NON-NEWTONIAN EFFECTS IN SOME ELASTICO-VISCOUS LIQUIDS WHOSE BEHAVIOUR AT SMALL RATES OF SHEAR IS CHARACTERIZED BY A GENERAL LINEAR EQUATION OF STATE

Abstract

Consideration is given to elastico-viscous liquids whose behaviour at small rates of shear is characterized by a general linear equation of state. Suitable equations of state for use under all conditions of motion and stress are formulated, and a number of steady flow problems are solved for the particular class of idealized liquids whose equations of state are linear in the stresses and include terms of the second degree in the stresses and rates of strain taken together. It is shown that certain liquids of this class, characterized by their relaxation spectrum N(r) and three further constants μ₀, v₁ and v₂ exhibit the kind of non-Newtonian behaviour that is often observed in real liquids, in the following respects: a decrease in apparent viscosity with increasing rate of shear is observed in simple shearing; the liquids exhibit the positive Weissenberg effect when sheared between rotating coaxial cylinders; the normal stress distribution in the case of flow between a horizontal flat plate and a cone of semi-angle very near to ½π is equivalent to an extra tension along the streamlines, with an isotropic state of stress existing in planes normal to the stream lines. Steady rectilinear flow through straight pipes of arbitrary section, under a constant pressure gradient, is possible in these liquids.