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Two-phase displacement in Hele Shaw cells: Theory. (English) Zbl 0567.76092
A theory of the slow displacement of one fluid by another in a Hele-Shaw cell is presented. Assuming that the displaced fluid wets the walls of the gap, the solution is developed as an asymptotic double expansion in the (assumed) small parameters Ca (the capillary number) and \(\epsilon\) (the ratio of gap width to transverse characteristic length). The expansion in \(\epsilon\) is found to be uniform while that in Ca is not; the small-Ca limit has been formulated as a matched asymptotic expansion. The asymptotic form of the jump conditions on the moving-boundary is derived.
Reviewer: D.Poliševski

MSC:
76T99 Multiphase and multicomponent flows
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References:
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