For the passive sheathless particle focusing in microfluidics,the equilibrium positions of particles are typically controlled by micro channels with V-shaped obstacle array (VOA).The design of the layout and shape of obstacles are mainly based on the streamline of fluid velocity field without considering the existence of the particles of which the diameters of particles are in the same order as the dimension of fluidic channel.We report the experimentally verified numerical modeling and simulation of particle tracing using the arbitrary Lagrangian-Eulerian (ALE) fluid-particle interaction simulation.Using the ALE method,we obtain the movement of particle in depth of micro channel which cannot be easily observed in experiment.Based on the verified numerical analysis,it is found that particle trajectory is gradually approaching the center of channel in depth because of the strong particle-wall interaction.Even though the ALE method exhibits good accuracy to simulate the particle trajectory,the advantage is achieved at a high computational cost.Therefore,a simplified dimensionless objective function,the line integration of the velocity component perpendicular to the main flow direction along the streamline,is proposed to optimize the performance of the particle focusing devices,instead of the deviation distance of the particle based the time-consuming ALE simulation.A particle focusing device with optimized key parameters of obstacle array is proposed based on the proposed design objective.