Incompressible rate type fluids with pressure and shear-rate dependent material moduli

Rate type constitutive theories are developed for describing the response of inhomogeneous fluids whose material properties can depend upon the shear rate and the mean normal stress, within a general thermodynamic setting. The classical Navier–Stokes fluid and the power-law fluid are special subclasses of the rate type fluids that have been developed. The models that have been obtained are particularly useful in describing the behavior of biological and geological fluids, and food products in view of their inherent inhomogeneity.