multi-body dissipative particle dynamics is explained:

[0049] a) Establish an initial model system, including:

[0050] (1) A periodic simulation region of 100×60×60 DPD units was established in the LAMMPS software; dimensionless DPD units were used in the multi-body dissipative force dynamics simulation.

[0051] (2) Construct a coarse-grained model of the droplet and solid substrate in the simulation area. Optionally, set the droplet diameter to 15, the density to 6, and the solid substrate size to 100×4×40, and the density to 12.

[0052] (3) Setting the interaction force between the liquid droplet particles and the solid particles; preferably, obtaining information such as the attraction parameters and repulsion parameters between the liquid droplet particles and the solid particles by consulting relevant data.

[0053] (4) Figure 2 As shown, acceleration g in different directions is applied to the droplet; preferably, the magnitude of the acceleration g is selected to be 0.000845; optionally, acceleration g in four different directions can be selected respectively.

[0054] (5) Figure 2 As shown, a model of different tilt angles α of the solid substrate is obtained; the four different tilt angles α of the substrate are calculated by calculating the four angles between the acceleration g and the substrate in the xy plane, which are 0°, 15°, 30°, and 45°.

[0055] like Figure 3 As shown, by modifying the direction of the acceleration g to match the periodic boundary, the droplet will return to the substrate from the other end when it passes through the periodic boundary on the tilted substrate, thereby achieving the purpose of collecting data for a long time and improving measurement accuracy.

[0056] b) Model calculation, including:

[0057] For each different tilt angle base, perform:

[0058] (1) Update the position and velocity of each particle using the modified Velocity-Verlet algorithm;

[0059] (2) Relax the model for 40,000 steps to allow the model to reach equilibrium;

[0060] (3) Perform 100,000 steps of iterative calculation on the model and output the information of the position change of each particle in the droplet model over time to the .lammpstrj file;

[0061] c) Obtaining the droplet contour coordinate points at the three contact lines, including:

[0062] For each tilt angle basis, perform:

[0063] (1) Figure 2 As shown, the .lammpstrj file described in step b) is read using Ovito software to visualize the numerical model;

[0064] (2) Figure 4As shown, it is preferred that a group of arc-shaped droplet particle subsets A and B are marked at the three contact lines on the left and right sides of the droplet every 10,000 steps in the motion animation, and a total of 10 moment subsets A and B are obtained.

[0065] Preferably, the heights of the subsets A and B are approximately 15% of the droplet height h.

[0066] (3) Obtain subset A and subset B at each moment and execute: Save the coordinate information of the droplet particles in subsets A and B in the Cartesian coordinate system in two TXT texts respectively;

[0067] d) Fitting a circular curve to obtain the contact angle, including:

[0068] Get subset A and subset B at each moment and execute:

[0069] (1) Using MATLAB software, read the TXT text containing the coordinate information of subset A and the TXT text containing the coordinate information of subset B in step c) respectively;

[0070] (2) fitting the first circular curve using the least squares method and the particle coordinate information in subset A, and fitting the second circular curve using the least squares method and the particle coordinate information in subset B;

[0071] (3) Figure 5 As shown, let the coordinate point of the particle at the three-term contact line in subset A be point a, draw a horizontal straight line P1 through point a, draw a tangent line L1 through the intersection of P1 and the first circle curve, and the angle formed by L1 and P1 is the contact angle θ1;

[0072] (4) Figure 6 As shown, let the coordinate point of the particle at the three-term contact line in subset B be point b, draw a horizontal straight line P2 through point b, draw a tangent line L2 through the intersection of P2 and the first circle curve, and the angle formed by L2 and P2 is the contact angle θ2;

[0073] e) obtaining a graph of each substrate tilt angle and the corresponding static or dynamic contact angle, including:

[0074] For each tilt angle basis, perform:

[0075] (1) Obtain θ1 and θ2 at 10 moments and calculate the average value to obtain θ1 * θ2 * ;

[0076] (2) Figure 7 As shown, the θ1 obtained by each tilt angle base * θ2 * Draw a line graph to obtain each substrate tilt angle and the corresponding static or dynamic contact angle line graph.

[0077] It can be seen that: α=0 corresponds to the static contact angle θ1 * =θ2 * =130°, α=15 corresponds to the advancing contact angle θ1 * =132° Receding contact angle θ2 * =126°、α=30Corresponding to the advancing contact angle θ1 * =142° Receding contact angle θ2 * =119°、α=45Corresponding to the advancing contact angle θ1 * =154° Receding contact angle θ2 * =108°.

