Interface equation and viscosity contrast in Hele-Shaw flow

Journal Article · Wed May 20 04:00:00 EDT 1992 · International Journal of Modern Physics B; (United States)

DOI:https://doi.org/10.1142/S0217979292000827· OSTI ID:7286059

Casademunt, J; Jasnow, D ^[1]; Hernandez-Machado, A ^[2]

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1. Pittsburgh Univ., PA (United States). Dept. of Physics and Astronomy
2. Dept. d'Estructura i Constituents de la Materia, Univ. de Barcelona, Diagonal 647, E-08028-Barcelona (ES)

In this paper, the authors derive an integro-differential equation for the evolution of the interface separating two immiscible viscous fluids in a Hele-Shaw cell with a channel geometry, for arbitrary viscosity contrast. The authors' equation differs from a previous one obtained by a vortex-sheet formulation of the problem, in that the normal component of the interface velocity is formally decoupled from the gauge-dependent tangential part. The result is thus a closed integral equation for the normal velocity. The authors briefly comment on the advantages of such a formulation and implement an alternative computational algorithm based on it. Preliminary numerical results confirm a highly inefficient finger competition in the zero viscosity contrast limit.

• OSTI ID: 7286059
• Journal Information: International Journal of Modern Physics B; (United States), Journal Name: International Journal of Modern Physics B; (United States) Vol. 6:10; ISSN 0217-9792; ISSN IJPBE
• Country of Publication: United States
• Language: English

Related Subjects

665000* -- Physics of Condensed Matter-- (1992-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ALGORITHMS
DATA
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID FLOW
FLUIDS
INFORMATION
INTEGRAL EQUATIONS
INTERFACES
MATHEMATICAL LOGIC
NUMERICAL DATA
VELOCITY
VISCOUS FLOW
VORTICES