Shear induced diffusion in viscoelastic materials with anisotropic rigid particles

In this paper constitutive equations are derived that describe shear induced diffusion in a viscoelastic material with anisotropic rigid particles. The entropy inequality is used to arrive at a set of flux-driving force relations, and these relations are used to derive a constitutive equation for the mass flux vector. This equation incorporates the coupling of the mass flux vector with the flow field in a manner that is consistent with non-equilibrium thermodynamics. The expression includes contributions from ordinary diffusion, pressure diffusion, forced diffusion, diffusion resulting from gradients in the orientation of the particles, diffusion driven by viscous bulk and shear stresses, diffusion arising from gradients in the rate of rotation of the particles, contributions from inertial effects, and contributions from the deformation and orientation histories.