TY - JOUR

T1 - Dynamics and steady state of squirmer motion in liquid crystal

AU - Berlyand, Leonid

AU - Chi, Hai

AU - Potomkin, Mykhailo

AU - Yip, Nung Kwan

N1 - Publisher Copyright:
© The Author(s), 2023. Published by Cambridge University Press.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

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U2 - 10.1017/S0956792523000177

DO - 10.1017/S0956792523000177

M3 - Article

AN - SCOPUS:85164993755

SN - 0956-7925

JO - European Journal of Applied Mathematics

JF - European Journal of Applied Mathematics

ER -