Basic Viscoelastic Fluid Flow Problems Under Harmonic Fluctuating Driving Force

Abstract

Analytical solutions are obtained for five basic viscoelastic fluid flow problems under harmonic fluctuating driving forces. Jeffrey’s model is adopted in the study. The five fundamental problems are the fluctuating Couette flow, fluctuating wind-driven flow over finite and infinite fluid domains, fluctuating Stokes’ first problem and the fluctuating Poiseuille flow. It is shown that the effect of the relaxation λ1 and retardation λ2 times on the flow behavior becomes more significant at large fluctuation frequencies (ω). It is found that increasing λ1 in velocity-type driving force problems causes a lag in the flow response and an increase in the fluctuation amplitude, while increasing λ2 in this type causes a lead in the flow response and an increase in the fluctuation amplitude. However, increasing λ1 in shear-type driving force problems causes a lead in the flow response and an increase in the amplitude, while increasing λ2 in this type causes a lag in the response and a decrease in the fluctuation amplitudes.