Mandal Shubhadeep, Mazza Marco G
Max-Planck-Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany.
Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom.
Phys Rev E. 2019 Jun;99(6-1):063319. doi: 10.1103/PhysRevE.99.063319.
Liquid crystals establish a nearly unique combination of thermodynamic, hydrodynamic, and topological behavior. This poses a challenge to their theoretical understanding and modeling. The arena where these effects come together is the mesoscopic (micron) scale. It is then important to develop models aimed at capturing this variety of dynamics. We have generalized the particle-based multiparticle collision dynamics (MPCD) method to model the dynamics of nematic liquid crystals. Following the Qian-Sheng theory [Phys. Rev. E 58, 7475 (1998)1063-651X10.1103/PhysRevE.58.7475] of nematics, the spatial and temporal variations of the nematic director field and order parameter are described by a tensor order parameter. The key idea is to assign tensorial degrees of freedom to each MPCD particle, whose mesoscopic average is the tensor order parameter. This nematic MPCD method includes backflow effect, velocity-orientation coupling, and thermal fluctuations. We validate the applicability of this method by testing (i) the nematic-isotropic phase transition, (ii) the flow alignment of the director in shear and Poiseuille flows, and (iii) the annihilation dynamics of a pair of line defects. We find excellent agreement with existing literature. We also investigate the flow field around a force dipole in a nematic liquid crystal, which represents the leading-order flow field around a force-free microswimmer. The anisotropy of the medium not only affects the magnitude of velocity field around the force dipole, but can also induce hydrodynamic torques depending on the orientation of dipole axis relative to director field. A force dipole experiences a hydrodynamic torque when the dipole axis is tilted with respect to the far-field director. The direction of hydrodynamic torque is such that the pusher- (or puller-) type force dipole tends to orient along (or perpendicular to) the director field. Our nematic MPCD method can have far-reaching implications not only in modeling of nematic flows, but also to study the motion of colloids and microswimmers immersed in an anisotropic medium.
液晶展现出热力学、流体动力学和拓扑行为几乎独一无二的组合。这对其理论理解和建模构成了挑战。这些效应共同作用的领域是介观（微米）尺度。因此，开发旨在捕捉这种多样动力学的模型很重要。我们已经推广了基于粒子的多粒子碰撞动力学（MPCD）方法来模拟向列型液晶的动力学。遵循向列相的钱 - 盛理论[《物理评论E》58, 7475 (1998)1063 - 651X10.1103/PhysRevE.58.7475]，向列型指向矢场和序参量的空间和时间变化由张量序参量描述。关键思想是为每个MPCD粒子赋予张量自由度，其介观平均值就是张量序参量。这种向列型MPCD方法包括回流效应、速度 - 取向耦合和热涨落。我们通过测试（i）向列 - 各向同性相变，（ii）指向矢在剪切流和泊肃叶流中的流动排列，以及（iii）一对线缺陷的湮灭动力学来验证该方法的适用性。我们发现与现有文献有很好的一致性。我们还研究了向列型液晶中力偶极周围的流场，它代表了无外力微游动器周围的主导阶流场。介质的各向异性不仅影响力偶极周围速度场的大小，还能根据偶极轴相对于指向矢场的取向诱导流体动力学扭矩。当偶极轴相对于远场指向矢倾斜时，力偶极会经历流体动力学扭矩。流体动力学扭矩的方向使得推动型（或拉动型）力偶极倾向于沿指向矢场取向（或垂直于指向矢场）。我们的向列型MPCD方法不仅在向列型流动建模方面有深远意义，而且对于研究浸没在各向异性介质中的胶体和微游动器的运动也有重要意义。
