  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.
