Stationary and oscillatory convection in bidisperse colloidal suspension

Abstract

The nonlinear evolution and properties of two-dimensional convection flows of a colloidal suspension arising in a horizontal layer heated from below are studied within the framework of a bidisperse model. Numerical simulation is carried out using the finite difference method. The layer has solid, ideally heat-conducting horizontal boundaries that are impervious to suspension. Periodic boundary conditions are used at the lateral boundaries of the computational domain to detect and analyze not only stationary convection and standing waves, but also traveling waves. We consider the case when, in a quiescent colloidal suspension, the thermodiffusion transport and gravitational settling of nanoparticles are directed oppositely, which causes the settling down of a heavy impurity and the onset of oscillatory instability. When the Rayleigh number reaches a certain critical value, an unstable standing wave (SW) appears in the layer. Its destruction, accompanied by the redistribution of nanoparticle concentration fields, leads to the emergence of a long transient regime of traveling waves, the characteristics of which are studied and analyzed. A bifurcation diagram (dependence of the maximum stream function on the Rayleigh number) showing how the nonlinear modes of a fluid flow change depending on heating intensity is constructed. It is shown that, at high heating intensity, convective mixing destroys the gravitational sedimentation of nanoparticles and leads to smoothing of concentration inhomogeneities. Due to the nonlinear evolution of oscillatory perturbations, a stationary convection regime characterized by the mirror symmetry of solutions is established. Stable traveling waves are found in a narrow subcritical range of Rayleigh numbers. The fields of stream function, temperature, and impurity concentrations of small and large nanoparticles are obtained.