TY - EJOU
AU - Subramanian, Pravin
AU - Zebib, Abdelfattah
TI - Solutocapillary Convection in Spherical Shells with a Receding and Deforming Interface
T2 - Fluid Dynamics \& Materials Processing
PY - 2008
VL - 4
IS - 3
SN - 1555-2578
AB - A theoretical and computational study of solutocapillary driven Marangoni instabilities in small spherical shells is presented. The shells contain a binary fluid with an evaporating solvent. The viscosity is a strong function of the solvent concentration, the inner surface of the shell is assumed impermeable and stress free, while non-linear boundary conditions are modeled and prescribed at the receding outer boundary. A time-dependent diffusive state is possible and may lose stability through the Marangoni mechanism due to surface tension dependence on solvent concentration (buoyant forces are negligible in this micro-scale problem). The Capillary number (*Ca*) provides a measure of the deviation from sphericity and to leading order in the limit *Ca* → 0 the outer surface evolves with time in a convective state as it does in the diffusive state. We model the motion in this limit and compute supercritical, nonlinear, time-dependent, axisymmetric and three-dimensional, infinite Schmidt number solutocapillary convection. The normal stress balance imposes compatibility restrictions and allows two admissible states: axisymmetric hemispherical convection and three-dimensional solutions exhibiting cubic symmetry. We employ global mass conservation to compute upper bounds on the companion *O(Ca)* free surface deformations.
KW -
DO - 10.3970/fdmp.2008.004.139