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Percolation and invasion percolation in the presence of mobile impurities

We present a model for the solidification process of two immiscible fluids interacting repulsively with mobile impurities on a two-dimensional square lattice. In the space of the fluids and impurity concentrations, the phase diagram exhibits a critical curve separating a percolating from a non-percolating phase. Estimated values for the fractal dimension and the exponent β of the order parameter reveal that the critical exponents do not vary along this curve, i.e., they are independent of the impurity concentration. The universality class is that of the ordinary percolation. On the basis of the ideas of the dynamic epidemic and invasion percolation models, we also propose a model that may be relevant to cleaning porous media by fluid injection. An analysis of the acceptance profile, the fractal dimension and the gap exponent strongly indicate that this model belongs to the universality class of the ordinary invasion percolation.