Laminar unsteady flow of a viscoelastic liquid in a flat channel

Abstract

The generalized Maxwell model is used to handle problems involving the unsteady flow of a viscoelastic liquid in a flat channel under the effect of a constant pressure gradient. Formulas for the distribution of velocity, fluid flow, and other hydrodynamic characteristics are found by addressing this issue. Considering the found formulas, transient processes in the nonstationary flow of a viscoelastic liquid in a flat channel are analyzed. The findings of the investigation revealed that the procedures of transition of the characteristics of a viscoelastic liquid from a nonstationary state to a stationary one, at small values of the Debord number, practically do not differ from the processes of transition of a Newtonian liquid. When the Debord numbers exceed, comparatively, one, It has been demonstrated that the transition of a viscoelastic liquid from a nonstationary to a stationary state is wave-like, as opposed to the transition of a Newtonian liquid, and the transition period is many times longer. It has also been found that perturbed processes can occur during the transition and they, occurring in unsteady flows of a viscoelastic liquid, can be stabilized by mixing a Newtonian liquid in it. The realization of this property is critical in technical and technological processes, preventing technical faults or malfunctions.