Interfacial forces and Marangoni flow on a nematic drop retracting in an isotropic fluid

Abstract

Nematic-isotropic interfaces exhibit novel dynamics due to anchoring of the liquid crystal molecules on the interface. The objective of this study is to demonstrate the consequences of such dynamics in the flow field created by an elongated nematic drop retracting in an isotropic matrix. This is accomplished by two-dimensional flow simulations using a diffuse-interface model. By exploring the coupling among bulk liquid crystal orientation, surface anchoring and the flow field, we show that the anchoring energy plays a fundamental role in the interfacial dynamics of nematic liquids. In particular, it gives rise to a dynamic interfacial tension that depends on the bulk orientation. Tangential gradient of the interfacial tension drives a Marangoni flow near the nematic-isotropic interface. Besides, the anchoring energy produces an additional normal force on the interface that, together with the interfacial tension, determines the movement of the interface. Consequently, a nematic drop with planar anchoring retracts more slowly than a Newtonian drop, while one with homeotropic anchoring retracts faster than a Newtonian drop. The numerical results are consistent with prior theories for interfacial rheology and experimental observations.  2005 Elsevier Inc. All rights reserved.

3D phase-field simulations of interfacial dynamics in Newtonian and viscoelastic fluids

“…Yue et al [7,11] have shown how the model can be extended to non-Newtonian fluids, and developed the AMPHI algorithm in two dimensional geometries based on finite elements with adaptive meshing [20]. The main ideas of the 3D algorithm are close to those in 2D.…”

“…In this section, we will briefly summarize these ideas and give the governing equations, using the mixture of a Newtonian and an Oldroyd-B fluid as an example. The method accommodates other types of complex fluids such as nematic liquid crystals [11,23,24,29,30], but we will confine this paper to Newtonian-Newtonian and Newtonian-Oldroyd-B mixtures.…”

“…(iii) The variational framework easily integrates interfacial treatment and non-Newtonian rheology, as the latter is almost always derivable from a microstructural free energy [11].…”

An Energetic Variational Formulation with Phase Field Methods for Interfacial Dynamics of Complex Fluids: Advantages and Challenges

“…Another important consequence of interfacial relaxation is the change in apparent interfacial tension [41,43]. To simulate an experiment with two immiscible fluids, one chooses appropriate values for the mixing energy λ and capillary width so as to match λ/ to the experimental interfacial tension σ according to a formula based on some equilibrium φ profile [34,41].…”

“…Taking advantage of the energy-based formulation, they are able to resolve the dual difficulties for complex fluid mixtures-moving interfaces and complex rheology-in a unified framework. So far, Yue and coworkers have applied the method to a number of problems on drop dynamics of viscoelastic and liquid crystalline fluids [42][43][44][45][46]. In the following, we first give a brief but self-contained derivation of the theoretical model, and describe a numerical algorithm using spectral methods.…”