Introducing the Concept of Effective Diffusivity to Evaluate the Effect of Bioconvection on Small Solid Particles
P. Geng and A.V. Kuznetsov
The effect of bioconvection to enhance mixing of small solid particles is evaluated by introducing a new parameter called the effective diffusivity of solid particles. The effective diffusivity is computed by matching (at steady state) the nonuniformities of number density distributions of small solid particles computed with and without bioconvection. Applications of bioconvection to enhance mixing of small solid particles may include microfluidic applications relevant to biotechnology and medicine, such as the analysis of blood samples when only limited volumes of blood can be extracted. Other applications including analyses of DNA or drugs, screening of patients, and combinatorial synthesis are very interesting as well. This paper considers monodispersed and bidispersed suspensions of small particles in a fluid that contains motile gyrotactic micro-organisms. The particles are assumed to be sufficiently small so that their Brownian diffusion is not negligible. It is shown that the effective diffusivity is a good parameter to evaluate the mixing effect of bioconvection.