A Multifaceted Study of Nematic Order Reconstruction in Microfluidic Channels

IF 1.9 4区 数学 Q1 MATHEMATICS, APPLIED
James Dalby, Yucen Han, Apala Majumdar, Lidia Mrad
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引用次数: 1

Abstract

SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2284-2309, December 2023.
Abstract. We study order reconstruction (OR) solutions in the Beris–Edwards framework for nematodynamics, for both passive and active nematic flows in a microfluidic channel. OR solutions exhibit polydomains and domain walls, and as such, are of physical interest. We show that OR solutions exist for passive flows with constant velocity and pressure, but only for specific boundary conditions. We prove the existence of unique, symmetric, and nonsingular nematic profiles for boundary conditions that do not allow for OR solutions. We compute asymptotic expansions for OR-type solutions for passive flows with nonconstant velocity and pressure, and active flows, which shed light on the internal structure of domain walls. The asymptotics are complemented by numerical studies that demonstrate the universality of OR-type structures in static and dynamic scenarios.
微流控通道中向列有序重构的多方面研究
SIAM应用数学学报,83卷,第6期,2284-2309页,2023年12月。摘要。我们在Beris-Edwards框架下研究了微流控通道中被动和主动向列流的有序重建(OR)解。OR解决方案展示了多域和域壁,因此具有物理意义。我们证明了对于恒速恒压被动流动存在OR解,但仅适用于特定的边界条件。在不允许或解的边界条件下,证明了唯一、对称和非奇异向列型轮廓的存在性。我们计算了非恒定速度和压力的被动流动和主动流动的or型解的渐近展开式,从而揭示了区域壁面的内部结构。数值研究补充了渐近性,证明了or型结构在静态和动态情况下的普遍性。
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来源期刊
CiteScore
3.60
自引率
0.00%
发文量
79
审稿时长
12 months
期刊介绍: SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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