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Hele Shaw flows with a free boundary produced by the injection of fluid into a narrow channel
Journal of Fluid Mechanics
A blob of Newtonian fluid is sandwiched in the narrow gap between two plane parallel surfaces so that, a t some initial instant, its plan-view occupies a simply connected domain Do. Further fluid, with the same material properties, is injected into the gap at some fixed point within Do, so that the blob begins to grow in size. The domain D occupied by the fluid at some subsequent time is to be determined. It is shown that the growth is controlled by the existence of an infinite number ofdoi:10.1017/s0022112072002551 fatcat:st7npc5kb5hdleu36sr6bi7ggi