Abstract
Despite a large number of publications on bioconvection in suspensions of motile microorganisms, bioconvection in a fluid saturated porous medium is a relatively new area of research. This paper is motivated by experimental research by Kessler (1986) who established that a porous medium prevents the development of convection instability in algal suspensions. This suggests that there may exist a critical value of the permeability of a porous medium. If the permeability is smaller than critical, the system is stable and bioconvection does not develop. If the permeability is larger than critical, bioconvection may develop. This paper presents a model of bioconvection of gyrotactic motile microorganisms in a fluid saturated porous medium. The focus of this research is the determination of the critical value of permeability of a porous medium by a linear stability analysis. A simple but elegant analytical solution for the critical Darcy number is obtained.
Similar content being viewed by others
References
Bees, M. A. and Hill, N. A.: 1997, Wavelengths of bioconvection patterns, J. Exp. Biol. 200, 1515–1526.
Ghorai, S. and Hill, N. A.: 1999, Development and stability of gyrotactic plumes in bioconvection, J. Fluid Mech. 400, 1–31.
Ghorai, S. and Hill, N. A.: 2000, Periodic arrays of gyrotactic plumes in bioconvection, Phys. Fluids 12, 5–22.
Harashima, A., Watanabe, M. and Fujishiro, I.: 1988, Evolution of bioconvection patterns in a culture of motile flagellates, Phys. Fluids 31, 764–775.
Kessler, J. O.: 1985a, Hydrodynamic focusing of motile algal cells, Nature 313, 218–220.
Kessler, J. O.: 1985b, Cooperative and concentrative phenomena of swimming microorganisms, Contemp. Phys. 26, 147–166.
Kessler, J. O.: 1986, The external dynamics of swimming micro-organisms, Progress in Phycological Research, Vol.4, Biopress, Bristol, pp. 257–307.
Kessler, J. O., Wiseley, D. A., Remick, K. E. and Marthaler, D. E.: 1997, Individual and collective dynamics of swimming bacteria, in: M. Schreckenberg and D. E. Wolf (eds), Proceedings of the Workshop on Traffic and Granular Flow'97, Springer, New York, pp. 37–51.
Kessler, J. O., Burnett, G. D. and Remick, K. E.: 2000, Mutual dynamics of swimming microorganisms and their fluid habitat, in: P. L. Christiansen, M. P. Sorensen and A. C. Scott (eds), Nonlinear Science at the Dawn of the 21st Century, Springer, New York, pp. 409–426.
Kuznetsov, A. V. and Avramenko, A. A.: 2002, A 2D Analysis of bioconvection in a fluid saturated porous medium – estimation of the critical permeability value, Int. Commun. Heat Mass Trans. 29, 175–184.
Kuznetsov, A. V. and Jiang, N.:2001, Numerical investigation of bioconvection of gravitactic microorganisms in an isotropic porous medium, Int. Commun. Heat Mass Trans. 28, 877–886.
Lapwood, E. R.: 1948, Convection of a fluid in a porous medium, Proc. Cambridge Philos. Soc. 44, 508–521.
Nield, D. A. and Bejan, A.: 1999, Convection in Porous Media, 2nd edn., Springer, New York.
Pedley, T. J. and Kessler, J. O.: 1987, The orientation of spheroidal microorganisms swimming in a flow field, Proc. R. Soc. Lond. B 231, 47–70.
Pedley, T. J. and Kessler, J. O.: 1992, Hydrodynamic phenomena in suspensions of swimming microorganisms, Ann. Rev. Fluid Mech. 24, 313–358.
Pedley, T. J., Hill, N. A. and Kessler, J. O.: 1988, The growth of bioconvection patterns in a uniform suspension of gyrotactic microorganisms, J. Fluid Mech. 195, 223–338.
Whitaker, S.: 1999, The Method of Volume Averaging, Kluwer, Dordrecht.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kuznetsov, A.V., Avramenko, A.A. Stability Analysis of Bioconvection of Gyrotactic Motile Microorganisms in a Fluid Saturated Porous Medium. Transport in Porous Media 53, 95–104 (2003). https://doi.org/10.1023/A:1023582001592
Issue Date:
DOI: https://doi.org/10.1023/A:1023582001592