Creeping thermocapillary motion of a two-dimensional deformable bubble - Existence theorem and numerical simulation
Abstract
The plane creeping free-boundary flow of a viscous incompressible liquid occupying an infinite domain, bounded by a simple closed curve and driven solely by thermocapillary traction forces, is analyzed. We use the bianalytic stress-stream function and applying methods from the theory of analytic functions construct a Fredholm boundary integral equation for the distribution of normal velocity on the free boundary. Its solution leads to a nonlocal Cauchy problem for the time-dependent conformal mapping of the unit disk of a parametric plane onto the unbounded flow domain. The existence of solutions is proved for a class of analytic curves describing the free boundary position, and some numerical simulations of the evolution of the shape of a two-dimensional bubble driven by thermocapillarity, are presented.
- Publication:
-
European Journal of Mechanics, B/Fluids
- Pub Date:
- 1992
- Bibcode:
- 1992EuJMB..11..741A
- Keywords:
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- Capillary Flow;
- Digital Simulation;
- Existence Theorems;
- Marangoni Convection;
- Two Dimensional Flow;
- Viscous Flow;
- Bubbles;
- Incompressible Flow;
- Stream Functions (Fluids);
- Fluid Mechanics and Heat Transfer