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...

The theoretical basis of continuum percolation has changed greatly since its beginning as little more than an analogy with lattice systems. Nevertheless, there is yet no comprehensive theory of this field. A basis for such a theory is provided here with the introduction of the Potts fluid, a system of interacting s-state spins which are free to move in the continuum. In the s → 1 limit, the Pot...

Application of the lattice Boltzmann method (LBM) to invasion percolation of single component multiphase fluids in porous media offers an opportunity for more realistic modeling of the configurations and dynamics of liquid/vapor and liquid/solid interfaces. The complex geometry of connected paths in standard invasion percolation models arises solely from the spatial arrangement of simple elemen...

I use a previously introduced mapping between the continuum percolation model and the Potts fluid to derive a mean field theory of continuum percolation systems. This is done by introducing a new variational principle, the basis of which has to be taken, for now, as heuristic. The critical exponents obtained are β = 1, γ = 1 and ν = 0.5, which are identical with the mean field exponents of latt...

A new kind of percolation problem is described which differs from ordinary percolation theory in that it automatically finds the critical points of the system. The model is motivated by the problem of one fluid displacing another from a porous medium under the action of capillary forces, but in principle it may be applied to any kind of invasion process which proceeds along a path of least resi...

When a nonviscous liquid is injected into a porous medium already filled with a viscous fluid the system can be found in two different regimes: one where the dominant forces are of capillary nature and another where the viscous forces are predominant. The theoretical description of such system is based on two models: diffusion-limited aggregation (DLA) 1 and invasion percolation . DLA describes...

A revised phase diagram for water shows three distinct fluid phases. There is no continuity of liquid and gas, and no “critical point” on Gibbs’ density surface as hypothesized by van der Waals. A supercritical colloidal mesophase bounded by percolation transition loci separates supercritical liquid water and gas-phase steam. The water phase is bounded by a percolation transition (PA) of availa...