Dynamics and steady state of squirmer motion in liquid crystal
Dynamics and steady state of squirmer motion in liquid crystal
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DOI：
10.1017/s0956792523000177
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发表时间：
2023-07-10
影响因子：
1.9
通讯作者：
Yip, Nung Kwan
中科院分区：
文献类型：
--
作者：
Berlyand, Leonid;Chi, Hai;Yip, Nung Kwan
我们分析了一个非线性偏微分方程系统描述的运动的微型游泳在液晶环境中。对于微型游泳者的运动，蠕动模型中使用的自推进进入模型通过在微型游泳者的表面上的滑移速度。液晶是使用公认的Beris-Edwards公式描述的。在以前的计算研究中，它表明，蠕动，无论其初始配置，最终取向本身平行或垂直于液晶所规定的优选取向。此外，耦合的非线性系统的相应的解收敛到一个稳定的状态。在这项工作中，我们严格建立的存在性的稳定状态，也是有限时间存在的时间依赖问题的周期区域。最后，我们将使用一个双尺度渐近展开，以获得一个均匀模型的集体游泳的蠕动，因为他们达到他们的稳定状态的方向和速度。
We analyse a nonlinear partial differential equation 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 in a periodic domain. Finally, we will use a two-scale asymptotic expansion to derive a homogenised model for the collective swimming of squirmers as they reach their steady-state orientation and speed.