Darcy–Brinkman Bio-Thermal Convection in a Porous Rotating Layer Saturated by a Newtonian Fluid Containing Gyrotactic Microorganisms


  • M.I. Kopp Institute for Single Crystals, Nat. Acad. of Sci. of Ukraine
  • V.V. Yanovsky V.N. Karazin Kharkiv National University




Darcy–Brinkman model, bio-thermal convection, Coriolis force, porous medium, gyrotactic microorganism


The bio-thermal convection in a rotating layer of a porous medium saturated with a Newtonian fluid with gyrotactic microorganisms is studied on the basis of the Darcy–Brinkman model. A linear analysis of the bio-thermal convection is carried out using the Galerkin method for rigid-rigid boundary conditions. In a stationary regime, we obtained a dispersion equation with a relation between the thermal Rayleigh–Darcy number and the Rayleigh–Darcy number of bioconvection. The influence of the Peclet number, gyrotaxis, Darcy number, Rayleigh–Darcy number, cell eccentricity, and rotation parameter on bioconvective processes is analyzed and shown graphically. The results indicate that an increase in the rotation parameter (Taylor number) delays the onset of the bioconvection, whereas an increase in the cell eccentricity can stimulate the onset of the bioconvection.


D. Ingham, L. Pop. Transport Phenomena in Porous Media (Elsevier, 2005).

D.A. Nield, A. Bejan. Convection in Porous Media (Springer, 2006).

P. Vadasz. Instability and convection in rotating porous media: A review. Fluids 4, 147 (2019).


T.J. Pedley, N.A. Hill, J.O. Kessler. The growth of bioconvection patterns in a uniform suspension of gyrotactic microorganisms. J. Fluid Mech. 195, 223 (1988).


N.A. Hill, T.J. Pedley, J.O. Kessler. Growth of bioconvection patterns in a suspension of gyrotactic microorganisms in a layer of finite depth. J. Fluid Mech. 208, 509 (1989).


T.J. Pedley, J.O. Kessler. Hydrodynamic phenomena in suspensions of swimming microorganisms. Ann. Rev. Fluid Mech. 24, 313 (1992).


A.V. Kuznetsov, A.A. Avramenko. Stability analysis of bioconvection of gyrotactic motile microorganisms in a fluid saturated porous medium. Transp. Porous Media 53, 95 (2003).


D.A. Nield, A.V. Kuznetsov, A.A. Avramenko. The onset of bioconvection in a horizontal porous-medium layer. Transp. Porous Media 54, 335 (2004).


A.A. Avramenko, A.V. Kuznetsov. The onset of convection in a suspension of gyrotactic microorganisms in superimposed fluid and porous layers: Effect of vertical throughflow. Transp. Porous Media 65, 159 (2006).


A.V. Kuznetsov. The onset of thermo-bioconvection in a shallow fluid saturated porous layer heated from below in a suspension of oxytactic microorganisms. Eur. J. Mech. B/Fluids 25, 223 (2006).


A.A. Avramenko. Model of Lorenz instability for bioconvection. Dopov. Nac. akad. nauk Ukr. 10, 68 (2010).

E. Lorenz. Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130 (1963).


Yongyun Hwang, T.J. Pedley. Bioconvection under uniform shear: Linear stability analysis. J. Fluid Mech. 738, 522 (2014).


N.P. Dmitrenko. Main aspects of the process of bioconvection in nanofluids and porous media. Industrial Heat Engineering 39 (5), 19 (2017).


Y.D. Sharma, V. Kumar. The effect of high-frequency vertical vibration in a suspension of gyrotactic microorganisms. Mech. Res. Commun. 44, 40 (2012).


A.K. Kushwaha, Y.D. Sharma, A. Sharma. Stability Analysis of Vibrational System of Shallow Layers Repleted with Random Swimming Gyrotactic Microorganisms (Research Square, 2022).


M. Zhao, S. Wang, H. Wang, U.S. Mahabaleshwar. Darcy-Brinkman bio-thermal convection in a suspension of gyrotactic microorganisms in a porous medium. Neural Comput. & Applic. 31, 1061 (2019).


A.V. Kuznetsov. Thermo-bio-convection in porous media. J. Porous Media 9, 581 (2006).


H.C. Brinkman. A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. A 1, 27 (1947).


B.A. Finlayson. The Method of Weighted Residuals and Variational Principles (Academic Press, 1972).




How to Cite

Kopp, M., & Yanovsky, V. (2023). Darcy–Brinkman Bio-Thermal Convection in a Porous Rotating Layer Saturated by a Newtonian Fluid Containing Gyrotactic Microorganisms. Ukrainian Journal of Physics, 68(1), 30. https://doi.org/10.15407/ujpe68.1.30



General physics