Abstract
On the basis of Darcy–Brinkman model, linear stability analysis is used to study bio-thermal convection in a suspension of gyrotactic microorganisms in a highly porous medium heated from below. A Galerkin method is performed to solve the governing equations generating a correlation between the traditional thermal Rayleigh number and the critical value of the bioconvection Rayleigh number. The effects of three variables including the bioconvection Péclet number, the gyrotaxis number and the modified Darcy number on both the wave number and the critical bioconvection Rayleigh number are analyzed and shown graphically. Results indicate that the critical bioconvection Rayleigh number becomes larger with increasing Darcy number.
Similar content being viewed by others
References
Childress S, Levandowsky M, Spiegel EA (1975) Pattern formation in a suspension of swimming microorganisms. J Fluid Mech 69:591–613
Kessler JO (1985) Cooperative and concentrative phenomena of swimming microorganisms. Contemp Phys 26:147–166
Bees MA, Hill NA (1997) Wavelength of bioconvection patterns. J Exp Biol 200:1515–1526
Pedley TJ, Hill NA, Kessler JO (1988) The growth of bioconvection patterns in a uniform suspension of gyrotactic micro-organisms. J Fluid Mech 195:223–338
Kessler JO (1984) Gyrotactic buoyant convection and spontaneous pattern formation in algal cell cultures. In: Velande MG (ed) Nonequilibrium Cooperative Phenomena in Physics and Related Fields. Plenum, New York, pp 241–248
Karimi A, Ardekani AM (2013) Gyrotactic bioconvection at pycnoclines. J Fluid Mech 733:245–267
Sharma YD, Kumar V (2012) The effect of high-frequency vertical vibration in a suspension of gyrotactic micro-organisms. Mech Res Commun 44:40–46
Kessler JO (1986) The external dynamics of swimming microorganisms. In: Round FE, Chapman DJ (eds) Progress in phycological research. Bio Press, Bristol, pp 257–307
Kuznetsov AV, Avramenko AA (2003) Analysis of stability of bioconvection of motile oxytactic bacteria in a horizontal fluid saturated porous layer. Int Commun Heat Mass Transf 30:593–602
Kuznetsov AV (2005) Modeling bioconvection in porous media. In: Handbook of porous media, 2nd ed. Taylor and Francis, New York
Shivakumara IS, Rudraiah N, Lee J, Hemalatha K (2011) The onset of Darcy–Brinkman electroconvection in a dielectric fluid saturated porous layer. Transp Porous Media 90:509–528
Kuznetsov AV (2006) Thermo-bio-convection in porous media. J Porous Media 9:581–589
Whitaker S (1999) The method of volume averaging. Kluwer, Berlin
Nield DA, Bejan A (2006) Convection in porous media, 3rd edn. Springer, New York
Hillesdon AJ, Pedley TJ (1996) Bioconvection in suspensions of oxytactic bacteria: linear theory. J Fluid Mech 324:223–259
Pedley TJ, Kessler JO (1987) The orientation of spheroidal micro-organisms swimming in a flow field. Proc R Soc Lond Ser B 231:47–70
Chandrasekhar S (1961) Hydrodynamic and hydromagnetic stability. Oxford University Press, Oxford
Finlayson BA (1972) The method of weighted residuals and variational principles. Academic Press, New York
Acknowledgements
This work is supported by the National Natural Science Foundation of China (No.11672164, 51509145, 11672163), Fundamental Research Funds of Shandong University (Grant No.2015JC019) and the Natural Science Foundation of Shandong Province (Grant No. ZR2014AM031, ZR2015EQ005).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there is no conflict of interest.
Rights and permissions
About this article
Cite this article
Zhao, M., Wang, S., Wang, H. et al. Darcy–Brinkman bio-thermal convection in a suspension of gyrotactic microorganisms in a porous medium. Neural Comput & Applic 31, 1061–1067 (2019). https://doi.org/10.1007/s00521-017-3137-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-017-3137-y