@Article{fdmp.2008.004.139,
AUTHOR = {Pravin  Subramanian, Abdelfattah  Zebib},
TITLE = {Solutocapillary Convection in Spherical Shells with a Receding and Deforming Interface},
JOURNAL = {Fluid Dynamics \& Materials Processing},
VOLUME = {4},
YEAR = {2008},
NUMBER = {3},
PAGES = {139--162},
URL = {http://www.techscience.com/fdmp/v4n3/24403},
ISSN = {1555-2578},
ABSTRACT = {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 (<i>Ca</i>) provides a measure of the deviation from sphericity and to leading order in the limit <i>Ca</i> → 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 <i>O(Ca)</i> free surface deformations.},
DOI = {10.3970/fdmp.2008.004.139}
}