A model of weak viscoelastic nematodynamics

TL;DR

This paper develops a continuum theory for weak viscoelastic nematodynamics of Maxwell type, capturing molecular elasticity and viscoelastic effects in liquid crystalline polymers and suspensions, with simplified models revealing rich flow behaviors.

Contribution

It introduces a novel Maxwell-type model for weak viscoelastic nematodynamics, incorporating algebraic properties of nematic operations to simplify the complex parameter structure.

Findings

The theory predicts soft deformation modes that minimize free energy and dissipation.

Analytical results show complex steady and unsteady flow behaviors in simple shear and elongation.

The model extends to include director evolution and non-symmetric stresses, capturing diverse material responses.

Abstract

The paper develops a continuum theory of weak viscoelastic nematodynamics of Maxwell type. It may describe the molecular elasticity effects in mono-domain flows of liquid crystalline polymers as well as the viscoelastic effects in suspensions of uniaxially symmetric particles in polymer fluids. Along with viscoelastic and nematic kinematics, the theory employs a general form of weakly elastic thermodynamic potential and the Leslie-Ericksen-Parodi type constitutive equations for viscous nematic liquids, while ignoring inertia effects and the Frank (orientation) elasticity in liquid crystal polymers. In general case, even the simplest Maxwell model has many basic parameters. Nevertheless, recently discovered algebraic properties of nematic operations reveal a general structure of the theory and present it in a simple form. It is shown that the evolution equation for director is also viscoelastic. An example of magnetization exemplifies the action of non-symmetric stresses. When the magnetic field is absent, the theory is simplified to the symmetric, fluid mechanical case with relaxation properties for both the stress and director. Our recent analyses of elastic and viscous soft deformation modes are also extended to the viscoelastic case. The occurrence of possible soft modes minimizes both the free energy and dissipation, and also significantly decreases the number of material parameters. In symmetric linear case, the theory is explicitly presented in terms of anisotropic linear memory functionals. Several analytical results demonstrate a rich behavior predicted by the developed model for steady and unsteady flows in simple shearing and simple elongation.