Fluid wetting properties and the invasion of square networks

Etched networks of ducts are a commonly adopted microscopic model for theoretical and experimental studies of fluid invasion in porous media. We study changes in the morphology of the invaded region with the wetting properties of the invading fluid, described through the static contact angle θ, in the limit of quasistatic flow. A critical transition occurs at an angle ${\mathrm{\theta }}_{\mathit{c}}$. Above ${\mathrm{\theta }}_{\mathit{c}}$ (less wetting) the invasion pattern is fractal and below ${\mathrm{\theta }}_{\mathit{c}}$ (more wetting) it is compact and faceted. A characteristic length, the finger width, diverges as θ approaches ${\mathrm{\theta }}_{\mathit{c}}$ from above. The value of ${\mathrm{\theta }}_{\mathit{c}}$ decreases as the degree of disorder in the porous medium increases, but remains greater than 45°. We compare our results to simulations on different model porous media and to work on domain-wall motion in the random-field Ising model.