Sensitivity of binary liquid thermal convection to confinement

The stable axisymmetric convective states of a binary liquid enclosed in a vertical cylinder heated from below are exhaustively and accurately identified by pseudo-spectral numerical integration. In order to gain some insight on the influence that nearby boundaries can exert on flow dynamics, three aspect ratios (1/2, 1, and 2), as well as two types of lateral kinematic boundary conditions (either no-slip or free-slip) are investigated. The ranges over which stable quiescent, oscillatory and steady convective states extend and coexist are given. The bifurcations leading to transitions from one branch of solutions to another, as well as those that occur along the oscillatory branch, are analyzed. The most significant effect of varying boundary conditions and aspect ratio involves the route from oscillatory to steady convection. For a given configuration, that route consists of a period doubling cascade followed by chaos, or a subcritical generalized Hopf (or Neimark–Sacker) bifurcation, or a homoclinic bifurcation. The dynamics of thermal convection of enclosed binary mixtures is clearly very sensitive to both boundary conditions and aspect ratio.