Creeping thermocapillary motion of a twodimensional deformable bubble  Existence theorem and numerical simulation
Abstract
The plane creeping freeboundary 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 stressstream 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 timedependent 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 twodimensional bubble driven by thermocapillarity, are presented.
 Publication:

European Journal of Mechanics B Fluids
 Pub Date:
 1992
 Bibcode:
 1992EJMF...11..741A
 Keywords:

 Capillary Flow;
 Digital Simulation;
 Existence Theorems;
 Marangoni Convection;
 Two Dimensional Flow;
 Viscous Flow;
 Bubbles;
 Incompressible Flow;
 Stream Functions (Fluids);
 Fluid Mechanics and Heat Transfer