Normal Stress Effects in Second-Order Fluids

Abstract

In the general theory of the behavior of simple fluids with fading memory in slow deformations, the constitutive equation of those fluids called second‐order fluids gives to the equation of Newtonian fluids a correction for viscoelasticeffects that is complete to within terms of order greater than two in the time scale. The hydrodynamical behavior of incompressible second‐order fluids is determined by three material constants: η0, β, γ, besides the density. We show here that not only the viscosity η0, but also the constant γ which governs certain normal stress effects, is determined by the shear‐relaxation modulus of classical infinitesimal viscoelasticity. This result enables us to show that in a slow Couette flow the viscoelastic contribution to the difference in normal thrusts on the inner and outer cylindrical walls has a sign opposite to that of the inertial contribution. We also suggest several practicable methods for measuring β and γ.