Spatial Pattern Formation of Motile Microorganisms: From Gravitactic Bioconvection to Protozoan Culture Dynamics - Porous Media: Applications in Biological Systems and Biotechnology - page 562

V ∗

Darcy velocity, m/sec

V c

Gravitactic cell velocity, m/sec

( X,Y,t ∗ ) Cartesian coordinates, m, and time, sec

( x, y,t ) Dimensionless coordinates

x = X/H ; y = Y/H , and time t = D c t ∗ /H 2

Greek symbols
β = ϑ ∆ ρ/ρ 0

Density variation coe cient of suspension

∆ ρ = ρ c − ρ w

Difference of cell and water densities,
kg/m 3

ψ = ψ ∗ /D c

Dimensionless stream function

v Kinematic viscosity of the suspension,

m 2 / sec

Density of suspension “fluid-cell,” kg/m 3

ρ

Cell density, kg/m 3

ρ c

Water density, kg/m 3

ρ w

Suspension density at the bottom, kg/m 3 ρ 0

Cell volume, m 3 /cell ϑ

14.7 References
Assar, H. (1988). Effect of Cadmium, Pentachlorophenol and Light on biocon-
vection patterns in Chlamydomonas reinhardtii. Master Thesis, University
of Montreal.

Bahloul, A., Nguyen-Quang, T., and Nguyen, T. H. (2005). Bioconvection of
gravitactic microorganisms in a fluid layer. International Communications
in Heat and Mass Transfer, 32 (1-2):64-71.

Bear, J. (1972). Dynamics of Fluids in Porous Media . Dovers.

Bees, M. A. and Hill, N. A. (1998). Linear bioconvection in a suspension
of randomly swimming, gyrotactic micro-organisms. Physics of Fluids,
10 (8):1864-1881.

Chandrasekhar, S. (1961). Hydrodynamic and Hydromagnetic Stability .
Clarendon Press, Oxford.

Childress, S. and Peyret, R. (1976). A numerical study of two-dimensional
convection by motile particles. Journal de Mecanique, 15 (5):753.

Childress, S., Levandowsky, M., and Spiegel, E. A. (1975). Pattern formation
in a suspension of swimming micro-organisms: equation and stability theory.
Journal of Fluid Mechanics, 63 :591.