Dynamic scaling of the interface in a diffusive front

A model is introduced to simulate irreversible wetting in a two-dimensional lattice system in which a fixed number of carriers, each diffusing from the source, wet the dry sites on their trail. The authors find that the propagation of the front of the wet phase is diffusive. The interface width is found to increase as a power of the average height with the exponent beta approximately=0.74. In a system of finite size L the width saturates to a constant value in the long time limit. The saturated interface width scales as L alpha with alpha approximately=1.