Method and apparatus for simulating the coupled dynamics of active swimmers and droplets

Abstract

The application provides a kind of active swimming particle and droplet coupling dynamics simulation method and device, it is related to the technical field of multiphase flow numerical simulation, including: through the isothermal Newton fluid control equation of Lagrange form, based on fluid particle set, establish particle momentum equation;Through the speed assignment processing of each boundary particle on the surface of active swimming particle model, obtain boundary velocity condition, and according to fluid particle set, particle momentum equation and boundary velocity condition, the conservative force, dissipation force, random force, particle distribution correction force and interface force suffered by each particle are calculated to determine the total fluid force and total torque suffered by active swimming particle;Based on total fluid force and total torque, the state of fluid particle and the state of active swimming particle are updated, and the coupling dynamics simulation result is output after updating is completed.The application can significantly improve the coupling dynamics simulation accuracy of active swimming particle and droplet.

Description

Technical Field

[0001] This invention relates to the technical field of numerical simulation of multiphase flow, and in particular to a method and apparatus for simulating the coupled dynamics of actively moving particles and droplets. Background Technology

[0002] Currently, the motion behavior of actively moving particles in complex fluid environments is a key issue in fields such as microfluidic chip design and targeted drug delivery. Related technologies propose that methods such as the lattice Boltzmann method, smooth particle hydrodynamics, dissipative particle dynamics, finite volume method, and multi-particle collision dynamics can be used to simulate the motion behavior of actively moving particles in complex fluid environments. However, existing simulation methods suffer from problems such as difficulty in capturing deformable interfaces, insufficient accuracy in applying active propulsion slip boundary conditions, lack of thermal fluctuation effects, and difficulty in coupling multiphase interfaces with active particles, resulting in low simulation accuracy. Summary of the Invention

[0003] In view of this, the purpose of the present invention is to provide a method and apparatus for simulating the coupling dynamics of actively moving particles and droplets, which can significantly improve the accuracy of simulating the coupling dynamics of actively moving particles and droplets.

[0004] In a first aspect, embodiments of the present invention provide a method for simulating the coupled dynamics of actively moving particles and droplets. The method includes: discretizing the fluid in the computational domain into a set of fluid particles based on smooth dissipative particle dynamics; establishing a particle momentum equation based on the set of fluid particles using the Lagrangian form of the isothermal Newtonian fluid control equations; wherein each fluid particle in the set of fluid particles includes: mass attribute, position attribute, and velocity attribute; and the Lagrangian form of the isothermal Newtonian fluid control equations includes: a continuity equation and a momentum conservation equation; assigning velocity values ​​to each boundary particle on the surface of the actively moving particle model to obtain boundary velocity conditions; and calculating the conservative force, dissipative force, random force, particle distribution correction force, and interface force acting on each particle according to the set of fluid particles, the particle momentum equation, and the boundary velocity conditions to determine the total fluid force and total torque acting on the actively moving particles; updating the fluid particle state and the actively moving particle state based on the total fluid force and total torque; and outputting the coupled dynamics simulation results after the update is completed.

[0005] In one embodiment, the step of calculating the interfacial force includes: using a color function, according to the fluid phase of the fluid particles, performing color marking processing and particle summation approximation processing on each fluid particle to obtain the color function gradient, and normalizing the color function gradient to obtain the interface normal vector; using a continuous surface stress model, calculating the surface stress tensor at the multiphase interface according to the interface normal vector, and discretizing the surface stress tensor to obtain the interfacial force.

[0006] In one embodiment, the step of obtaining boundary velocity conditions by assigning velocity values ​​to various boundary particles on the surface of the active floating particle model includes: modeling the active floating particle as a rigid sphere with the boundary particles covering the surface to obtain an active floating particle model, and obtaining the surface sliding velocity based on the tangential sliding velocity distribution on the surface of the sphere of the active floating particle model; and calculating the assigned velocities corresponding to various boundary particles on the surface of the active floating particle model according to the surface sliding velocity to obtain the boundary velocity conditions.

[0007] In one embodiment, the step of obtaining the surface slip velocity based on the tangential slip velocity distribution of the sphere surface using an active floating particle model includes: obtaining the floating parameters corresponding to the active floating particles, wherein the floating parameters are used to classify the active floating particles into propulsion type, pulling type or neutral type; and calculating the tangential slip velocity of the surface of the active floating particles based on the floating parameters to determine the surface slip velocity.

[0008] In one embodiment, the step of calculating the assigned velocities of each boundary particle on the surface of the active floating particle model based on the surface slip velocity to obtain the boundary velocity conditions includes: for any fluid particle adjacent to the outer surface of the active floating particle, determining the nearest point of the fluid particle on the surface of the active floating particle model, and determining the target boundary velocity at the nearest point based on the rigid body motion velocity and surface slip velocity of the active floating particle at the nearest point, wherein the rigid body motion velocity includes the translational velocity and rotational velocity of the active floating particle; determining the assigned velocity of the boundary particle corresponding to the nearest point based on the target boundary velocity, and determining the boundary velocity conditions based on the assigned velocities of each boundary particle on the surface of the active floating particle.

[0009] In one embodiment, the step of updating the fluid particle state and the active swimming particle state based on the total fluid force and total torque includes: within a preset time threshold, iteratively updating the fluid particle state using a velocity Wieleret time integral model, and iteratively updating the active swimming particle state based on the total fluid force and total torque using the Newton-Euler equations, to obtain the target fluid particle state and the target active swimming particle state corresponding to the termination time of the particle simulated motion.

[0010] In one embodiment, the step of outputting the coupled dynamics simulation results includes: when the initial position of the active swimming particle is inside the droplet composed of fluid particles, if the active swimming particle is propulsive or neutral, the coupled dynamics simulation result is determined to be reverse enveloping co-swimming; if the active swimming particle is pulling, the coupled dynamics simulation result is determined to be forward dragging co-swimming. When the initial position of the active swimming particle is outside the droplet, if the active swimming particle is propulsive or neutral, the coupled dynamics simulation result is determined to be forward pushing co-swimming; if the active swimming particle is pulling, the coupled dynamics simulation result is determined to be reverse dragging co-swimming.

[0011] Secondly, embodiments of the present invention also provide a coupled dynamics simulation device for actively moving particles and droplets. The device includes: a system construction module, which discretizes the fluid in the computational domain into a set of fluid particles based on smooth dissipative particle dynamics, and establishes a particle momentum equation based on the fluid particle set using the Lagrangian isothermal Newtonian fluid control equations. Each fluid particle in the fluid particle set includes mass, position, and velocity attributes, and the Lagrangian isothermal Newtonian fluid control equations include a continuity equation and a momentum conservation equation; a force calculation module, which assigns velocity values ​​to each boundary particle on the surface of the actively moving particle model to obtain boundary velocity conditions, and calculates the conservative force, dissipative force, random force, particle distribution correction force, and interface force acting on each particle based on the fluid particle set, particle momentum equation, and boundary velocity conditions to determine the total fluid force and total torque acting on the actively moving particles; and a coupled motion state output module, which updates the fluid particle state and the actively moving particle state based on the total fluid force and total torque, and outputs the coupled dynamics simulation results after the update is completed.

[0012] Thirdly, embodiments of the present invention also provide a server, including a processor and a memory, the memory storing computer-executable instructions executable by the processor, the processor executing the computer-executable instructions to implement any of the methods provided in the first aspect.

[0013] Fourthly, embodiments of the present invention also provide a computer-readable storage medium storing computer-executable instructions, which, when invoked and executed by a processor, cause the processor to implement any of the methods provided in the first aspect.

