Interface equation and viscosity contrast in Hele-Shaw flow

Journal Article · Wed May 20 00:00:00 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), Vol. 6:10; ISSN 0217-9792
• Country of Publication: United States
• Language: English

Related Subjects

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