Buoyancy-driven instabilities of partially miscible fluids in inclined porous media
- 14 September 2021
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
Abstract
This study presents a buoyancy-driven stability analysis in a three-dimensional inclined porous medium with a capillary transition zone that is formed between a non-wetting and an underlying wetting phase. In this two-phase, two-component, partially miscible system, a solute from a non-wetting phase diffuses into a porous layer saturated with a wetting-phase fluid, creating a dense diffusive boundary layer beneath an established capillary transition zone. Transient concentration and gravity-driven velocity fields are derived for the wetting phase while the saturation field remains fixed. Linear stability analysis with the quasi-steady-state approximation is employed to determine the onset of solutal convective instability for buoyancy-dominant, in-transition and capillary-dominant systems. The analysis of the problem leads to a differential eigenvalue problem composed of a system of three complex-valued equations that are numerically solved to determine the critical times, critical wavenumbers and neutral stability curves as a function of inclination angle for different Bond numbers. The layer inclination is shown to play an essential role in the stability of the problem, where the gravity-driven flow removes solute concentrations in the diffusive boundary layer. The results indicate that the horizontal porous layer exhibits the fastest onset of instability, and longitudinal rolls are always more unstable than oblique and transverse rolls. The inclination angle has a more substantial impact on stabilizing the diffusive boundary layer in the buoyancy-dominant than in the capillary-dominant systems. Furthermore, for both buoyancy-dominant and capillary-dominant systems, the critical times and wavenumbers vary exponentially with inclination angle ≤ 60° and follow the Stirling model.This publication has 48 references indexed in Scilit:
- Linear stability analysis on the onset of buoyancy-driven convection in liquid-saturated porous mediumPhysics of Fluids, 2012
- Thermoconvective instabilities in an inclined porous channel heated from belowInternational Journal of Heat and Mass Transfer, 2011
- The Stability of a Developing Thermal Front in a Porous Medium. I Linear TheoryJournal of Porous Media, 2007
- The onset of Darcy-Bénard convection in an inclined layer heated from belowActa Mechanica, 2000
- Partial Differential Equations for Scientists and EngineersAmerican Journal of Physics, 1985
- Mathematics Applied to Deterministic Problems in the Natural Sciences.The American Mathematical Monthly, 1976
- Secondary convection in a Hele Shaw cellJournal of Fluid Mechanics, 1975
- The onset of cellular convection in a fluid layer with time-dependent density gradientsJournal of Fluid Mechanics, 1969
- The unstable thermal interfaceJournal of Fluid Mechanics, 1968
- The instability of a fluid layer with time-dependent heatingJournal of Fluid Mechanics, 1965