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The Quarterly Journal of Mechanics and Applied Mathematics 1959 12(3):265-279; doi:10.1093/qjmam/12.3.265
© 1959 by Oxford University Press
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A NOTE ON THE MOTION OF BUBBLES IN A HELE-SHAW CELL AND POROUS MEDIUM

SIR GEOFFREY TAYLOR and P. G. SAFFMAN

Exact solutions are presented for the steady motion of a symmetrical bubble through a parallel-sided channel in a Hele-Shaw cell containing a viscous liquid. The solutions also describe two-dimensional motion in a porous medium, since the two cases are mathematically analogous. It is shown that the solutions are not mathematically unique and a purely analytical criterion for specifying a particular solution is given. When the bubble is large, these particular solutions are such that the maximum width of the bubble is almost half that of the channel. Solutions are also presented for the motion of large asymmetric bubbles through the channel. The three-dimensional motion of bubbles in a porous medium of infinite extent is also considered briefly.


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