[0014] The embodiments of the present invention bring the following beneficial effects: This invention provides a method and apparatus for simulating the coupled dynamics of active floating particles and droplets. The method discretizes the fluid within the computational domain into a set of fluid particles based on smooth dissipative particle dynamics. Using the Lagrangian form of the isothermal Newtonian fluid control equations, a particle momentum equation is established based on the fluid particle set. Then, by assigning velocity values ​​to various boundary particles on the surface of the active floating particle model, boundary velocity conditions are obtained. Based on the fluid particle set, particle momentum equation, and boundary velocity conditions, conservative forces, dissipative forces, random forces, particle distribution correction forces, and interfacial forces acting on each particle are calculated to determine the total fluid force and total torque acting on the active floating particles. Finally, based on the total fluid force and total torque, the states of the fluid particles and the active floating particles are updated, and the coupled dynamics simulation results are output after the update is completed. This invention can significantly improve the accuracy of the coupled dynamics simulation of active floating particles and droplets.

[0015] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention are realized and obtained in accordance with the structures particularly pointed out in the description, claims and drawings.

[0016] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0017] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0018] Figure 1 A schematic flowchart illustrating a method for simulating the coupling dynamics of an active floating particle and a droplet, provided in an embodiment of the present invention; Figure 2 A schematic diagram illustrating the specific process of a coupling dynamics simulation method between an active floating particle and a droplet, provided in an embodiment of the present invention; Figure 3 A schematic diagram of the structure of a coupling dynamics simulation device for actively moving particles and droplets provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the structure of a server provided in an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Currently, active matter is an important research direction in the fields of soft condensed matter physics and biophysics. Typical active particles include microorganisms (such as bacteria, sperm, ciliates, and other biological micromotors) and artificially synthesized micro- and nano-motors (such as Janus particles and catalytic micromotors). The common characteristic of these particles is their ability to extract energy from the surrounding environment and convert it into their own directional propulsion.

[0021] The behavior of active particles in complex fluid environments has attracted widespread attention, especially when active particles are encapsulated inside droplets or interact with droplet interfaces. Their motion and the droplet's deformation response constitute a typical fluid-structure interaction and multiphase flow coupling problem. This type of problem has significant application value in fields such as microfluidic chip design, targeted drug delivery, micro / nano robot control, and active emulsion systems.

[0022] To describe the propulsion behavior of microparticles, existing techniques propose a simplified model that approximates the flow field generated by ciliary motion by applying an effective slip velocity to the surface of a sphere. This model can distinguish different types of movement by adjusting the movement parameters: pusher (e.g., E. coli), puller (e.g., Chlamydomonas), and neutral (Neutral Squirmer). The Squirmer model has become a standard tool for studying the hydrodynamic behavior of active particles due to its physical clarity and computational feasibility.

[0023] Related technologies have been proposed, and several computational methods are currently available for numerical simulation of microscale active particles: The Lattice Boltzmann Method (LBM) solves the fluid transport equations on a fixed Euler grid. LBM is efficient when dealing with simple geometric boundaries, but it requires additional interface tracking and interpolation processing when dealing with moving boundaries of active particles and interfaces of large-deformation droplets, which significantly increases the algorithm complexity.

[0024] Smoothed Particle Hydrodynamics (SPH) is a classic meshless Lagrangian particle method that describes continuous media using discrete particles. SPH is naturally well-suited for handling free surfaces and moving interfaces, but standard SPH lacks a proper description of microscale thermal fluctuations and has certain limitations in terms of viscous stress and angular momentum conservation.

[0025] Dissipative Particle Dynamics (DPD) is a mesoscale particle method that can correctly handle thermal fluctuations, but the mapping relationship between transport coefficients such as viscosity and physical parameters in its coarse-grained equations is not intuitive enough, which limits its application in quantitative simulations.

[0026] Finite Volume Method (FVM): A traditional computational fluid dynamics method based on Eulerian meshes, which faces the challenge of mesh regeneration when dealing with large deformation problems at moving boundaries of rigid particles and droplet interfaces.

[0027] Multiparticle Collision Dynamics (MPCD): Suitable for simulating mesoscale fluids, but has limited capabilities in handling multiphase interfaces.

[0028] However, existing technologies face the following key challenges when simulating the coupled dynamics of the interface between actively moving particles and deformable droplets: Deformable interfaces are difficult to capture: When active particles move inside a droplet and approach the interface, the droplet undergoes large local or even global deformations. Traditional Eulerian mesh methods require specialized interface tracking or capture algorithms (such as Level-Set, VOF, etc.), which suffer from problems of mass non-conservation or decreased computational accuracy when dealing with large deformations and topological changes.

[0029] Insufficient precision in applying active propulsion slip boundary conditions: The propulsion mechanism of the Squirmer model relies on the non-uniform tangential slip velocity distribution on the particle surface. In the discrete particle method, a key technical challenge is how to accurately apply this continuous slip velocity boundary condition to the rigid body surface so that the surrounding fluid can accurately perceive the active propulsion effect.

[0030] Coupling between multiphase interfaces and active particles is difficult: When active particles cross or approach the droplet interface, three-phase coupling is involved between the solid boundary particles, the droplet interface and the external fluid. The calculation of forces and momentum transfer require special handling, which can easily lead to numerical instability.

[0031] Lack of thermal fluctuation effect: At the micro- and nano-scale, thermal fluctuations have a non-negligible impact on particle motion. Macroscopic methods such as SPH cannot accurately describe this effect, while DPD, although capable of handling thermal fluctuations, suffers from insufficient quantitative precision.

[0032] Insufficient stability of fluid-structure interaction calculations: When active particles move at high speeds in confined spaces (such as inside droplets), they may cause drastic changes in the local flow field, which places higher demands on the stability of numerical methods.

[0033] Based on this, the present invention provides a method and apparatus for simulating the coupled dynamics of active floating particles and droplets, which aims to solve technical problems such as low precision in applying slip boundary conditions, difficulty in handling large interface deformations, incompatibility of thermal fluctuation effects, and difficulty in accurately capturing coupled motion modes during the interaction between active particles and deformable droplets at the microscale, and significantly improves the accuracy of the coupled dynamics simulation of active floating particles and droplets.

[0034] See Figure 1 The diagram shows a flowchart of a method for simulating the coupled dynamics of an active floating particle and a droplet. This method mainly includes the following steps S102 to S106: Step S102: Discretize the fluid in the computational domain into a set of fluid particles based on smooth dissipative particle dynamics, and establish a particle momentum equation based on the set of fluid particles using the Lagrangian form of the isothermal Newtonian fluid control equation. Each fluid particle in the set of fluid particles has a mass attribute, a position attribute, and a velocity attribute. The Lagrangian form of the isothermal Newtonian fluid control equation includes a continuity equation and a momentum conservation equation.

[0035] In one implementation, the fluid within the computational domain first needs to be discretized. The computational domain refers to the finite spatial range in which the fluid and actively moving particles reside during the simulation. Fluid discretization refers to the process of decomposing a continuously distributed fluid medium into a finite number of discrete units. Specifically, this invention employs the smooth dissipative particle dynamics method for discretization. This method is a meshless Lagrangian particle method that represents continuous fluid as a series of particles with physical properties, each particle representing a tiny fluid particle cluster. Through this discretization process, a set of fluid particles is obtained, where each fluid particle is assigned three basic attributes: mass, position, and velocity. The mass attribute represents the mass of the fluid particle cluster it represents, the position attribute represents the spatial coordinates of the particle in the computational domain, and the velocity attribute represents the speed and direction of the particle's motion.

