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 viscoelastic effects 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.
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Coleman et al. (1964) studied this question.