Study Of Periodic Migration Of Particle Based On Lattice Boltzmann Method

Over the past 30 years,Lattice Boltzmann Method(LBM)has become a popular computational fluid dynamics method with the rapid development of computer performance.LBM has a clear physical background and simple efficient high accuracy,and good stability on calculation.It is widely used in the study of complex fluid motions such as multiphase flow,microfluidics,thermal flow,and turbulence.In particular,utilizing LBM for simulation to study fluid-structure coupling motion performed obvious advantages,while avoiding the boundary integral in traditional fluid mechanics methods.The research group proposed a Galilean-invariant Momentum Exchange(GME)method to solve fluid-structure coupling problems.Based on the momentum theorem,GME uses distribution functions and discrete velocities to calculate hydraulic interactions directly.This method is simple,stable,accurate and efficient in programming and calculation,and has nothing to do with the shape of the boundary.Hence,it is suitable for calculating the moving boundary of complex geometric shapes in the flow.In this paper,the GME method is mainly used to study the lateral migration of square particles in the pipeline flow and the periodic movement of the particles in the microfluidic curved pipeline.Non-circular particles are used in experimental research and industrial applications frequently,which have special motion laws in fluids.We had simulated the migration of square particles in the pipe flow,and found that the square particles also have lateral migration and equilibrium phenomena,but the motion contains periodic fluctuations and non-uniform rotation.Be similar to the round particles,the larger the blocking ratio of the square particles are,the closer the equilibrium position is closed to the center of the pipe,and the greater the fluctuation amplitude is.Affected by the shape of particle,the particle undergoes four fluctuations in one rotation period,but the waveform is discrepant under different Reynolds numbers.A series of contour drawings are used to exhibit the changes in the particles surrounding flow field under different postures,showing the complexity of the movement of the square particles.This is very meaningful for controlling the aggregation and the sorting of particles in the pipeline flow,and the research model can also be further extended to any regular polygonal particles.In the study of inertial microfluidics,in order to improve the efficiency of particle collection,curved channels are utilized,and the principle of secondary flow is used to achieve rapid particle sequencing.However,in the simulation study,because the curved pipeline does not meet the pressure boundary and body force driving application conditions,there is a great gap between the simulation result and the experimental study.Based on the periodic pressure boundary conditions,we propose a revised momentum exchange method(Revised-GME)to calculate the hydraulic force of particles when crossing the boundary of the domain entrance and exit,which lays the basis for the study of particle migration in curved channels.We designed a variety of Reynolds number particle migration examples with straight pipelines.The simulated results of Revised-GME are in good agreement with the GME simulation in particle migration trajectories,proving that Revised-GME is relatively stable when calculating in cross-domain and the numerical error hardly affects the hydraulic calculation where inside the flow field.Combining periodic pressure boundary conditions and Revised-GME,we designed annular and S-shaped pipes as typical curved pipes for simulation.With the annular pipe,the peak velocity of the flow deviates toward the inner ring,and round particles is in equilibrium under the action of the wall-induced lift force and peak velocity distribution,and led to reach a relatively stable equilibrium position.In addition,the effect of the particle size on the equilibrium position was investigated,and it was concluded that the particle size significantly affected equilibrium position,and the change in radius had little effect on particle migration speed.With the S-shaped pipe,the fluid density distribution exhibits a nonlinear change related to the shape of the pipe,so that the center line of the peak velocity band produces a regular sway in the amplitude direction relative to the center line of the pipe.The difference in the flow velocity where the particles on the side of the centerline are unevenly distributed,which causes the shear inertial lift force and the Saffman lift force to compete with each other.The minimum value on the particle's amplitude-oriented position appears near the entrance and exit of pipeline,and the maximum value appears near the inner ring area where in the middle of the flow field.Based on the above analysis,it can be speculated that the particle migration trajectory which released below the center line will be like the current simulation situation.As mentioned above,the utilization of GME and periodic pressure boundary not only facilitates the simulation of the two-phase particle movement in the straight shape fluid field,but also expediently apply to the curved pipeline whose physical parameters change nonlinearly,and clearly reflects that the fluid velocity distribution and the appearance of the pipeline impacts on particle migration physically.These studies are beneficial for understanding in deep the secondary flow effect of curvilinear channels and developing the efficient inertial microfluidic devices for rapid aggregation and separation of particles in the pipeline flow.