[0036] After discretizing the fluid particles, it is necessary to establish governing equations describing the fluid motion. This invention employs the Lagrangian form of the isothermal Newtonian fluid governing equations. The Lagrangian form describes fluid motion from the perspective of following moving fluid particles; that is, the trajectory of each fluid particle is tracked, which contrasts with the Eulerian form, which observes fluid motion from a fixed spatial point. The isothermal Newtonian fluid governing equations assume a constant fluid temperature and adherence to Newton's law of viscosity, meaning that the fluid's shear stress is proportional to its shear strain rate. These governing equations specifically consist of two parts: a continuity equation and a momentum conservation equation. The continuity equation describes the conservation of fluid mass during motion; that is, the difference in fluid mass flowing into and out of a volume element per unit time is equal to the rate of change of fluid mass within that volume element. The momentum conservation equation describes the change in fluid momentum under external forces; that is, the rate of change of momentum of a fluid element is equal to the net external force acting on it, including pressure gradient forces, viscous forces, and volume forces.

[0037] Based on the aforementioned Lagrangian form of the isothermal Newtonian fluid governing equations and combined with the established fluid particle set, this invention further establishes a particle momentum equation. The particle momentum equation is the equation of motion for each discrete fluid particle, discretizing the continuous momentum conservation equation into the relationship between the net force acting on each particle and its acceleration. Specifically, the mass of each fluid particle multiplied by its acceleration equals the sum of all forces exerted on it by surrounding particles. These forces include conservative forces, dissipative forces, random forces, particle distribution correction forces, and interfacial forces, which together determine the motion state of the fluid particles. By establishing the particle momentum equation, the momentum conservation principle of macroscopic continuous fluids is transformed into a numerical form that can be calculated and iteratively updated particle by particle on a computer.

[0038] Step S104: By assigning velocity values ​​to the boundary particles on the surface of the active floating particle model, the boundary velocity conditions are obtained. Based on the fluid particle set, particle momentum equation and boundary velocity conditions, the conservative force, dissipative force, random force, particle distribution correction force and interface force on each particle are calculated to determine the total fluid force and total torque on the active floating particles.

[0039] In one implementation, it is necessary to assign velocity values ​​to the boundary particles on the surface of the actively moving particle model. The actively moving particle model refers to a particle model capable of autonomously generating propulsive motion. This model constructs the actively moving particle as a rigid sphere covered by boundary particles. The boundary particles are discrete points attached to the surface of the actively moving particle; they do not move independently but undergo rigid body motion along with the actively moving particle, simultaneously acting as a medium for interaction between the fluid particles and the actively moving particle. The velocity assignment process involves calculating and assigning a suitable velocity value to each boundary particle. This velocity value is not simply equal to the rigid body motion velocity of the actively moving particle, but rather a modified artificial velocity. By assigning velocity values ​​to all boundary particles, the boundary velocity conditions are obtained, i.e., the set of velocity values ​​for all boundary particles. These boundary velocity conditions are crucial input parameters for subsequent mechanical calculations.

[0040] After obtaining the boundary velocity conditions, it is necessary to calculate the various forces acting on each particle based on the fluid particle ensemble, particle momentum equation, and boundary velocity conditions. The fluid particle ensemble provides basic information such as the position, velocity, and density of the fluid particles; the particle momentum equation provides the calculation formulas and forms for various forces; the boundary velocity conditions provide the velocity values ​​of the boundary particles, which are used to calculate the relative velocity between the fluid particles and the boundary particles. Each particle includes fluid particles and boundary particles on the surface of actively moving particles. The calculated forces include five types: conservative forces correspond to pressure gradients, reflecting the driving effect caused by uneven pressure distribution in the fluid; dissipative forces correspond to viscous stress, reflecting the frictional resistance generated by velocity differences within the fluid; random forces are used to describe thermal fluctuation effects at the micro-nano scale, i.e., the pulsating force generated by random collisions of fluid molecules; particle distribution correction forces are used to suppress numerical errors caused by uneven particle distribution and improve the stability of the simulation; and interfacial forces are used to describe the surface tension effect between different fluid phases and maintain the interface shape of the droplets.

[0041] After calculating the various forces acting on each particle, it is necessary to sum the fluid-solid interaction forces on all boundary particles on the surface of the actively moving particle to obtain the total fluid force and total torque acting on the actively moving particle. The total fluid force is the vector sum of the forces acting on all boundary particles and determines the translational acceleration of the actively moving particle; the total torque is the vector sum of the moments of the forces acting on all boundary particles about the center of mass of the actively moving particle and determines the angular acceleration of the actively moving particle. The total fluid force and total torque are key input parameters for subsequent updates to the motion state of the actively moving particle.

[0042] Step S106: Based on the total fluid force and total torque, update the fluid particle state and the active swimming particle state, and output the coupled dynamics simulation results after the update is completed.

[0043] In one implementation, after completing the various mechanical calculations and determining the total fluid force and total torque acting on the actively moving particle, the states of the fluid particle and the actively moving particle need to be updated based on these two key physical quantities. State updating refers to advancing the particle's position and velocity from the current moment to the next moment; this is the core step of time progression in numerical simulation. The fluid particle state includes the fluid particle's position and velocity, while the actively moving particle state includes the actively moving particle's position, translational velocity, and angular velocity. The total fluid force determines the translational acceleration of the actively moving particle's center of mass, and the total torque determines the angular acceleration of the actively moving particle around its center of mass.

[0044] The state of fluid particles is updated using the Velocity-Verlet time integration scheme (i.e., the Velocity-Verlet time integration model). Velocity-Verlet is a numerical method for solving equations of motion. Its basic idea is: first, calculate the velocity half a step later based on the resultant force at the current moment; then, update the position using the half-step velocity; next, recalculate the resultant force based on the new position; and finally, update the complete velocity using the recalculated resultant force. This scheme can maintain computational accuracy while exhibiting good numerical stability, making it particularly suitable for complex physical systems involving multiple interaction forces. Through the Velocity-Verlet scheme, the velocities and positions of all fluid particles are synchronously updated to the next time step, resulting in the updated fluid particle state.

[0045] The state update of the actively moving particle is achieved using Newton's and Euler's equations. These equations, fundamental to rigid body motion, consist of translational and rotational equations. The translational equation states that the total mass of the actively moving particle multiplied by its center-of-mass translational acceleration equals the total fluid force; that is, force determines translational acceleration. Integrating the acceleration yields the translational velocity, and integrating the velocity yields the position. The rotational equation states that the inertial tensor of the actively moving particle multiplied by its angular acceleration, plus a gyroscopic term, equals the total torque; that is, torque determines angular acceleration. Integrating the angular acceleration yields the angular velocity, and integrating the velocity yields the direction. Using Newton's and Euler's equations, the translational velocity, angular velocity, and position of the actively moving particle are synchronously updated to the next time step, resulting in the updated state of the actively moving particle.

[0046] After completing the state update, it is necessary to determine whether the preset simulation termination time has been reached. If not, proceed to the next time step and repeat the mechanical calculation and state update process; if the time has been reached, terminate the loop and output the coupled dynamics simulation results. The coupled dynamics simulation results include the motion trajectory of the active floating particles, the deformation parameters of the droplets, and the flow field distribution information. These results can be used to analyze the coupled motion behavior of the active floating particles and the droplets.

[0047] The coupling dynamics simulation method for active swimming particles and droplets provided in this invention can accurately simulate the propulsion characteristics of active swimming particles, stably capture the dynamic deformation response of the droplet interface under the action of active particles, correctly describe the microscale thermal fluctuation effect, and identify and distinguish various coupling motion modes, including reverse wrapping co-swimming and forward dragging co-swimming in the internal wrapping scenario, and forward pushing co-swimming and reverse dragging co-swimming in the external collision scenario, thereby significantly improving the accuracy of coupling dynamics simulation of active swimming particles and droplets.

