Comparison of three thermodynamic descriptions of nonlocal effects in viscoelasticity

Three different thermodynamic approaches to nonlocal effects in a constitutive equation for the viscous pressure tensor are compared in order to illustrate the relative merits of different choices of independent variables. The first one considers a coupling between viscous pressure and diffusion flux; the second one, a coupling between viscous pressure and its flux, given by a third-order tensor, and the third approach includes higher-order gradients of the velocity. The two approaches based on the fluxes predict the correct sign for the coefficient of the nonlocal term, in contrast with the approach based on the gradients of the velocity.