Rheological Materials

Abstract

In ordinary incompressible fluids the flow and transport phenomena are fairly well described by Newton’ linear constitutive equation for the viscous pressure tensor P^v

$$ P^v = - 2\eta V, $$

(15.1)

V is the symmetric (and traceless, because of incompressibility) part of the velocity gradient and n the dynamic viscosity, which may depend on the temperature and the pressure, but not on the velocity gradient However, it has been observed that there exists a wide class of materials, such as polymers, soap solutions, some honeys, asphalts, and physiological fluids, that fail to obey ((15.1)): these materials are generally referred to as viscoelastic materials. They behave as fluids with a behaviour reminiscent of solids by exhibiting elastic effects. In ordinary fluids, the relaxation of the pressure tensor is very short, in elastic bodies it is infinite so that no relaxation is observed: viscoelastic materials are characterized by relaxation times between these two limits. Materials with the above property are also called non-Newtonian in the technical literature. The terms ‘viscoelastic’ and ‘non-Newtonian’ are used rather loosely; here we shall reserve the term ‘non-Newtonian’ for any material described by a non-linear constitutive relation between the pressure tensor and the velocity gradient tensor, and the term ‘linear viscoelastic’ will be used for systems exhibiting both viscous and elastic effects in the linear regime and described by material coefficients independent of the velocity gradient.