[0048] See Figure 2 The diagram illustrates a specific flowchart of a method for simulating the coupled dynamics of actively moving particles and droplets. This embodiment of the invention also provides an implementation method for simulating the coupled dynamics of actively moving particles and droplets, with the complete calculation flow as follows: Initialization: Set the computational domain, particle resolution, fluid parameters (density, viscosity, sound velocity), interface parameters (surface tension coefficient), and Squirmer parameters. , ,radius ), initialize the position and velocity of droplet particles, external fluid particles, and Squirmer boundary particles.

[0049] Density calculation: Summing the kernel function over all particles to calculate the particle number density. Solving the state equations: Calculate the pressure of each particle using the state equations. .

[0050] Conservative force calculation: Calculate the conservative forces between all particle pairs. Dissipative force calculation: Calculate the dissipative force between all particle pairs. Random force calculation: Generate Wiener process increments and calculate random forces. Particle distribution correction force calculation: Calculate the corrected transport velocity and thus calculate the correction force. Interfacial tension calculation: Calculate the color function gradient and surface stress tensor to obtain the interfacial force. .

[0051] Apply artificial velocity boundary conditions: For each Squirmer boundary particle, calculate the artificial velocity (i.e., assign a velocity) based on the velocity and geometry of the nearest fluid particle.

[0052] Force calculation for Squirmer: Summarize the fluid-solid interaction forces on all boundary particles to obtain the total force and torque on Squirmer.

[0053] Velocity update: Update the fluid particle velocities according to the Velocity-Verlet scheme; update the Squirmer's translational and angular velocities according to the Newton-Euler equations; Position update: Update the positions of all particles.

[0054] Output and Post-processing: Records the Squirmer's trajectory, droplet deformation state, and flow field distribution information. Iterative Loop: Returns to the density calculation step and repeats until the simulation reaches the set termination time.

[0055] In one implementation, the above process is specifically described in (1) to (7) below: (1) Establishment of SDPD fluid particle model.

[0056] (1-1) Particle Discretization Method. The fluid within the computational domain is discretized into a set of SDPD particles. Each particle... Having quality ,Location ,speed The same properties are used for fluid particles, droplet particles, and external fluid particles. The particle spacing is initialized. Active particles (Squirmer) are initialized in spherical coordinates, while other fluid particles are initialized at cubic grid points in Cartesian coordinates.

[0057] Define the relative position, relative velocity, distance, and unit direction vector between particles:

[0058]

[0059]

[0060] The position of each particle is updated according to the following rules:

[0061] (1-2) Calculation of particle number density. Particle number density Defined as density With quality The ratio is calculated using the kernel function summation method:

[0062] in, This is a smooth kernel function. The above density summation formula, combined with the position update equation, automatically satisfies the Lagrange form of the continuity equation:

[0063] Therefore, there is no need to solve the continuity equation separately using discrete methods.

[0064] (1-3) Kernel function selection. A quintic spline kernel is used, with the following form:

[0065] in, , For smooth length, Let be the spatial dimension. Normalization constant (two-dimensional: 3D: The smooth length is taken as... This kernel function has tight support, that is... The kernel function value is zero, and it simultaneously satisfies the normalization condition and the property of converging to the Dirac delta function.

[0066] (1-4) Governing Equations. The Lagrangian form of the governing equations for isothermal Newtonian fluids includes the continuity equation and the momentum conservation equation:

[0067]

[0068] in, For fluid density, For speed, For pressure, For dynamic viscosity, For volume forces, This is a stochastic stress term (used in mesoscale simulations to describe thermal fluctuations).

[0069] (1-5) Equation of State. The pressure and density are related using a weakly compressible equation of state:

[0070] in, To balance density, The artificial velocity of sound (its value should be chosen to keep density fluctuations within a small range to ensure quasi-incompressibility). It is a positive constant (used to ensure that the pressure on discrete particles is positive). This equation of state guarantees the quasi-incompressible nature of the fluid.

[0071] (2) SDPD particle momentum equation.

[0072] Each SDPD particle The momentum equation is:

[0073] Among them, each item For conservative force, For dissipative force, For particle distribution correction force, For random forces, The surface tension of the interface.

[0074] (2-1) Conservative forces. Discretization of the pressure gradient term in the corresponding Navier-Stokes equations:

[0075] Among them, pressure It is obtained from the state equations.

[0076] (2-2) Dissipative forces. Dissipative forces Discretization of the corresponding viscous stress term:

[0077] in, Let be the spatial dimension. For particles The dynamic viscosity. The harmonic average viscosity of particle pairs is used here. and harmonic mean density This makes it suitable for situations where viscosity is discontinuous in multiphase flow.

[0078] (2-3) Particle distribution correction force. To suppress numerical errors caused by non-uniform particle distribution in macroscopic flow simulations, a particle distribution correction force is introduced. :

[0079] in, To correct the tensor, The actual velocity of the particle. To correct the transport speed. The discrete form of the corrected transport speed is:

[0080] Among them, positive numbers It only appears in the calculation of the modified transport velocity and does not affect the momentum equation itself.

[0081] (2-4) Random forces. In order to accurately describe the thermal fluctuation effect at the mesoscale, random forces... Based on the GENERIC thermodynamic framework and the fluctuation-dissipation theorem, the following is determined:

[0082] in, Boltzmann constant, For temperature, The symmetric part of the increment of the independent Wiener process:

[0083] And it satisfies symmetry This ensures the conservation of momentum. Dissipative and stochastic forces strictly satisfy the fluctuation-dissipation theorem, guaranteeing the correct statistical behavior of the system under thermodynamic equilibrium.

[0084] (3) Droplet interface model and surface tension calculation. Using the color function, based on the fluid phase of the fluid particles, color marking and particle summation approximation are performed on each fluid particle to obtain the color function gradient. The color function gradient is then normalized to obtain the interface normal vector. Subsequently, using the continuous surface stress model, the surface stress tensor at the multiphase interface is calculated based on the interface normal vector. The surface stress tensor is then discretized to obtain the interface force.

[0085] (3-1) Color function labeling. To distinguish different fluid phases (e.g., fluid inside a droplet, fluid outside a droplet, and active particles), a color function is introduced. For those belonging to the phase particles Its color index is defined as:

[0086] And it satisfies the normalization condition. The gradient of the color function is approximated by summing the particles:

[0087] Among them, superscript This indicates two different fluid phases.

[0088] (3-2) Interface normal vector and surface stress tensor. The interface normal vector is obtained by normalizing the gradient of the color function:

[0089] Using the Continuous Surface Stress (CSS) model, the surface stress tensor at the interface is defined as:

[0090] in, For the sake of the prime minister With phase The surface tension coefficient between them It is a unit tensor.

[0091] The above surface stress tensor is equivalent to the classical... Form, in which Let be the spatial dimension.

[0092] (3-3) Calculation of interfacial forces. Interfacial tension. Discretization calculation is performed using the divergence of the surface stress tensor:

[0093] in, This represents the total surface stress tensor at the interface. Only related to... Particles that do not belong to phase Neighboring particles (i.e., belonging to other phases) The particles are subjected to interfacial forces.

[0094] (4) Active Squirmer model.

[0095] (4-1) Definition of surface slip velocity. The active floating particle is modeled as a rigid sphere with boundary particles covering the surface, resulting in an active floating particle model. Based on the tangential slip velocity distribution on the surface of the sphere of the active floating particle model, the surface slip velocity is obtained. In one embodiment, the floating parameters corresponding to the active floating particle can be obtained. Then, the tangential slip velocity on the surface of the active floating particle is calculated based on the floating parameters to determine the surface slip velocity. The floating parameters are used to classify the active floating particles into propulsion type, pulling type, or neutral type.

