Island size distribution in stochastic simulations of the Saffman-Taylor instability

A stochastic numerical scheme is used to simulate radial motion of a fluid interface through a two-dimensional porous medium. The point at which the interface moves is chosen with a probability proportional to the local pressure gradient. The interface can intersect itself, enclosing islands of the original fluid. The number of islands of area s is found to scale approximately as s - alpha , where alpha lies in the range 2.07+or-0.7.