Crossover effects in chemical-dissolution phenomena: A renormalization-group study

We study the patterns formed when a reactive fluid with viscosity μ is injected into a two-dimensional porous medium filled with a nonreactive fluid with unit viscosity. We consider the ‘‘mass-transfer limit,’’ where the time scale of chemical reaction between the injected fluid and porous medium is much smaller than the time scale of reactant transport. Also, the surface tension between two fluids is ignored. We formulate three-parameter position-space-renormalization-group equations for this system. We find two crossovers: (i) from the first diffusion-limited-aggregation (DLA) fixed point to the Eden fixed point due to finite viscosity, and (ii) from the Eden to the second DLA due to chemical dissolution. The time evolution between patterns is independent of the injection rate following a trivial rescaling of time. These results are checked by direct numerical simulations. The second crossover is characterized by the crossover radius ${\mathit{r}}_{\mathit{c}}$∼${\mathit{v}}^{\mathrm{-}1/\mathrm{\beta }\mathrm{\phi }}$, where v is the total volume of the injected fluid, and β=3/2, φ≃1.63. We also study the effect of consumption of the reactant, and find that it stabilizes the pattern from a DLA fractal to a compact shape.