Onset of Buoyancy-Driven Convection in a Liquid-Saturated Cylindrical Anisotropic Porous Layer Supported by a Gas Phase

• Published in: Transport in porous media 2014-03, Vol.102 (1), p.31-42
• Main Author: Kim, Min Chan
• Format: Article
• Language: English
• Subjects: Anisotropy; Approximation; Boundary layer stability; Boussinesq approximation; Buoyancy driven convection; Civil Engineering; Classical and Continuum Physics; Earth and Environmental Science; Earth Sciences; Earth, ocean, space; Engineering and environment geology. Geothermics; Exact sciences and technology; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Hydrology. Hydrogeology; Hydrology/Water Resources; Industrial Chemistry/Chemical Engineering; Mathematical analysis; Motion stability; Pollution, environment geology; Stability analysis; Vapor phases
• ISSN: 0169-3913; 1573-1634
• DOI: 10.1007/s11242-013-0259-2

A theoretical analysis of convective instability driven by buoyancy forces under the transient concentration fields is conducted in an initially quiescent, liquid-saturated, and anisotropic cylindrical porous layer supported by a gas phase. Darcy’s law and Boussinesq approximation are used to explain the characteristics of fluid motion, and linear stability theory is employed to predict the onset of buoyancy-driven motion. Under the quasi-steady-state approximation, the stability equations are derived in a similar boundary layer coordinate and solved by the numerical shooting method. The critical R a D is determined as a function of the anisotropy ratio. Also, the onset time and corresponding wavelength are obtained for the various anisotropic ratios. The onset time becomes smaller with increasing R a D and follows the asymptotic relation derived in the infinite horizontal porous layer. Anisotropy effect makes the system more stable by suppressing the vertical velocity.