The onset of thermo-bioconvection in a shallow fluid saturated porous layer heated from below in a suspension of oxytactic microorganisms

Abstract The aim of this paper is to present a continuum model for thermo-bioconvection of oxytactic bacteria in a porous medium and investigate the combined effects of microorganisms' upswimming and heating from below on the stability of bioconvection in a horizontal layer filled with a fluid saturated porous medium. Different from traditional bioconvection, thermo-bioconvection has two destabilizing mechanisms that contribute to creating the unstable density stratification. This problem may be relevant to a number of geophysical applications, such as the investigation of the dynamics of oxytactic species of thermophiles (heat loving microorganisms) living in hot springs, microbial-enhanced oil recovery, and modeling oil- and gas-bearing sedimentary basins. The utilization of the Galerkin method to solve a linear stability problem leads to a correlation between the critical value of the bioconvection Rayleigh number and the traditional “thermal” Rayleigh number.

[1]  Kambiz Vafai,et al.  The role of porous media in modeling flow and heat transfer in biological tissues , 2003 .

[2]  Andrey V. Kuznetsov,et al.  Investigation of the onset of thermo-bioconvection in a suspension of oxytactic microorganisms in a shallow fluid layer heated from below , 2005 .

[3]  T. L. Stewart,et al.  Biomass plug development and propagation in porous media. , 2001, Biotechnology and bioengineering.

[4]  T J Pedley,et al.  The development of concentration gradients in a suspension of chemotactic bacteria. , 1995, Bulletin of mathematical biology.

[5]  B. Finlayson.  The method of weighted residuals and variational principles : with application in fluid mechanics, heat and mass transfer , 1972 .

[6]  S. Chandrasekhar.  Hydrodynamic and Hydromagnetic Stability , 1961 .

[7]  S. Whitaker.  The method of volume averaging , 1998 .

[8]  Timothy J. Pedley,et al.  Falling plumes in bacterial bioconvection , 2001, Journal of Fluid Mechanics.

[9]  N. Hill,et al.  The growth of bioconvection patterns in a uniform suspension of gyrotactic micro-organisms , 1988, Journal of Fluid Mechanics.

[10]  T. Pedley,et al.  Bioconvection in suspensions of oxytactic bacteria: linear theory , 1996, Journal of Fluid Mechanics.

[11]  Kambiz Vafai,et al.  Analysis of dispersion effects and non-thermal equilibrium, non-Darcian, variable porosity incompressible flow through porous media , 1994 .

[12]  T. Pedley,et al.  Hydrodynamic Phenomena in Suspensions of Swimming Microorganisms , 1992 .

[13]  A. Bejan,et al.  Convection in Porous Media , 1992 .

[14]  H. S. Fogler,et al.  Biomass evolution in porous media and its effects on permeability under starvation conditions. , 2000, Biotechnology and bioengineering.