Gravity-driven flow of a shear-thinning power-law fluid over a permeable plane

Abstract

The flow of a thin layer of power-law fluid on a porous inclined plane is considered. The unsteady equations of motion are depth-integrated according to the von Karman momentum integral method. The variation of the velocity distribution with the depth is accounted for, and it is furthermore assumed that the flow through the porous medium is governed by the modified Darcy's law. The stability condition is deduced considering the hierarchy of kinematic and gravity waves. The response of the linearized model to a Dirac-delta disturbance in unbounded domain is analytically deduced, in both stable and unstable conditions 1624 C. Di Cristo, M. Iervolino and A. Vacca of flow. The influence of the effect of power-law exponent and bottom permeability on the disturbance propagation is finally analyzed, suggesting indications about the choice of the bottom permeability in order to improve the performance of industrial processes.

A Strategy for Passive Control of Natural Roll-Waves in Power-Law Fluids through Inlet Boundary Conditions

“…in agreement with the results of the normal mode analysis and of the Green's function study performed by Ng and Mei (1994) and by Di Cristo et al(2013b), respectively.…”

On the applicability of minimum channel length criterion for roll-waves in mud-flows

“…With reference to power-law fluids, Ng and Mei (1994) individuated the flow stability conditions of the linearized mass and momentum conservation equations. The results of Ng and Mei (1994) have been generalized accounting for a surface tension (Hwang et al, 1994), considering a porous bottom (Di Cristo et al, 2013c;Pascal, 2006) and including a superficial shear stress effect (Pascal and D'Alessio, 2007). In presence of yield stress and with reference to the two-equation model, linear stability conditions have been found by Trowbridge (1987) for Bingham fluids and by Coussot (1994) for Herschel and Bulkley fluids.…”