Transient Processes during Nonstationary Flow of an Elastic-Viscous Liquid in a Flat Channel

The paper considers the solution to the problem of unsteady flow of an elastic-viscous fluid in a flat channel under the influence of a constant pressure gradient based on the generalized Maxwell model. By solving the problem, formulas for velocity distribution, fluid flow, and other hydrodynamic quantities are determined. Based on the formulas found, transient processes during unsteady flow of an elastic-viscous fluid in a flat channel are analyzed. Based on the results of the analysis, it is shown that transient processes under the influence of the Deborah number, which determines the elasticity properties of a fluid in an elastic-viscous flow, are fundamentally different from the transient process in a Newtonian fluid. At the same time, it is discovered that the process of transition of the characteristics of an elastic-viscous fluid from an unsteady state to a stationary state at small values of the Deborah number are almost not different from the processes of transition of a Newtonian fluid. When the Deborah number exceeds unity, it is established that the process of transition of an elastic-viscous fluid from an unsteady state to a stationary state is a wave-type change, 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 is also revealed that disturbances may occur during the transient process. This disturbance, occuring in the unsteady flow of an elastic-viscous fluid, will be stabilized by mixing a Newtonian fluid into it. That is, the instantaneous maximum increase in the velocity of the viscoelastic fluid as a result of an increase in the concentration of the Newtonian fluid is normalized. The implementation of this property is important in technical and technological processes, in preventing technical failures or malfunctions.

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