[0078] The present invention realizes the simulation of long-distance migration of droplets on an inclined solid substrate by introducing the effect of gravity in multi-body dissipative force dynamics simulation, and more accurately measures the static contact angle and dynamic contact angle of the droplets.

[0079] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A method for obtaining the contact angle of a droplet based on multi-body dissipative particle dynamics simulation, characterized by: The following steps are involved: a) Establish an initial model system, including: Establish periodic simulation regions in the software; Construct a coarse-grained droplet numerical model of multi-body dissipative particle dynamics between a droplet and a solid substrate; Set the interaction force between droplet particles and solid particles; Apply acceleration g in different directions to the droplet to simulate the acceleration of gravity; Obtain models of solid substrates at different tilt angles α; b) Model calculation, including: For each tilt angle basis, perform: Update the position and velocity of each particle using the modified Velocity-Verlet algorithm; Relax the model to reach equilibrium; Output the information of the position change of each particle in the droplet model over time to the output file; c) Obtaining the droplet contour coordinate points at the three contact lines, including: For each tilt angle basis, perform: Using software to read the output file in step b), visualize the numerical model, and obtain an animation of the motion of the droplet on the solid substrate; Mark a set of arc-shaped droplet particle subsets A and B at the three contact lines on the left and right sides of the droplet at n moments in the motion animation; Obtain subset A and subset B at each moment and execute: Save the coordinate information of the droplet particles in subsets A and B in the Cartesian coordinate system in two TXT files respectively; d) Fitting a circular curve to obtain the contact angle, including: Get subset A and subset B at each moment and execute: Using software to read the TXT text containing the coordinate information of subset A and the TXT text containing the coordinate information of subset B in step c) respectively; The first circular curve is fitted using the least squares method and the particle coordinate information in subset A, and the second circular curve is fitted using the least squares method and the particle coordinate information in subset B; Let the coordinate point of the particle at the three-term contact line in subset A be point a, draw a horizontal straight line P1 through point a, draw a tangent line L1 through the intersection of P1 and the first circle curve, and the angle formed by L1 and P1 is the contact angle θ1; Let the coordinate point of the particle at the three-term contact line in subset B be point b, draw a horizontal straight line P2 through point b, draw a tangent line L2 through the intersection of P2 and the first circle curve, and the angle formed by L2 and P2 is the contact angle θ2; e) obtaining a graph of each substrate tilt angle and the corresponding static or dynamic contact angle, including: For each tilt angle basis, perform: The average value of θ1 and θ2 obtained at n moments is used to obtain θ1 * θ2 * ; θ1 obtained using each tilt angle basis * θ2 * Draw a line graph to obtain each substrate tilt angle and the corresponding static or dynamic contact angle line graph.

2. The method for obtaining the contact angle of a droplet based on multi-body dissipative particle dynamics simulation according to claim 1, characterized in that: The magnitude of the acceleration g applied in step a) is always 0.000845 DPD units; the direction of the acceleration g is modified by the spatial vector of g, the position of the substrate remains unchanged, and different inclination angles α of the substrate are calculated and simulated by forming different angles between the acceleration direction and the substrate.

3. The method for obtaining the contact angle of a droplet based on multi-body dissipative particle dynamics simulation according to claim 1, characterized in that: The periodic simulation area in step a) cooperates with the acceleration g with adjustable direction to ensure that the droplet returns to the solid substrate from the other side when it slides out of the simulation area on one side without falling off the solid substrate, thereby ensuring the continuity of the simulation.

4. The method for obtaining the contact angle of a droplet based on multi-body dissipative particle dynamics simulation according to claim 1, characterized in that: In step c), the height of subsets A and B is 15% of the total height h of the droplet; the method for selecting particles in the subset is to select them from the intersection of the three contact lines upward along the droplet contour.

5. The method for obtaining the contact angle of a droplet based on multi-body dissipative particle dynamics simulation according to claim 1, characterized in that: When α is 0°, the measured θ1 and θ2 are both static contact angles; when α is greater than 0°, the droplet begins to slide to one side, and the measured θ1 and θ2 are both dynamic contact angles; the dynamic contact angles include: advancing contact angle and receding contact angle; θ on the advancing side of the droplet is the advancing contact angle, and θ on the receding side of the droplet is the receding contact angle.

6. The method for obtaining the contact angle of a droplet based on multi-body dissipative particle dynamics simulation according to claim 1, characterized in that: The software in step a) is LAMMPS software, and the output file in step b) is a .lammpstrj file.

7. The method for obtaining a droplet contact angle based on multi-body dissipative particle dynamics simulation according to claim 1, characterized in that: The software in step c) is Ovito software, and the software in step d) is Matlab software.

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