[0096] Specifically, the model of an actively moving particle is a particle with a radius of... A sphere has a surface with an effective sliding velocity along the tangential direction. For the axisymmetric case, the surface sliding velocity in spherical coordinates can be expressed as:

[0097] in, Polar angle (from the direction of Squirmer's head) and surface position vector (Definition of the included angle between them) and These are the tangential and radial unit vectors, respectively.

[0098] For the simplified steady-state Squirmer model, only the first two modes of the tangential component are considered. and The surface slip velocity can be simplified as:

[0099] in, The first modal coefficient determines the magnitude of the swimming speed; The swimming parameter is defined as:

[0100] when When the Squirmer is a pusher, its fluid thrust mainly comes from the tail, and its flow field characteristics are similar to those of flagellated microorganisms such as E. coli.

[0101] when At this time, the Squirmer is a puller type, and its fluid pull mainly comes from the head, with flow field characteristics similar to ciliated microorganisms such as Chlamydomonas.

[0102] when At that time, it is a neutral swimming body.

[0103] (4-2) Squirmer free-floating velocity. In an infinitely large uniform fluid (Stokes flow), the steady-state free-floating velocity of the Squirmer is determined solely by the first mode. Sure:

[0104] (4-3) Squirmer kinematics. Considering the translation and rotation of the Squirmer, the absolute velocity of any point on the surface of the sphere is:

[0105] in, and These are the translational velocity and angular velocity of Squirmer's center of mass, respectively.

[0106] (4-4) Equations of rigid body dynamics. As a rigid body, the motion of the Squirmer is governed by the following equations:

[0107]

[0108] in, and These represent the total external force and total torque acting on Squirmer, respectively. For total mass, It is the inertial tensor.

[0109] (5) Artificial velocity boundary method. Based on the surface slip velocity, the assigned velocities corresponding to various boundary particles on the surface of the active floating particle model are calculated and processed to obtain the boundary velocity conditions. In one embodiment, for any fluid particle adjacent to the outer surface of the active floating particle, the nearest point of the fluid particle on the surface of the active floating particle model can be determined, and the target boundary velocity at the nearest point can be determined based on the rigid body motion velocity and surface slip velocity of the active floating particle at the nearest point. Then, based on the target boundary velocity, the assigned velocity of the boundary particle corresponding to the nearest point is determined, and the boundary velocity conditions are determined based on the assigned velocities of various boundary particles on the surface of the active floating particle. The rigid body motion velocity includes the translational velocity and rotational velocity of the active floating particle.

[0110] (5-1) Method Principle. To accurately apply the slip velocity boundary conditions to the Squirmer surface in the SDPD particle method, this invention proposes an Artificial Velocity Method. The core idea of ​​this method is: for each boundary particle on the Squirmer surface... Assign a modified artificial velocity to the fluid particles interacting with it. The correct slip velocity effect is felt at the boundary.

[0111] (5-2) Definition of geometric relations. For a fluid particle and a boundary particle Define the following geometric quantities: fluid particles Construct an interface plane tangent to the Squirmer sphere; Normal direction The point of intersection with the interface plane (the closest point on the sphere); For fluid particles The normal distance to the sphere; Boundary particles The normal distance to the tangent plane.

[0112] Establish a local coordinate system: normal direction Perpendicular to the cutting plane, tangential Within the cut and within the included and the direction of Squirmer's head In the plane, Perpendicular to the former two.

[0113] (5-3) Formula for calculating artificial speed (i.e., assignment speed).

[0114] Boundary particles The artificial velocity components in the three local coordinate directions are as follows: Tangential component ( Direction (including sliding speed):

[0115] Normal components ( direction):

[0116] Third direction component ( direction):

[0117] in, For fluid particles The components of velocity in the local coordinate system; Intersection The surface slip velocity at that location (calculated using the Squirmer model formula); Intersection The velocity component generated by the rigid body motion (i.e. ); This is a correction factor, with typical values... ; For smooth lengths. In the denominator The introduction of the term is to prevent when A division-by-zero error occurs when the value approaches zero.

[0118] (5-4) Physical meaning. The physical meaning of the artificial velocity method is: assuming that the fluid velocity originates from the fluid particles... Linear variation between solid surfaces and boundary particles, through the boundary particles Extrapolate a corresponding velocity value at a given position, such that on the sphere... The given boundary velocity condition (rigid body motion velocity plus slip velocity) is exactly satisfied at the point. This guarantees the non-penetration condition (normal velocity matching) and the slip condition (tangential velocity includes slip velocity). Both are satisfied at the same time.

[0119] (5-5) Boundary particle pressure treatment. To ensure the correct pressure gradient near the boundary, the pressure of each boundary particle is obtained by interpolation of the values ​​of its neighboring fluid particles.

[0120] (6) Calculation of forces and torques on active particles. The total fluid forces and torques on the Squirmer are obtained by summing the fluid-solid interaction forces on all boundary particles:

[0121] in, Boundary particles The position vector relative to Squirmer's center of mass. The forces and moments obtained from this are then substituted into the rigid body dynamics equations for solution.

[0122] (7) Time integration scheme. Within a preset time threshold, the fluid particle state is iteratively updated using the velocity Wielerite time integration model, and the active swimming particle state is iteratively updated using the Newton-Euler equation based on the total fluid force and total torque, to obtain the target fluid particle state and target active swimming particle state corresponding to the termination time of the particle simulation motion.

[0123] (7-1) Time step constraint.

[0124] To ensure numerical stability, the global time step Take the minimum value among the following constraints: Capillary wave condition (Courant-Friedrichs-Lewy condition):

[0125] Viscous diffusion conditions:

[0126] Sound speed conditions:

[0127] Body force conditions:

[0128] The final time step is the minimum value that satisfies all the above conditions.

[0129] (7-2) Velocity-Verlet integration scheme (i.e., velocity Verlet time integration model). Fluid particles use the Velocity-Verlet time integration scheme for state updates: Half-step speed update:

[0130] Location update:

[0131] Recalculate particle density and forces Full-step speed update:

[0132] For Squirmer particles, the motion of boundary particles follows rigid body dynamics and is updated by the Newton-Euler equations.

[0133] In practical applications: 1. Example setup.

[0134] A three-dimensional computational domain was constructed to study the coupling dynamics between actively moving particles and spherical droplets under two initial scenarios: Scenario A, Internal Envelope Scenario: Squirmer is initially located at the center of a spherical droplet, which is surrounded by external fluid.

[0135] Scenario B, External Collision Scenario: The Squirmer is initially located outside the droplet, and its initial centroid is at a distance of [missing information - likely a distance from the droplet center]. The head is facing the direction of the droplet (along) (In the positive direction of the axis), it moves towards the droplet and collides with it.

[0136] The common parameter settings for both scenarios are as follows: Computational domain: side length is The cube is given periodic boundary conditions; Squirmer radius: Droplet radius: Take respectively (Large droplets) (Medium droplet) (Small droplets); Droplet and external fluid density: Droplet viscosity: External fluid viscosity: Surface tension coefficient: droplet-external fluid interface Squirmer - External Fluid Interface Swimming parameters: steady-state swimming speed Swimming type: tested separately (Pusher) (Neutral) and (Puller); Reynolds number: Capillary count: .

[0137] 2. Simulation results for scenario A: Internal envelopment scenario. When the initial position of the active swimming particle is inside the droplet composed of fluid particles, if the active swimming particle is propulsive or neutral, the coupling dynamics simulation result is determined to be reverse envelopment co-swimming; if the active swimming particle is pulling, the coupling dynamics simulation result is determined to be forward dragging co-swimming.

[0138] 2-1. Movement Mode 1: Reversing-Encapsulating Co-swimming Mode.

