Nematohydrodynamics for colloidal self-assembly and transport phenomena

Abstract

The viscous and NLC forces act on an individual particle in opposing directions, resulting in a critical location in the channel where the particle experiences zero net force in the direction perpendicular to the flow. For multi-particle aggregation we show that the final arrangement is independent of the initial configuration, but the path towards achieving equilibrium is very different. These results uncover new mechanisms for particle separation and routes towards self-assembly.

Controllable particle migration in liquid crystal flows

“…The governing equations of hydrodynamic motion are the equation of mass conservation, also known as the continuity equation, and the Navier-Stokes equation that describes the conservation of linear momentum. In tensor notation they read q t r + q a (ru a ) = 0 (12) and q t (ru a ) = q b P (LC) ab + q b P (HD) ab ,…”

“…respectively. Eqn (12) relates the local rate of change of the density r to the advection of mass by the fluid velocity u a . Eqn ( 13) is Newton's second law of momentum change for the fluid and involves the thermotropic stress tensor P (LC) ab and the hydrodynamic stress tensor P (HD) ab .…”

“…The pressure p is related to the density via an ideal gas equation of state as p = c s 2 r with c s as lattice speed of sound as is standard in lattice Boltzmann. The last term vanishes in incompressible fluids as eqn (12) becomes @ a u a = 0. Noslip and no-penetration boundary conditions are applied on the walls and particle surfaces, and the boundary conditions for Q are found from the minimisation of the free energy 31…”

“…Much less is known about the dynamics and migration of particles in liquid crystalline host phases, whose internal structure offers additional possibilities in terms of elastic and order-driven control. Theoretical studies have considered the Stokes drag of a particle in a nematic host 10 or particle aggregates 11,12 , and simulation studies have investigated flow-order tensor interactions around colloidal particles 13 for fixed or simply advected particles. Experimental studies of nematics in microfluidic geometries have been concerned with pure phases [14][15][16][17][18][19][20][21] .…”

Flow and Nematic Director Profiles in a Microfluidic Channel: The Interplay of Nematic Material Constants and Backflow

“…In parallel, there are several papers that focus on the role of backflow in the hydrodynamics of defects, in the Beris-Edwards framework, see for example [12,21,22]. In recent years, there are rigorous existence and regularity results for the Beris-Edwards framework too [11,14,23] and numerical simulations for microfluidic set-ups in [24,25]. The various dynamical theories of nematic liquid crystals and the key results are surveyed in [26] and in [27]; the authors rigorously derive the Ericksen-Leslie equations from the Beris-Edwards model.…”