A model of weak viscoelastic nematodynamics

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.

Recent Advances in the Rheology of Thermotropic Liquid Crystal Polymers

“…These assumptions seem to be appropriate for LCPs with rigid enough macromolecules, and for slow flows of viscoelastic suspensions with uniaxially shaped particles (Leonov 2008b).This theory utilized a specific viscoelastic and nematic kinematics and ignored inertia effects and in cases of LCPs, the effects of Frank elasticity (Leonov 2008b). The rigid rod like molecules are often called as "selfreinforcing thermoplastic" (Ophir and Ide 1983).…”

“…The term nematodynamics was first introduced by de Gennes and Prost in 1974 (Leonov 2008b). In 2002, Leonov and Volkov, proposed a theory of viscoelastic nematodynamics for nematic liquid crystal polymers (Leonov and Volkov 2002).…”

“…Recently, Leonov (Leonov 2008a, b;Leonov and Chen 2010) had a significant breakthrough in viscoelastic nematodynamics. In Leonov's nematodynamics some new theoretical techniques (Leonov 2008b) were employed to derive the simplest form of the continuum theory of weakly nonlinear viscoelastic nematodynamics.…”

“…This model was developed based on a continuum theory of weak viscoelastic nematodynamics of Maxwell type, which can 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 (Leonov 2008b). The viscoelastic nematodynamics combined the viscous and the elastic stresses and expressed them as total stress.…”

Simulation Study of Thermotropic LCPs and Prediction of Normal Stress Difference at High Shear Rate

“…The term nematodynamics introduced in the text by de Gennes and Prost (1974) means as pecific set of problems for deformation and flow of the nematic systems under stress, which could be solved or analyzed using specific macroscopic field equations (Leonov, 2008b). The research on polymer nematics has attracted academic and industrial interests for more than three decades, but with limited practical use due to the lack of knowledge of the complicated behavior of these systems (Chen, 2008).…”