[0139] For pusher type, ) and neutral (Neutral, Squirmer, regardless of droplet size, exhibited the following behavioral characteristics: Squirmer starts from the center of the droplet and moves along the head direction (positive). (Direction) accelerates; as it approaches the droplet edge, due to the resistance of surface tension to interfacial deformation, the Squirmer decelerates and its direction of movement reverses; finally, the Squirmer turns around and moves along the negative direction. The droplet moves in the opposite direction to the initial direction of Squirmer's motion, always remaining enveloped by the droplet; the droplet as a whole moves in the opposite direction (negative) to the initial direction of Squirmer's motion. (Direction) moving at low speed, forming a reverse package swimming together.

[0140] Squirmer remained completely enveloped by droplets throughout the process, and there were three different droplet sizes ( They all exhibited similar co-travel characteristics.

[0141] 2-1. Movement Mode Two: Forward-Dragging Co-swimming Mode.

[0142] For pull-type (Puller, The Squirmer, whose behavior is quite different from that of the Propulsion type, is as follows: The Squirmer accelerates along its head, and the strong fluid suction in this direction causes the droplet tip interface to thin rapidly. When the Squirmer's propulsion force is sufficient to overcome surface tension, it penetrates the droplet interface. After penetration, the Squirmer continues along its head... Moving in the positive direction of the axis, the body part is still surrounded by residual fluid from the droplet; eventually forming a Squirmer that drags the droplet along the positive direction. A forward dragging and swimming mode of directional coordinated motion.

[0143] Puller has the largest steady-state co-swimming velocity amplitude, and its co-swimming direction is consistent with the initial head direction (positive direction), which is much higher than the reverse co-swimming velocity of Pusher and Neutral.

[0144] 2-3. Characteristics of velocity evolution.

[0145] With medium droplets ( Taking as an example, convergence analysis was performed at different particle resolutions ( The simulation results under these conditions show good convergence.

[0146] Pusher: Steady-state cooperative swimming speed is slightly lower than Neutral, and the speed direction is negative (reverse wrapping cooperative swimming); Neutral: Reverse wrapping cooperative swimming speed is between Pusher and Puller; Puller: Forward drag cooperative swimming speed is the highest, and the speed direction is positive, much higher than the other two types.

[0147] 3. Simulation results for Scenario B: External collision scenario. Select medium-sized droplets ( The initial distance between the Squirmer centroid and the droplet center is... The remaining parameters are consistent with the droplet encapsulation scenario described above. The Squirmer head faces along... Positive axis direction. When the initial position of the active swimming particle is outside the droplet, if the active swimming particle is propulsive or neutral, the coupled dynamics simulation result is determined to be positive propulsion co-swimming; if the active swimming particle is pulling, the coupled dynamics simulation result is determined to be reverse dragging co-swimming.

[0148] 3-1. Movement Mode Three: Forward-Pushing Co-swimming Mode.

[0149] For pusher type, ) and neutral (Neutral, After Squirmer collides with the droplet from the outside, the following behavioral characteristics were observed: Squirmer accelerates from rest, along... The Squirmer moves in the positive direction towards the droplet; after colliding with the droplet, due to interfacial tension, the Squirmer neither penetrates the droplet interface nor enters the droplet interior; the Squirmer maintains its initial direction of movement, pushing the droplet a certain distance behind it; eventually, the two maintain a certain distance and move together along... Steady-state motion in the positive direction of the axis forms a positive-driven co-travel mode.

[0150] A key characteristic of this mode is that there is no direct contact between the Squirmer and the droplet; they maintain a stable co-flow state through hydrodynamic interactions. The droplet, propelled by the Pusher and Neutral, remains approximately spherical with minimal interfacial deformation.

[0151] 3-2, Movement Mode Four: Reversing-Dragging Co-swimming Mode.

[0152] For pull-type (Puller, After the Squirmer collides with the droplet from the outside, its behavior is quite different from that of the Pusher and Neutral: The Squirmer accelerates toward the droplet. Due to the strong suction field at the Puller head, after the collision, the Squirmer penetrates the droplet interface and merges with the droplet. After merging, the velocity of the complex reverses 180 degrees. Finally, the swimmer-droplet complex moves along... Steady-state co-travel in the negative axis direction (i.e. opposite to the initial motion direction of Squirmer) forms a reverse dragging co-travel mode.

[0153] The physical mechanism of this mode is that after the Puller merges with the droplet, the interaction between the suction flow field at its head and the droplet interface causes the overall motion direction of the complex to reverse. This is a novel coupled dynamic behavior that is different from the internal encapsulation scenario.

[0154] 4. Flow field structure analysis and equivalent floating behavior mapping.

[0155] 4-1. Flow field characteristics of internal wrapping scene.

[0156] Under steady-state conditions, the flow field characteristics of the swimmer-droplet complex in the internal encapsulation scenario are as follows: Pusher-droplet (reverse encapsulation co-flow): The complex is macroscopically equivalent to a head along the... A Puller-type floating body that moves in the negative direction of the axis generates an additional vortex structure at its tail.

[0157] Neutral-droplet (reverse encapsulation co-flow): The complex is equivalent to a head along... Neutral-type swimming bodies that move in the negative direction of their axis.

[0158] Puller-Droplet (Forward Dragging Co-trajectory): The complex is equivalent to a head along... For a Neutral-type floating body moving in the positive direction of the axis, the flow field changes relatively gently.

[0159] 4-2. Flow field characteristics in external collision scenarios.

[0160] The flow field characteristics of a steady-state co-moving body in an external collision scenario are as follows: Pusher / Neutral-Droplet (Forward Propulsion Co-movement): Since the Squirmer and the droplet do not come into contact, the flow field structure changes only to a limited extent, and the original vortex characteristics of the moving body are still maintained.

[0161] Puller-droplet (counter-drag co-flow): The flow field of the merged complex is equivalent to that of a head along... Neutral-type swimming bodies that move in the negative direction of the axis belong to the "-neutral" complex.

[0162] 4-3. Equivalent Floating Behavior Mapping Theory.

[0163] Based on the above flow field analysis, the swimmer-droplet complex can be equivalently mapped to a novel type of active particle, and classified according to the equivalent swimming behavior of the complex: The "-puller" complex: a reverse-encapsulating co-flowing entity formed by the original Pusher and the droplet in an encapsulating scenario, which is equivalent to a head-along... A Puller-type swimming body that moves in the negative direction of its axis.

[0164] The "-neutral" complex: the reverse-enveloping co-flowing body formed by the original Neutral and the droplet in the enveloping scenario, and the reverse-dragging co-flowing body formed by the original Puller merging with the droplet in the collision scenario, are both collectively equivalent to a head-edge... Neutral-type swimming bodies that move in the negative direction of their axis.

[0165] The "+neutral" complex: a positively dragging, co-flowing entity formed by the original Puller and the droplet in a wrapping scenario, which is equivalent to a head-along... Neutral-type swimming bodies that move in the positive direction of their axis.

[0166] The aforementioned equivalent mapping theory not only helps simplify the dynamic analysis of co-swimming bodies in multiphase flow, but also provides a new classification perspective and control basis for the design of droplet-based microswimming bodies.

[0167] 5. Analysis of the influence of physical parameters.

[0168] The effects of the following physical parameters on the coupled motion modes were simulated and analyzed: Droplet-to-particle radius ratio The smaller the droplet, the stronger the constraint on the particles. In the internal encapsulation scenario, when the radius ratio decreases to 1.5, the counter-movement of the Pusher and Neutral within the small droplet is more restricted, but the Puller can still penetrate the interface to form a forward dragging co-movement. The droplet size does not affect the classification of co-movement modes, but it does affect the steady-state co-movement velocity.

