Study of non-stationary flow of viscoelastic incompressible fluid in a flat channel

Abstract

The problems of the non-stationary flow of a viscoelastic fluid in a flat channel under the influence of a constant pressure gradient are solved based on the generalized Maxwell model. By solving the problem, formulas for velocity distribution, fluid flow rate, and other hydrodynamic quantities were determined. Based on the formulas derived, transient processes in the unsteady flow of a viscoelastic fluid in a flat channel are analysed. Based on the results of the analysis, it was shown that transient processes depending on the Deborah number, which determines the elasticity property in an elastic-viscous fluid, differ fundamentally from the transient process in a Newtonian fluid. It was discovered that the transition processes of the characteristics of an elastic-viscous fluid from an unsteady to a stationary state at small values of the Deborah number practically do not differ from the transition processes of a Newtonian fluid. At large values of the Deborah number, it was established that the process of transition of an elastic-viscous fluid from an unsteady state to a stationary one is of a wave nature, in contrast to the transition process of a Newtonian fluid, and the transition time is several times longer than the transition time of a Newtonian fluid. It was also revealed that perturbed processes can arise during the transition.