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Investigation of the onset of bioconvection in a suspension of oxytactic microorganisms subjected to high-frequency vertical vibration

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Abstract

This paper investigates the effect of vertical vibration on the stability of a dilute suspension of oxytactic microorganisms in a shallow horizontal fluid layer. For the case of high-frequency vibration, an averaging method is utilized to derive the equations describing the mean flow by decomposing the solutions of governing equations into two components: one that varies slowly with time, and a second that varies rapidly with time. Linear stability analysis is used to investigate the stability of the obtained averaged equations. It is predicted that high-frequency, low-amplitude vertical vibration has a stabilizing effect on a suspension of oxytactic microorganisms confined in a shallow horizontal layer.

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References

  1. Bardan, G., Knobloch, E., Mojtabi, A., Khallouf, H.: Natural doubly diffusive convection with vibration. Fluid Dyn. Res. 28, 159–187 (2001)

    Article  ADS  Google Scholar 

  2. Bardan, G., Mojtabi, A.: On the Horton-Rogers-Lapwood convective instability with vertical vibration: onset of convection. Phys. Fluids 12, 2723–2731 (2000)

    Article  MathSciNet  Google Scholar 

  3. Bardan, G., Razi, Y.P., Mojtabi, A.: Comments on the mean flow averaged model. Phys. Fluids 16, 4535–4538 (2004)

    Article  ADS  Google Scholar 

  4. Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability. Oxford University Press, Oxford (1961)

    MATH  Google Scholar 

  5. Cisse, I, Bardan, G., Mojtabi, A.: Rayleigh Bénard instability of a fluid under high-frequency vibration. Int. J. Heat Mass Trans. 47, 4101–4112 (2004)

    Article  MATH  Google Scholar 

  6. Finlayson, B.A.: The Method of Weighted Residuals and Variational Principles. Academic Press, New York, Chap. 6 (1972)

  7. Hillesdon, A.J., Pedley, T.J.: Bioconvection in suspensions of oxytactic bacteria: linear theory. J. Fluid Mech. 324, 223–259 (1996)

    Article  MATH  ADS  Google Scholar 

  8. Hillesdon, A.J., Pedley, T.J., Kessler, J.O.: The development of concentration gradients in a suspension of chemotactic bacteria. Bull. Math. Biol. 57, 299–344 (1995)

    Article  PubMed  MATH  Google Scholar 

  9. Gershuni, G.Z., Lyubimov, D.V.: Thermal Vibrational Convection. Wiley, New York (1998)

    Google Scholar 

  10. Kessler, J.O.: The external dynamics of swimming micro-organisms. Prog. Phycolog. Res. 4, Biopress, Bristol, Chap. 6, 257–307 (1986)

    Google Scholar 

  11. Kuznetsov, A.V.: Investigation of the onset of thermo-bioconvection in a suspension of oxytactic microorganisms in a shallow fluid layer heated from below. Theor. Comput. Fluid Dyn. 19, 287–299 (2005)

    Article  MATH  Google Scholar 

  12. Metcalfe, M., Pedley, T.J.: Bacterial bioconvection: weakly nonlinear theory for pattern selection. J. Fluid Mech. 370, 249–270 (1998)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. Metcalfe, M., Pedley, T.J.: Falling plumes in bacterial bioconvection. J. Fluid Mech. 445, 121–149 (2001)

    Article  MATH  ADS  Google Scholar 

  14. Mojtabi, M.C.C., Razi, Y.P., Maliwan, K., Mojtabi, A.: Influence of vibration on Soret-driven convection in porous media. Num. Heat Trans. A 46, 981–993 (2004)

    Article  Google Scholar 

  15. Simonenko, I.B.: A justification of the averaging method for a problem of convection in a field rapidly oscillating forces and other parabolic equations. Mat. Sb. 129(2), 245–263 (1972)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910, Raleigh, NC, 27695-7910, USA

    A. V. Kuznetsov

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  1. A. V. Kuznetsov
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Correspondence to A. V. Kuznetsov.

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Communicated by O. E. Jensen

PACS 47.27 Te; 68.60 Dv

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Kuznetsov, A.V. Investigation of the onset of bioconvection in a suspension of oxytactic microorganisms subjected to high-frequency vertical vibration. Theor. Comput. Fluid Dyn. 20, 73–87 (2006). https://doi.org/10.1007/s00162-006-0007-0

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  • DOI: https://doi.org/10.1007/s00162-006-0007-0

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