论文标题
液晶中蠕动运动的动力和稳态
Dynamics and steady state of squirmer motion in liquid crystal
论文作者
论文摘要
我们分析了一个非线性PDE系统，该系统描述了在近代液晶环境中微型威格斯的运动。对于微型威格默的运动性，使用了蠕动模型，其中自我推广通过微晶木表面的滑动速度进入模型。使用公认的Beris-Edwards配方来描述液晶。在以前的计算研究中，有证据表明，无论其初始配置如何，蠕动器最终都与液晶所决定的首选方向平行或垂直于垂直方向。此外，耦合非线性系统的相应解会收敛到稳态。在这项工作中，我们严格地确定了稳态的存在，也是时间依赖问题的有限时间存在。最后，使用两尺度的渐近扩展，我们得出了一个减少的模型，用于蠕动者达到稳定状态的方向和速度时的集体游泳。
We analyze a nonlinear PDE system describing the motion of a microswimmer in a nematic liquid crystal environment. For the microswimmer's motility, the squirmer model is used in which self-propulsion enters the model through the slip velocity on the microswimmer's surface. The liquid crystal is described using the well-established Beris-Edwards formulation. In previous computational studies, it was shown that the squirmer, regardless of its initial configuration, eventually orients itself either parallel or perpendicular to the preferred orientation dictated by the liquid crystal. Furthermore, the corresponding solution of the coupled nonlinear system converges to a steady state. In this work, we rigorously establish the existence of steady state and also the finite-time existence for the time-dependent problem. Finally, using a two-scale asymptotic expansion we derive a reduced model for the collective swimming of squirmers as they reach their steady state orientation and speed.
