Hele Shaw flows with a free boundary produced by the injection of fluid into a narrow channel

S. Richardson
1972 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 of
more » ... nts of the motion, which are of a purely geometric character. For sufficiently simple initial domains Do these allow the problem to be reduced to the solution of a finite system of algebraic equations. For more complex initial domains an approximation scheme leads to a similar system of equations to be solved.
doi:10.1017/s0022112072002551 fatcat:st7npc5kb5hdleu36sr6bi7ggi