Modeling anisotropic fluids within the framework of bodies with multiple natural configurations
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This is a follow up of a paper on a thermodynamic framework for rate type models [J. Non-Newtonian Fluid Mech. 88 (2000) 207] published in this journal. The previous paper used the notion that certain materials have multiple natural configurations and that their response can be characterized as a class of elastic responses from an evolving set of natural configurations, and used this framework to model the behavior of a class of visoelastic fluids that are isotropic with regard to their viscous as well as their elastic response. Here, we extend the framework to the modeling of anisotropic fluids. Anisotropic fluids are invariably modeled within the framework of director theories, and such theories require boundary conditions for the directors for the resolution of boundary value problems. Here, we present an approach to the modeling of anisotropic fluids, which is not a director theory; no balance laws for directors are posited nor is there a notion of a director body force, director (or cosserat) stress or director kinetic energy. Thus, the present approach does not require specifying any additional boundary conditions other than that usually specified for viscous fluids, even for flows that involve spatially inhomogeneous fields. Moreover, the framework is based on sound thermodynamical footing, the evolution of the natural configurations being determined by the rate of dissipation of the material. To delineate the efficacy of the theory, we solve a problem associated with a shearing flow of the fluid in which we discuss the tumbling and alignment of certain vectors that represent the axes of anisotropy of the fluid and which may be associated with rod-like structures in the fluid. 2001 Elsevier Science B.V. All rights reserved.
