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Solutocapillary Convection in Spherical Shells with a Receding and Deforming Interface

Pravin Subramanian1, Abdelfattah Zebib1
Mechanical & Aerospace Engineering, Rutgers University, Piscataway, NJ, 08854

Fluid Dynamics & Materials Processing 2008, 4(3), 139-162. https://doi.org/10.3970/fdmp.2008.004.139

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 (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.

Cite This Article

Subramanian, P., Zebib, A. (2008). Solutocapillary Convection in Spherical Shells with a Receding and Deforming Interface. FDMP-Fluid Dynamics & Materials Processing, 4(3), 139–162.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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