Cross‐diffusion and viscoelastic effects on multidiffusive porous convection

Abstract

AbstractThe onset of triply cross‐diffusive convection in a viscoelastic fluid‐saturated porous layer is investigated as the study is found very relevant for describing natural phenomena (contaminant transport, underground water flow, improved oil recovery, polymer processing). A modified Darcy‐Oldroyd‐B model is used to describe the viscoelastic fluid flow in a porous medium with full cross‐diffusion terms in the diffusivity matrix. A normal mode analysis yields an exact dispersion equation of fifth degree and accordingly the criterion for the onset of stationary and oscillatory convection is obtained. The numerical computations are carried out for diffusivity elements experimentally determined for lysozyme‐sodium chloride‐bovine serum albumin (BSA)‐water system. Instability is found to occur via oscillatory mode for a certain choice of governing parameters. The relaxation and retardation viscoelastic parameters portray opposing contributions on the oscillatory onset and an increase in the relaxation parameter is to increase the range of retardation parameter up to which the oscillatory convection is preferred. The cross‐diffusion is to either delay/hasten the onset of instability based on the magnitude of the stratifying agents. Even minute variations in the cross‐diffusion elements indict complete change in the linear instability criteria. The topology of neutral curves disclosed the occurrence of disconnected closed convex oscillatory neutral curve revealing the requirement of three critical solute Darcy‐Rayleigh numbers to state fully the instability criteria instead of the usual single value; a novel result ensured from the study. Moreover, the nature of instability for Oldroyd‐B, Maxwell and Newtonian fluids turns out to be dissimilar for the same governing parameters.