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The present article focuses on the analytical approach to discuss the thermo–vibrational convection in a suspension of the active (gyrotactic) swimmers. The onset of instability criterion is investigated for the stationary and oscillatory modes of convection in a shallow fluid layer with no–slip and rigid–free walls. The eigenvalue problem is tackled by Galerkin scheme to get the desired stability diagram and the correlation between the critical Rayleigh numbers. The overstability in suspension is possible when the unstable density gradient of the gyrotactic particles is opposed by the density variation due to thermo–vibrational influence. The suspension is destabilized due to gyrotactic up–swimming while the increase in Péclet number stabilizes the system. The stabilizing influence of vertical vibration is considerably affected due to thermal gradient which destabilizes the suspension. An interesting result of this study is the influence of thermo–vibrational parameter which is associated with applied thermal and vibrational properties. We reported that the destabilizing nature of thermo–vibrational parameter becomes thermally or vibrationally governed when the suspension is heated or cooled from below. When compared to the rigid–rigid boundaries, the displayed profiles for rigid–free walls yielded less stableness in the suspension.

An overstability analysis of vertically vibrated suspension of active swimmers subjected to thermal stratification