The effect of high-frequency vertical vibration in a suspension of gyrotactic micro-organisms

Abstract

Recently, many researchers have shown interest in the study of bioconvection formation due to suspension of swimming micro-organisms and have published large number of papers on bioconvection. In the present study, the effect of high-frequency vertical vibration on the onset of bioconvection in a dilute suspension of gyrotactic micro-organisms is examined analytically and numerically. The governing equations describing the mean flow are obtained using the time averaging method and a linear stability analysis is performed. Galerkin technique is applied to obtain the solution of system satisfying no-slip boundary conditions and a secular relation involving bioconvection Rayleigh number and vibrational Rayleigh number has been obtained. The numerical computations are carried out by varying the values of different parameters involved. It is reported that vertical vibration, bioconvection Péclet number and cell eccentricity have stabilizing effects, whereas, gyrotaxis has destabilizing effect on the suspension of shallow fluid layer of finite depth.