Linear Stability Analysis for the Thermotactic Microorganisms in Porous Media

: cc. 41-48
Université El-Hadj-Lakhdar Batna
Biofluids and Biosystems Modeling Lab (BBML) Department of Engineering, Faculty of Agriculture, Dalhousie University

Thermotaxis or motion in the field of temperature gradient is a very common phenomenon and can be found in many events in nature, from biological ones to the migration of colloidal particles. In this paper, we suggest a deterministic model to describe the collective behavior of a microorganism population with a general form of stimuli gradient-based taxis in porous media. This population has the mass density slightly heavier than the water density and forms a suspension. The suspended cells are actively in motion with a thermotaxis behavior (temperature gradient follower). Based on an Eulerian framework, the model comprises basically the Darcy equation for the fluid motion in porous media, equation of cell conservation for the microorganism population and equation of  conservation for the considered stimuli. To take into account the density effects, the Boussinesq’s approximation will be used. Linear stability analysis shows that there are interesting effects of temperature on the bioconvection pattern of the thermotactic microorganisms.

[1] A. F. Mare, A. V. Panfilov, P. Hogeweg, Migration and thermotaxis of Dictyostelium discoideum slugs, a model study, Journal of Theoretical Biology 199 (1999) 297–309.

[2] J. Watmough, S. Camazine, Self-organized thermoregulation of honeybee clusters, Journal of Theoretical Biology 176 (1995) 391–402.

[3] T. Matsuoka, S. Gomi, R. Shingai, Simulation of C. elegans thermotactic behavior in a linear thermal gradient using a simple phenomenological motility model, Journal of Theoretical Biology 250 (2008) 230–243.

[4] A. Bahat, M. Eisenbach, Sperm thermotaxis, Molecular and Cellular Endocrinology 252 (2006) 115–119.

[5] A. Bahat, S.R. Caplan, M. Eisenbach, Thermotaxis of human sperm cells in extraordinarily shallow temperature gradients over a wide range, PLoS ONE 7 (2012) 1–9.

[6] R. Golestanian, Collective behavior of thermally active colloids, Physical Review Letters 108 (2012) 038303-1-038303-5.

[7] N. J. Savill, P. Hogeweg, Modeling morphogenesis: from single cells to crawling slugs, J. theor. Biol. 184 (1997) 229–235.

[8] H. Ito, H. Inada, I. Mori, Quantitative analysis of thermotaxis in the nematode Caenorhabditis elegans, J. Neurosci. Methods 154 (2006) 45–52.

[9] K. Nakazato, A. Mochizuki, Steepness of thermal gradient is essential to obtain a unified view of thermotaxis in C. elegans, Journal of Theoretical Biology 260 (2009) 56–65.

[10] A. V. Kuznetsov, Modeling Bioconvection in Porous Media, Handbook of Porous Media, Taylor&Francis, New York, 2005.

[11] A.V. Kuznetsov, New Developments in Bioconvection in Porous Media: Bioconvection Plumes, Bio–Thermal Convection, and Effects of Vertical Vibration, Emerging Topics in Heat and Mass Transfer in Porous Media – From Bioengineering and Microelectronics to Nanotechnology, Springer, Dordrecht, 2008.

[12] T. Nguyen-Quang, T. H. Nguyen, F. Guichard, Spatial pattern formation of gravitactic microorganisms: from bioconvection to population dynamics. In Porous Media: Applications in Biological Systems and Biotechnology, Taylor&Francis, CRC Press, 2010.

[13] T. J. Pedley, J. O. Kessler, Hydrodynamic phenomena in suspensions of swimming micro-organisms. Ann. Rev. Fluid. Mech. 24 (1992) 313–358.

[14] S. Whitaker, The method of volume averaging, Dordrecht, Boston: Kluwer Academic, 1999.

[15] T. Nguyen-Quang, A. Bahloul, T. H. Nguyen. Stability of gravitactic micro-organisms in a fluid-saturated porous medium, International Communication Journal in Heat and Mass Transfer 32 (2005) 54–63.

[16] T. Nguyen-Quang, T. H. Nguyen, G. LePalec, Gravitactic bioconvection in a fluid-saturated porous medium with double diffusion, Journal of Porous Media 11 (2008) 751–764.

[17] D. A. Nield, A. Bejan, Convection in porous media, Springer, 2012.

[18] E. L. Koschmieder, Benard cells and Taylor vorticities, Cambridge University Press, 1993.

[19] R. Shiurba, T. Hirabayashi, M. Masuda, et al., Cellular responses of the ciliate, Tetrahymena thermophila, to far infrared irradiation , Photochemical&Photobiological Sciences 5 (2006) 799–807.