Fluctuation-lattice Boltzmann Method Based On Tree Grid Refinement Technology And The Application In Micro-particle Motion

Micro-scale physical phenomena have always been a hot topic,such as micro-scale flow,microbial motion and micro-particle motion.The motion of particles at the micro-scale is a typical Brownian motion with a large randomness.In order to achieve the directional movement of micro-particles,a type of synthetic motor has been developed that can generate self-driven motion in a specific environment.Micro-motors have potential applications in the fields of biology,medicine,and the environment.The motion of self-driven particles at micro-scale is a complex multi-field coupled motion and its essence is the superposition of self-driven and Brownian motion.Therefore,the research on the motion characteristics of self-driven micro-particles in theoretical,simulation and experimental is difficult,which greatly limits its application.The lattice Boltzmann method(LBM)is a mesoscopic simulation method often used in micro-scale research.It has great advantages in the study of micro-scale problems,such as natural parallel characteristics,simple and intuitive wall boundary processing.In order to accurately simulate the Brownian motion of particles,the fluctuation-lattice Boltzmann method(FLB)is used to describe the thermal fluctuation of fluid around the particles.On the other hand,due to the huge difference between the characteristic scale of the micro-particles and the characteristic scale of the macroscopic diffusion phenomenon of the particles,the long-term microscopic simulation can exhibit the macroscopic diffusion phenomenon,which leads to a huge calculation amount.Therefore,in order to improve the simulation efficiency,this paper focuses on the application of tree grid refinement technology in the fluctuation-lattice Boltzmann method.The tree grid structure is a hierarchical data structure with simple algorithm,high computational efficiency and easy implementation of the multi-layer grid refinement.On this basis,the Brownian motion of micro-particles near the wall is studied.The diffusion coefficient of Brownian motion at different heights is compared.The study of micro-scale particle motion has great significance for the control of micro-particle motion,such as micro-pump technology and targeted drug therapy.In this paper,the FLB method based on tree grid refinement technology is used to simulate the motion of micro-particles.The following conclusions are obtained:Firstly,this paper takes Stokes flow as an example to study the effects of relaxation time,grid layer and grid growth rate on simulation efficiency and simulation accuracy.The results show that when the resolution is 12,the calculation time of the 2-layer grid is 85.2% less than that of the single-layer grid,and the calculation time of the 3-layer grid is 98.4% less than that of the 2-layer grid.The simulation errors of 2-layer grid are 1.9% compared with the single-layer grid,and the simulation errors of 3-layer grid are 1.6% compared with the 2-layer grid.Secondly,the method is verified and improved by simulating the movement of micro-particles and self-driven particles in infinite space.The results show that the mean square displacement and diffusion coefficient of micro-particles and self-driven particles simulated by local mesh refinement technology are in good agreement with the simulation results using uniform grid.And when the number of grid layers is three,the calculation efficiency can be increased by more than 80%.This fully proves the applicability and accuracy of the fluctuation-lattice Boltzmann method with tree grid structure.Finally,the Brownian motion of the micro-particles near the wall is studied.The results show that the wall can hinder the Brownian motion of the particles.Whether the horizontal wall or the vertical wall reduces the diffusion coefficient in the direction of the vertical wall,and the closer the particles to the wall are,the smaller the diffusion coefficient perpendicular to the wall direction is.