EXACT SOLUTIONS FOR THE GROWTH OF FINGERS FROM A FLAT INTERFACE BETWEEN TWO FLUIDS IN A POROUS MEDIUM OR HELE-SHAW CELL

Abstract

A family of exact solutions of the equations of motion for the two-dimensional unsteady motion of a viscous liquid driven by a fluid of negligible viscosity in a porous medium or Hele-Shaw cell is obtained. The solutions represent the growth of a particular disturbance of a state of uniform motion and its development into a motion in which long fingers of arbitrary width and spacing penetrate the viscous liquid.