Pattern selection near the onset of convection in binary mixtures in cylindrical cells

Abstract

We report numerical investigations of three-dimensional pattern formation of binary mixtures in a vertical cylindrical container heated from below. Negative separation ratio mixtures, for which the onset of convection occurs via a subcritical Hopf bifurcation, are considered. We focus on the dynamics in the neighbourhood of the initial oscillatory instability and analyze the spatio-temporal properties of the patterns for different values of the aspect ratio of the cell, 0.25 less than or similar to Gamma less than or similar to 11 (Gamma equivalent to R/d, where R is the radius of the cell and d its height). Despite the oscillatory nature of the primary instability, for highly constrained geometries, Gamma less than or similar to 2.5, only pure thermal stationary modes are selected after long transients. As the aspect ratio of the cell increases, for intermediate aspect ratio cells such as Gamma = 3, multistability and coexistence of stationary and time-dependent patterns is observed. In highly extended cylinders, Gamma approximate to 11, the dynamics near the onset is completely different from the pure fluid case, and a startling diversity of confined patterns is observed. Many of these patterns are consistent with experimental observations. Remarkably, though, we have obtained persistent large amplitude highly localized states not reported previously.