[0169] swimming parameters : The sign and size determine the type of coupled motion mode. Puller ( Due to the unique structure of the suction flow field at the head, it is easier to break through the interface and generate positive dragging behavior in a wrapping scenario, while in a collision scenario it will penetrate the droplet and cause a reversal of motion. Pusher and Neutral exhibit completely different behaviors, swimming in reverse in a wrapping scenario and pushing forward in a collision scenario.

[0170] capillary Capillary number characterizes the ratio of viscous force to surface tension. This invention innovatively investigates the finite capillary number (FNC) The dynamic behavior of droplets under certain conditions, where they undergo significant deformation during swimmer movement, leads to a crucial new phenomenon: swimmers may penetrate the droplet interface, fundamentally altering the classification of motion modes and propulsion efficiency. Capillary number should be considered a key control parameter in the design of microswimming body-droplet systems; by adjusting the capillary number, active switching of motion modes and optimized control of propulsion efficiency can be achieved.

[0171] In summary, the present invention has the following beneficial effects: High-precision slip boundary description: The artificial velocity method proposed in this invention can accurately apply the surface slip velocity distribution of the Squirmer model within the particle method framework, breaking through the slip velocity accuracy limitation of the traditional particle method at solid-liquid coupling boundaries.

[0172] Stable large deformation interface tracking: The Lagrangian properties of SDPD combined with the CSS surface tension model can adaptively handle the large deformation, stretching and even interface penetration of droplets under the action of active particles without the need for additional interface tracking algorithms.

[0173] Correct handling of thermal fluctuations: The SDPD method is based on the GENERIC thermodynamic framework, and the dissipative forces and random forces automatically satisfy the fluctuation-dissipation theorem, which can correctly describe the thermal fluctuation effect at the micro-nano scale.

[0174] Multiple coupling mode capture: This method can distinguish the coupling motion modes of different types of active particles (propulsive, dragging, and neutral) with droplets under different initial conditions. In the internal encapsulation scenario, it can capture the reverse encapsulation co-swimming mode and the forward dragging co-swimming mode; in the external collision scenario, it can capture the forward pushing co-swimming mode and the reverse dragging co-swimming mode. In addition, it can also equivalently map the swimmer-droplet complex as a novel active particle, revealing the equivalent swimming behavior of the complex.

[0175] Generality and scalability: This method can be directly extended to more complex physical scenarios such as multi-particle swarm behavior simulation, viscosity ratio change research, and capillary number effect analysis.

[0176] Regarding the coupling dynamics simulation method for actively moving particles and droplets provided in the foregoing embodiments, this invention provides a coupling dynamics simulation device for actively moving particles and droplets, see [link to relevant documentation]. Figure 3 The diagram shows a structural schematic of a device for simulating the coupling dynamics of actively moving particles and droplets. The device includes the following components: The system construction module 302 discretizes the fluid in the computational domain into a set of fluid particles based on smooth dissipative particle dynamics. Based on the set of fluid particles, a particle momentum equation is established using the Lagrangian form of the isothermal Newtonian fluid control equation. Each fluid particle in the set of fluid particles has a mass attribute, a position attribute, and a velocity attribute. The Lagrangian form of the isothermal Newtonian fluid control equation includes a continuity equation and a momentum conservation equation. The force calculation module 304 assigns velocity values ​​to various boundary particles on the surface of the active floating particle model to obtain boundary velocity conditions. Based on the fluid particle set, particle momentum equation, and boundary velocity conditions, it calculates the conservative force, dissipative force, random force, particle distribution correction force, and interface force on each particle to determine the total fluid force and total torque on the active floating particles. The coupled motion state output module 306 updates the fluid particle state and the active swimming particle state based on the total fluid force and total torque, and outputs the coupled dynamics simulation results after the update is completed.

[0177] The coupling dynamics simulation device for active floating particles and droplets provided in this application embodiment can significantly improve the accuracy of the coupling dynamics simulation of active floating particles and droplets.

[0178] In one embodiment, when performing the step of calculating the interfacial force, the force calculation module 304 is further configured to: use a color function to perform color marking and particle summation approximation on each fluid particle according to the fluid phase of the fluid particles, obtain the color function gradient, and normalize the color function gradient to obtain the interface normal vector; use a continuous surface stress model to calculate the surface stress tensor at the multiphase interface according to the interface normal vector, and discretize the surface stress tensor to obtain the interfacial force.

[0179] In one embodiment, when performing the step of assigning velocity values ​​to various boundary particles on the surface of the active floating particle model to obtain boundary velocity conditions, the force calculation module 304 is further configured to: model the active floating particle as a rigid sphere with boundary particles covering its surface to obtain an active floating particle model, and obtain the surface sliding velocity based on the tangential sliding velocity distribution on the surface of the sphere of the active floating particle model; and calculate the assigned velocities corresponding to various boundary particles on the surface of the active floating particle model according to the surface sliding velocity to obtain boundary velocity conditions.

[0180] In one embodiment, when performing the step of calculating the tangential sliding velocity distribution on the surface of a sphere based on an active floating particle model to obtain the surface sliding velocity, the force calculation module 304 is further used to: obtain the floating parameters corresponding to the active floating particles, wherein the floating parameters are used to classify the active floating particles into propulsion type, pulling type or neutral type; calculate the tangential sliding velocity on the surface of the active floating particles according to the floating parameters to determine the surface sliding velocity.

[0181] In one embodiment, when performing the step of calculating the assigned velocities of each boundary particle on the surface of the active floating particle model based on the surface sliding velocity to obtain the boundary velocity conditions, the force calculation module 304 is further configured to: for any fluid particle adjacent to the outer surface of the active floating particle, determine the nearest point of the fluid particle on the surface of the active floating particle model, and determine the target boundary velocity at the nearest point based on the rigid body motion velocity and surface sliding velocity of the active floating particle at the nearest point, wherein the rigid body motion velocity includes: the translational velocity and rotational velocity of the active floating particle; determine the assigned velocity of the boundary particle corresponding to the nearest point based on the target boundary velocity, and determine the boundary velocity conditions based on the assigned velocities of each boundary particle on the surface of the active floating particle.

[0182] In one embodiment, when performing the step of updating the fluid particle state and the active swimming particle state based on the total fluid force and total torque, the coupled motion state output module 306 is further configured to: within a preset time threshold, iteratively update the fluid particle state using the velocity Wieleret time integral model, and iteratively update the active swimming particle state based on the total fluid force and total torque using the Newton-Euler equation, to obtain the target fluid particle state and the target active swimming particle state corresponding to the termination time of the particle simulated motion.

[0183] In one embodiment, when performing the step of outputting the coupling dynamics simulation results, the coupling motion state output module 306 is further configured to: when the initial position of the active swimming particle is inside the droplet composed of fluid particles, if the active swimming particle is of the propulsive or neutral type, determine the coupling dynamics simulation result as reverse enveloping co-swimming; if the active swimming particle is of the pulling type, determine the coupling dynamics simulation result as forward dragging co-swimming; when the initial position of the active swimming particle is outside the droplet, if the active swimming particle is of the propulsive or neutral type, determine the coupling dynamics simulation result as forward pushing co-swimming; if the active swimming particle is of the pulling type, determine the coupling dynamics simulation result as reverse dragging co-swimming.

[0184] The device provided in this embodiment of the invention has the same implementation principle and technical effect as the aforementioned method embodiment. For the sake of brevity, any parts not mentioned in the device embodiment can be referred to the corresponding content in the aforementioned method embodiment.

[0185] This invention provides a server, specifically, the server includes a processor and a storage device; the storage device stores a computer program, which, when run by the processor, executes the method described in any of the above embodiments.

