Nonequilibrium statistical thermodynamics and rheology of non-Newtonian fluids II. Rheological models

The generalized transport relations obtained in the first part of the work are used to derive rheological relations describing different types of flows of non-Newtonian fluids. Rheological models are obtained by expanding the space-time correlation functions with respect to the time derivatives of the macroscopic fields near a frozen nonequilibrium state under the assumption that there exist two time scales. A connection is established between these models and the relations known from phenomenological theology, including the Goddard–Miller and Oldroyd relations.