This study aims to examine the Rayleigh–Taylor instability at the planar interface between a couple stress fluid and a Newtonian viscous fluid in a rectangular channel under the influence of heat and mass transfer across the interface.
The channel is divided into two regions: the upper region is occupied by the couple stress fluid and the lower region is filled with a porous medium saturated with the Newtonian fluid. The flow in the porous region is governed by the Brinkman extension of Darcy’s law. Using the viscous potential flow theory, the governing equations are linearized and the normal mode analysis is applied to derive a second-order dispersion relation connecting the temporal growth rate with the wave number. This dispersion relation is solved numerically using the Newton–Raphson method.
The results indicate that interfacial heat and mass transfer and the Froude number stabilize the interface by suppressing the perturbation growth rate. While, the Reynolds number, Weber number, Atwood number and the couple stress fluid layer thickness promote instability. The model is validated by reducing it to the classical Newtonian–Newtonian case in the limit and and the obtained results show close agreement with the existing literature.
The findings of this study are useful in enhanced oil recovery and drilling-fluid displacement in petroleum reservoirs. The obtained results of the present model may also be used in the transport of blood and synovial fluid through biological tissues, in lubrication by additive-laden oils in porous bearings and in the control of interfacial mixing in chemical processing units.
The present work integrates the couple stress fluid microstructure, Darcy–Brinkman porous resistance and interfacial heat and mass transfer within a unified Rayleigh–Taylor instability frame-work. These mechanisms have been studied individually in earlier works, but their simultaneous interaction has not been explored previously.
