© 1993 by Oxford University Press
CAPILLARITY-DRIVEN PLANE STOKES FLOW EXTERIOR TO A PARABOLA
( Chemistry and Materials Science Department, Lawrence Livermore National Laboratory Livermore, California 94550, USA )
The free creeping viscous incompressible plane flow of the infinite region exterior to a parabola, driven solely by surface tension, is analysed. The rigid-body motion is arbitrary, so the velocity at the apex set to zero. With no further conditions, the flow is incompletely determined. There is a basic field that gives a surface velocity tangent to the surface of the parabola and directed towards its apex. This would leave the boundary unchanging and stationary. Superimposed is a flow involving an arbitrary constant. When this is real, the shape evolves through a continuous sequence of parabolas of changing apex curvature, changing at a rate determined by supplemental boundary conditions. These must be consistent with the specified conditions on the parabola. It appears difficult to devise a realistic far field that would ‘select’ a particular parabola.