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Based on the invasion percolation model, a lattice model for the sweepinginterface dynamics is constructed to describe the pattern forming process by asweeping interface upon drying the water-granule mixture. The model is shown toproduce labyrinthine patterns similar to those found in the experiment[Yamazakiand Mizuguchi, J. Phys. Soc. Jpn. \textbf{69} (2000) 2387]. Upon changing theinitial granular density, resulting patterns undergo the percolationtransition, but estimated critical exponents are different from those of theconventional percolation. Loopless structure of clusters in the patternsproduced by the sweeping dynamics seems to influence the nature of thetransition.Comment: 6 pages, 7 figure

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