[0186] Figure 4 This is a schematic diagram of the structure of a server provided in an embodiment of the present invention. The server 100 includes: a processor 40, a memory 41, a bus 42 and a communication interface 43. The processor 40, the communication interface 43 and the memory 41 are connected through the bus 42. The processor 40 is used to execute executable modules, such as computer programs, stored in the memory 41.

[0187] The memory 41 may include high-speed random access memory (RAM) or non-volatile memory, such as at least one disk storage device. Communication between this system network element and at least one other network element is achieved through at least one communication interface 43 (which can be wired or wireless), such as the Internet, wide area network, local area network, metropolitan area network, etc.

[0188] Bus 42 can be an ISA bus, PCI bus, or EISA bus, etc. The bus can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 4 The symbol is represented by a single double-headed arrow, but this does not mean that there is only one bus or one type of bus.

[0189] The memory 41 is used to store programs. After receiving an execution instruction, the processor 40 executes the program. The method executed by the device for defining the flow process disclosed in any of the foregoing embodiments of the present invention can be applied to the processor 40 or implemented by the processor 40.

[0190] Processor 40 may be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method can be completed by the integrated logic circuitry in the hardware of processor 40 or by instructions in software form. Processor 40 can be a general-purpose processor, including a Central Processing Unit (CPU), a Network Processor (NP), etc.; it can also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this invention. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this invention can be directly embodied in the execution of a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. The storage medium is located in memory 41. The processor 40 reads the information in memory 41 and, in conjunction with its hardware, completes the steps of the above method.

[0191] The computer program product of the readable storage medium provided in the embodiments of the present invention includes a computer-readable storage medium storing program code. The instructions included in the program code can be used to execute the methods described in the foregoing method embodiments. For specific implementation, please refer to the foregoing method embodiments, which will not be repeated here.

[0192] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0193] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for simulating the coupled dynamics of actively moving particles and droplets, characterized in that, The method includes: The fluid in the computational domain is discretized into a set of fluid particles based on smooth dissipative particle dynamics. Based on the set of fluid particles, a particle momentum equation is established using the Lagrangian form of the isothermal Newtonian fluid control equation. Each fluid particle in the set of fluid particles has a mass attribute, a position attribute, and a velocity attribute. The Lagrangian form of the isothermal Newtonian fluid control equation includes a continuity equation and a momentum conservation equation. By assigning velocity values ​​to the boundary particles on the surface of the active floating particle model, the boundary velocity conditions are obtained. Based on the fluid particle set, the particle momentum equation, and the boundary velocity conditions, the conservative force, dissipative force, random force, particle distribution correction force, and interface force acting on each particle are calculated to determine the total fluid force and total torque acting on the active floating particle. Based on the total fluid force and the total torque, the states of fluid particles and actively moving particles are updated, and the coupled dynamics simulation results are output after the update is completed.

2. The method for simulating the coupled dynamics of actively moving particles and droplets according to claim 1, characterized in that, The step of calculating the interfacial force includes: Using the color function, based on the fluid phase of the fluid particles, color marking and particle summation approximation are performed on each fluid particle to obtain the color function gradient. The color function gradient is then normalized to obtain the interface normal vector. Using a continuous surface stress model, the surface stress tensor at the multiphase interface is calculated based on the interface normal vector, and the surface stress tensor is discretized to obtain the interface force.

3. The method for simulating the coupled dynamics of actively moving particles and droplets according to claim 1, characterized in that, The step of assigning velocity values ​​to various boundary particles on the surface of the actively moving particle model to obtain the boundary velocity conditions includes: The active floating particle is modeled as a rigid sphere with boundary particles covering the surface, thus obtaining the active floating particle model. Based on the tangential sliding velocity distribution on the surface of the sphere of the active floating particle model, the surface sliding velocity is obtained. Based on the surface slip velocity, the assigned velocities of each boundary particle on the surface of the active floating particle model are calculated to obtain the boundary velocity conditions.

4. The method for simulating the coupling dynamics of actively moving particles and droplets according to claim 3, characterized in that, The step of obtaining the surface slip velocity based on the tangential slip velocity distribution of the sphere surface according to the active floating particle model includes: Obtain the swimming parameters corresponding to the actively swimming particles, wherein the swimming parameters are used to classify the actively swimming particles into propulsive, pulling, or neutral types; The tangential sliding velocity of the surface of the actively moving particles is calculated based on the said swimming parameters to determine the surface sliding velocity.

5. The method for simulating the coupled dynamics of actively moving particles and droplets according to claim 3, characterized in that, The step of calculating the assigned velocities of each boundary particle on the surface of the active moving particle model based on the surface slip velocity to obtain the boundary velocity conditions includes: For any fluid particle adjacent to the outer surface of the active swimming particle, determine the nearest point of the fluid particle on the surface of the active swimming particle model, and determine the target boundary velocity at the nearest point based on the rigid body motion velocity and the surface sliding velocity corresponding to the active swimming particle at the nearest point, wherein the rigid body motion velocity includes the translational velocity and rotational velocity of the active swimming particle. Based on the target boundary velocity, the assigned velocity of the boundary particle corresponding to the nearest point is determined, and the boundary velocity condition is determined based on the assigned velocities of the boundary particles on the surface of the actively moving particle.

6. The method for simulating the coupled dynamics of actively moving particles and droplets according to claim 1, characterized in that, The step of updating the fluid particle state and the active swimming particle state based on the total fluid force and the total torque includes: Within a preset time threshold, the fluid particle state is iteratively updated using the velocity Wieleret time integral model, and the active swimming particle state is iteratively updated using the Newton-Euler equations based on the total fluid force and the total torque, to obtain the target fluid particle state and the target active swimming particle state corresponding to the termination time of the particle simulation motion.

7. The method for simulating the coupled dynamics of actively moving particles and droplets according to claim 1, characterized in that, The steps for outputting the coupled dynamics simulation results include: When the initial position of the active swimming particle is inside the droplet composed of the fluid particles, if the active swimming particle is propulsive or neutral, the coupling dynamics simulation result is determined to be reverse enveloping co-swimming; if the active swimming particle is pulling, the coupling dynamics simulation result is determined to be forward dragging co-swimming. When the initial position of the active swimming particle is outside the droplet, if the active swimming particle is propulsive or neutral, the coupling dynamics simulation result is determined to be positive propulsion co-swimming; if the active swimming particle is pulling, the coupling dynamics simulation result is determined to be reverse dragging co-swimming.

8. A device for simulating the coupling dynamics of actively moving particles and droplets, characterized in that, The device includes: The system construction module discretizes the fluid in the computational domain into a set of fluid particles based on smooth dissipative particle dynamics. Based on the set of fluid particles, a particle momentum equation is established using the Lagrangian form of the isothermal Newtonian fluid control equation. Each fluid particle in the set of fluid particles has a mass attribute, a position attribute, and a velocity attribute. The Lagrangian form of the isothermal Newtonian fluid control equation includes a continuity equation and a momentum conservation equation. The force calculation module assigns velocity values ​​to various boundary particles on the surface of the active floating particle model to obtain boundary velocity conditions. Based on the fluid particle set, the particle momentum equation, and the boundary velocity conditions, it calculates the conservative force, dissipative force, random force, particle distribution correction force, and interface force acting on each particle to determine the total fluid force and total torque acting on the active floating particle. The coupled motion state output module updates the fluid particle state and the active swimming particle state based on the total fluid force and the total torque, and outputs the coupled dynamics simulation results after the update is completed.

9. A server, characterized in that, The method includes a processor and a memory, the memory storing computer-executable instructions executable by the processor, the processor executing the computer-executable instructions to implement the method of any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions that, when invoked and executed by a processor, cause the processor to perform the method according to any one of claims 1 to 7.

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