Analysis of the boundary conditions for a Hele--Shaw bubble

Journal Article · Sun Jul 01 00:00:00 EDT 1990 · Physics of Fluids A; (USA)

DOI:https://doi.org/10.1063/1.857610· OSTI ID:6761474

Burgess, D ^[1]; Foster, M R ^[2]

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1. Department of Physics, Ohio State University, Columbus, OH (USA)
2. Department of Aeronautical and Astronautical Engineering, Ohio State University, Columbus, OH (USA)

Effective boundary conditions are derived to be used with the classical Hele--Shaw equations in calculating the shape and motion of a Hele--Shaw bubble. The main assumptions of this analysis are that the displaced fluid wets the plates, and that the capillary number Ca and the ratio of gap width to characteristic bubble length {epsilon} are both small. In a small region at the sides of the bubble, it is found that the thin-film thickness scales with {epsilon}{sup 2/5} Ca{sup 4/5}, rather than the Ca{sup 2/3} scaling that is valid over most of the thin film above and below the bubble.

• DOE Contract Number: FG02-88ER13916
• OSTI ID: 6761474
• Journal Information: Physics of Fluids A; (USA), Vol. 2:7; ISSN 0899-8213
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
FLUID FLOW
BUBBLES
BOUNDARY CONDITIONS
CAPILLARY FLOW
EQUATIONS OF MOTION
PLATES
SHAPE
THIN FILMS
WETTABILITY
DIFFERENTIAL EQUATIONS
EQUATIONS
FILMS
PARTIAL DIFFERENTIAL EQUATIONS
640410* - Fluid Physics- General Fluid Dynamics