Plane stokes flow driven by capillarity on a free surface: Overview and status
This article summarizes some recent work on the creeping viscous incompressible plane flow in a region, bounded by a simple smooth closed curve and driven solely by surface tension. Such problems are self-contained in that the applied tractions are intrinsic in the geometry. The objective is to determine exactly the time evolution of the shape of the region. The problems are fundamentally nonlinear due to the large changes in shape, and it is emphasized that no mathematical approximations are made. For finite regions, the shape in the complex z-plane is described in terms of a time-dependent conformal mapping function {Omega}({zeta}, t) on the fixed region {vert bar} {zeta} {vert bar} {le} 1 of the complex {zeta}-plane. In practice, it has been necessary to conjecture an explicit parametric form {Omega}({zeta};{alpha}{sub 1}(t), {alpha}{sub 2}(t), {hor ellipsis}) whose validity must be verified using the shape- evolution equation. Suitable parameterizations are not always obvious. When the conjectured form holds and the equations can be solved, the evolution of the shape with time is obtained in simple, exact and closed form except for the value of the time, which requires a mere quadrature. Internal velocity and stress fields can be obtained.
- Research Organization:
- Lawrence Livermore National Lab., CA (United States)
- Sponsoring Organization:
- USDOE; USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 5597423
- Report Number(s):
- UCRL-JC-103243-Rev.2; CONF-900684-1-Rev.2; ON: DE92011469
- Resource Relation:
- Conference: 5. international colloquium on free boundary problems: theory and applications, Montreal (Canada), 13-22 Jun 1990
- Country of Publication:
- United States
- Language:
- English
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