Quasistatic model for the motion of a viscous capillary liquid drop
Abstract
In the modeling of a very viscous drop that moves freely under the influence of surface tension it may be convenient to omit the inertial terms. Thus, a quasistatic model is obtained for which an exact statement is given using Lagrange coordinates. At any time the velocity and pressure field fulfill the Stokes equations with natural boundary conditions of Neumann type. It is shown that the solution of this problem for fixed time exists and is defined up to rigid body motions. For the investigation of the timedependent problem a result on global invertibility of small C(sup 2)deformations is proved and the dependence of the solution on such deformations is investigated. A condition concerning this dependence is formulated under which the timedependent problem has a unique solution on a short interval of time. Finally, a study of the asymptotic behavior of globally existing solutions shows that (under resonable regularity presumptions) our model resembles the fact that the drop approaches the state of a ball of resting liquid.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 November 1993
 Bibcode:
 1993STIN...9523172P
 Keywords:

 Boundary Value Problems;
 Drops (Liquids);
 Incompressible Flow;
 Interfacial Tension;
 Lagrange Coordinates;
 Viscous Flow;
 Asymptotic Properties;
 Boundary Conditions;
 Matrix Methods;
 NavierStokes Equation;
 Time Dependence;
 Fluid Mechanics and Heat Transfer