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 引用本文: 彭方远, 潘定一, 陈杏藩, 林昭武. 基于虚拟区域法的黏弹性流体中微生物游动的数值模拟和应用. 力学学报, 2023, 55(1): 84-94.
Peng Fangyuan, Pan Dingyi, Chen Xingfan, Lin Zhaowu. A numerical algorithm based on fictitious domain method for the simulation of microorganisms swimming in a viscoelastic fluid. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 84-94.
 Citation: Peng Fangyuan, Pan Dingyi, Chen Xingfan, Lin Zhaowu. A numerical algorithm based on fictitious domain method for the simulation of microorganisms swimming in a viscoelastic fluid. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 84-94.

## A NUMERICAL ALGORITHM BASED ON FICTITIOUS DOMAIN METHOD FOR THE SIMULATION OF MICROORGANISMS SWIMMING IN A VISCOELASTIC FLUID

• 摘要: 微生物是自然生态系统的重要组成部分, 掌握微生物在复杂流体中的运动特性可以为微型器件的设计制造提供理论指导. 壁面效应是微生物游动研究中的重要问题之一, 已有研究表明微生物在壁面附近存在复杂的行为特征. 然而已有研究大多集中于微生物在牛顿流体中的游动模拟, 仅有少数涉及黏弹性流体等非牛顿流体. 本文采用直接力虚拟区域法与乔列斯基分解相结合的数值方法, 引入Squirmer微生物游动模型, 研究了微生物在黏弹性流体中的游动问题. 首先给出求解黏弹性流体本构方程的数值格式; 并将该方法应用于研究微生物游动中的壁面效应. 研究结果表明, 游动方向是影响微生物颗粒壁面效应的重要因素. 流体弹性应力会对微生物产生一个反向转矩, 影响微生物的游动方向, 从而阻碍微生物逃离壁面. 微生物颗粒在黏弹性流体中与壁面作用时间较长, 几乎达到牛顿流体的两倍以上.

Abstract: Microorganisms are one of the important parts of natural ecosystem, understanding the kinematic behaviors of microorganisms swimming in complex fluids could provide guidance for the design and manufacturing of MEMS. Wall effects are one of the most important scientific problems of the research of microorganism swimming, and recent work reveals that microorganisms show complicated swimming behaviors near the wall. However, most of the work reported in the literatures focused on microorganism swimming in Newtonian fluid, less attention is paid on microorganism swimming in viscoelastic fluid or other non-Newtonian fluids. A direct-forcing fictitious domain method combined with Cholesky decomposition for the simulation of microorganisms swimming in a viscoelastic fluid is reported in this paper. The squirmer model is applied to represent the swimming of microorganisms. The numerical schemes for the discretization of Giesekus constitutive equation are first presented and validated. The newly developed simulation model is then applied to investigate the effect of planar wall on swimming dynamics of current squirmer in viscoelastic flow, i.e., Giesekus fluid. The results show that the swimming direction of squirmer is a critical factor of the wall-trapping effect. The fluid elasticity affects the swimmer motion near solid wall by generating an elastic torque which reorient the swimming direction. The time for the squirmer to contact planar wall in viscoelastic fluid is almost twice of that in Newtonian fluid.

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