Analysis of Shear Stress Growth Experiments for Linear Constitutive Equations

Shear stress growth curves for viscoelastic fluids at low shear rates are analyzed using two linear rheological constitutive equations, an integral constitutive equation and a mixed type constitutive equation. It is shown that some published solutions do not satisfy all of the pertinent boundary conditions. For the low shear rate region, available experimental shear stress curves show a monotonic increase with decreasing slope in the shear stress. Shear stress curves calculated using a mixed type constitutive equation are found to exhibit this type of behavior while curves calculated using an integral constitutive equation do not. For the mixed type constitutive equation, the calculated developing velocity distribution is used to examine its effect on the developing shear stress distribution. For low values of E (the elasticity number), there is a moderate effect, but, for sufficiently large values of E, the developing velocity distribution has a negligible effect. It is also shown that results consistent with experimental data obtained at low shear rates can be attained using a single relaxation time. Additionally, incompressible Newtonian fluids are considered, and it is found that there can be single maxima in some shear stress curves with no maxima occurring in the velocity curves. Multiple maxima were not obtained in the Newtonian shear stress results unlike some published results.