ANALYSIS OF THE BOUNDARY-CONDITIONS FOR A HELE-SHAW BUBBLE

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 ∈ are both small. In a small region at the sides of the bubble, it is found that the thin-film thickness scales with ∈2/5 Ca4/5, rather than the Ca2/3 scaling that is valid over most of the thin film above and below the bubble. © 1990 American Institute of Physics.