Percolation with trapping

A novel form of percolation is considered which is motivated by models of the displacement of one fluid by another from a porous medium. The physical idea is that if the displaced phase is incompressible, then regions of it which are surrounded by the displacing fluid become ‘trapped’ and cannot subsequently be invaded. We thus consider a new percolation process, ‘percolation with trapping’, in which one species (th.: displaced fluid) starts out at occupation fraction p = 1, but a s p decreases only the infinite (connected) cluster is depleted; the finite (disconnected) clusters remain the same as when they are first detached from the infinite cluster. It is argued that the critical behaviour of percolation with trapping can be understood in terms of ordinary percolation exponents. In particular, the size distribution of the finite clusters at the end of the process has the same power law behaviour as in ordinary percolation. Relations with the process of invasion percolation are discussed.