Weak Viscoelastic Nematodynamics of Maxwell Type

Abstract

A constitutive theory for weak viscoelastic nematodynamics of Maxwell type is developed using the standard local approach of non-equilibrium thermodynamics. Along with particular viscoelastic and nematic kinematics, the theory uses the weakly elastic potential proposed by de Gennes for nematic solids and the LEP constitutive equations for viscous nematic liquids, while ignoring the Frank (orientation) elasticity and inertia effects. In spite of many basic parameters, algebraic properties of nematic operations investigated in Appendix, allowed us to reveal a general group 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 clarifies the situation with non-symmetric stresses. When the sources of stress asymmetry are absent, the theory is simplified and its relaxation properties are described by a symmetric subgroup of nematic algebraic operations. A purely linear constitutive behavior exemplifies the symmetric situation.