Bioconvective Linear Stability of Gravitactic Microorganisms

Abstract

Interesting results on the linear bioconvective instability of a suspension of gravitactic microorganisms have been calculated. The hydrodynamic stability is characterized by dimensionless parameters such as the bioconvection Rayleigh number R, the gyrotaxis number G, the motility of microorganisms d, and the wavenumber k of the perturbation. Analytical and numerical solutions are calculated. The analytical one is an asymptotic solution for small wavenumbers (and for any motility number) which agrees very well with the numerical solutions. Two numerical methods are used for the sake of comparison. They are a shooting method and a Galerkin method. Marginal curves of R against k for fixed values of d and G are presented along with curves corresponding to the variation of the critical values of R c and k c. Moreover, those critical values are compared with the experimental data reported in the literature, where the gyrotactic algae Chlamydomonas nivalis is the suspended microorganism. It is shown that the agreement between the present theoretical results and the experiments is very good.