Scaling of diffusion-driven displacing patterns in porous media

We present visualization experiments in etched-glass micromodels to identify micromechanics of drying processes. We develop a scaling theory which shows that above a certain critical length, the front dynamics change from those corresponding to invasion percolation to those of self-affine growth. The latter is characterized by gradient percolation in a stabilizing gradient, which predicts a front width that scales with the (appropriately modified) capillary number of the process. The drying pattern is thus self-similar only within a finite region (the front width) but remains compact further downstream. A stability analysis of the front dynamics is also used to support the percolation-to-compact transition. The scaling theory is used to determine this characteristic length scale in terms of the process parameters. The theory is in agreement with earlier experiments by Shaw[1].