Stability of the axisymmetric buoyant-capillary flows in a laterally heated liquid bridge

Abstract

The axisymmetric steady-states solutions of buoyant-capillary flows in a cylindrical liquid bridge are calculated by means of a pseudo-spectral method. The free surface is undeformable and laterally heated. The working fluid is a liquid metal, with a Prandtl number value Pr=0.01. Particular care was taken to preserve the physical regularity in our model, by writing appropriate flux boundary conditions. The location and nature of the bifurcations undergone by the flows are investigated in the space of the dimensionless numbers (Marangoni, Ma∈[0,600]; Rayleigh, Ra∈[0,5 × 104]). Saddle-node and Hopf bifurcations are found. By analyzing the steady state structures and the energy budgets, the saddle-node bifurcations are observed to play a determinant role. Only two sets of stable steady-states, connected by saddle-nodes, are allowed by the coupling of buoyancy and capillarity. Most of the solutions of the explored part of the (Ma, Ra) plane belong to these states. © 1999 American Institute of Physics.