Vibration effect on a stability of stationary flow of pseudoplastic fluid in vertical slot

In this paper, we study the effect of vibrations on the stability of a stationary plane-parallel flow of a pseudoplastic fluid in an infinite vertical layer between two rigid perfectly heat conducting boundaries, maintained at different temperatures. It is assumed that the layer performs vertical high-frequency vibrations perpendicular to the imposed temperature gradient. Vibration intensity is characterized by the dimensionless parameter V, typical values of which in the terrestrial conditions vary from 0 to 1. The fluidity of liquid is found to increase with increasing vibration intensity. The stability of a stationary plane-parallel flow with respect to small plane normal-mode perturbations, periodic along the layer, is investigated for Prandtl number values Pr = 1 and Pr = 100. The results show that, for Pr = 1, at any values of rheological parameters under examination, the monotonic hydrodynamic perturbations having a form of immovable vortices at the boundary of counter-current flows are responsible for the instability of a stationary flow. The value of the modified Grashof number, which determines the base flow stability threshold, decreases monotonically as the pseudoplastic properties of fluid become stronger. Vibrations also produce a destabilizing effect. For Pr = 100 there are three instability modes: the monotonic hydrodynamic instability mode and the thermal oscillatory Rayleigh mode, which exist in the absence of vibrations, and the vibrational oscillatory mode. In the case of low-intensity vibrations, the thermal Rayleigh mode is the most dangerous one. An increase in the vibration intensity, vibration mode becomes the most dangerous. The growth of dynamic yield stress leads to a decrease in the value of the vibration parameter V at which the vibrational mode becomes the most dangerous mode.