# Accession Number:

## ADA242984

# Title:

## Evolution of Hele Shaw Interface for Small Surface Tension

# Descriptive Note:

## Contractor rept.,

# Corporate Author:

## INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

# Personal Author(s):

# Report Date:

## 1991-11-01

# Pagination or Media Count:

## 64.0

# Abstract:

For time evolution of a Hele-Shaw interface described by a conformal map zzeta,t that maps a unit circle or semi-circle in the zera plane into the viscous fluid flow region in the physical z-plane, we present results on the motion of singularities outside the unit circle. For zero surface tension, we extend earlier results to show that for any initial condition, each singularity of zzeta,t present initially in the absolute value of zeta 1 continually approaches the interfacial boundary the absolute value of zeta 1 without any change of form. However, depending on the singularity type, it may or may not impinge the absolute value of zeta 1 in finite time. Under some assumptions, we give analytical evidence to suggest that the ill-posed problem in the physical domain the absolute value of zeta or 1 can be imbedded in a well- posed problem in the absolute value of zeta or 1. We present a numerical scheme to calculate such solutions. For each initial singularity of certain type, which in the absence of surface tension would have merely moved to a new location zeta sub s t at time t from an initial zeta sub s O, we find an immediate transformation of the singularity structure for nonzero surface tension Beta however, for O Beta 1, surface tension effects on this singularity are limited to a small inner neighborhood of zeta sub s t when t 1Beta.

# Descriptors:

# Subject Categories:

- Numerical Mathematics
- Fluid Mechanics