A regular perturbation approach to surface tension driven flows
Abstract
Surface tension induced convection is analyzed in a liquid bridge held between two parallel, coaxial solid disks under microgravity conditions. The surface tension gradient is produced by a small temperature gradient parallel to the undisturbed surface. A mathematic regular perturbation method is used, based on the small parameter, epsilon, which measures the deviation of the imposed temperature field from its mean value. The first order velocity field is given by a Stokestype problem with simple boundary conditions. The first order temperature field is imposed by end disks on a liquid bridge immersed in a nonconductive fluid; the second order temperature field, which accounts for the convective effects, has three components, one due to bulk motion and the other two due to the distortion of the free surface. The dimensionless axial velocity at the free surface is shown to decrease when the slenderness of the bridge increases, because of the dragging effects of viscosity; annular cross section bridges are used to enhance convection. The critical slenderness of the bridge is shown to correspond to static conditions. Finally, the overall heat transfer enhancement at the end disks for an imposed temperature field is small, unless this temperature field is symmetrical.
 Publication:

Rome International Astronautical Federation Congress
 Pub Date:
 September 1981
 Bibcode:
 1981rome.iafcS....D
 Keywords:

 Convection;
 Fluid Mechanics;
 Interfacial Tension;
 Perturbation Theory;
 Small Perturbation Flow;
 Boundary Conditions;
 Boundary Value Problems;
 Free Boundaries;
 Microgravity Applications;
 Space Commercialization;
 Temperature Distribution;
 Temperature Gradients;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer