Influence of Sedimentation Length on the Convective Stability of a Colloidal Suspension

Abstract

The сonvective stability of a colloidal suspension is studied in the case when the vertical dimension of the cavity is less than or comparable with the sedimentation length of nanoparticles. The analysis is carried out within the Boussinesq approximation on the basis of a modified model that takes into account the dependence of a thermodiffusion flow on the local value of impurity concentration. A new parameter of the problem is the ratio of the sedimentation length to the vertical dimension of the cavity. For a quiescent colloidal suspension, exact and approximate (in the case of small concentrations) solutions are obtained that describe the distributions of nanoparticles. A transformation is obtained that allows one to investigate the convective stability of a colloidal suspension stratified in the gravitational field by the Galerkin method with a set of simple trial functions. Instability boundaries and the characteristics of critical perturbations are determined. It is shown that, in the case of negative thermodiffusion, a decrease in the sedimentation length leads to a decrease in the convection threshold and the frequency of neutral oscillations.