Viscous Fluids

Abstract

The equations of motion for viscous fluids are obtained from the mass and momentum equations by parametrization of the viscous stress tensor as an isotropic function of the strain rate tensor D with scalar coefficients, which are themselves functions of the invariants of the latter (and possibly additional scalar field quantities such as e.g., the temperature and salinity). Newtonian fluid materials emerge by linearization of this parametrization in D. They are materially described by a shear viscosity and for compressible liquids (gases) an additional bulk viscosity. The emerging equations appear as Navier-Stokes equations. For water, experimentally supported expressions for these parameters are given in Chap. 1. The simplest nonlinear forms of the viscosity functions generate the material descriptions of dilatant and pseudoplastic liquids, which appear in rheology as power law fluids for which plane wall shear flows are studied. Applications address viscometry, hover craft and viscous Hagen-Poiseuille flows, the Reynolds-Sommerfeld slide bearing model, shallow three-dimensional free surface flows applied to the flows in large ice sheets such as Greenland and Antarctica, significant for estimations of sea level rise due to anthropogenic production of greenhouse gases.