Examining laminar, non-stationary viscoelastic fluid flow between two parallel planes

Abstract

The generalized Maxwell model is used to handle problems involving the unsteady flow of a viscoelastic fluid in a flat channel under the effect of a constant pressure gradient. Formulas for fluid flow, velocity distribution, and other hydrodynamic characteristics were found. Transient processes during unsteady flow of a viscoelastic fluid in a flat channel are investigated based on the discovered formulas. The analysis’s conclusions demonstrated that, at small Debord number values, the procedures of changing a viscoelastic fluid’s properties from an unstable to a stationary state essentially don’t differ from those of a Newtonian fluid. Exceeding the Debord number relatively unity, it has been established that the process of transition of a viscoelastic fluid from an unsteady state to a stationary state is of a wave nature, in contrast to the transition process of a Newtonian fluid, and the transition time is several times longer than that of a Newtonian fluid. It was also discovered that perturbed processes can arise during the transition. These disturbances occurring in unsteady flows of a viscoelastic fluid can be stabilized by mixing the Newtonian fluid within it. The implementation of this property is important in preventing technical failures or malfunctions.