Lattice Model of Sweeping Interface for Drying Process in Water-Granule Mixture

Based on the invasion percolation model, a lattice model for the sweeping interface dynamics is constructed to describe the pattern forming process by a sweeping interface upon drying the water-granule mixture. The model is shown to produce labyrinthine patterns similar to those found in the experiment[Yamazaki and Mizuguchi, J. Phys. Soc. Jpn. textbf{69} (2000) 2387]. Upon changing the initial granular density, resulting patterns undergo the percolation transition, but estimated critical exponents are different from those of the conventional percolation. Loopless structure of clusters in the patterns produced by the sweeping dynamics seems to influence the nature of the transition.