Effect of surface roughness on the bulk properties of simulated porous media

We generate a porous structure by computer simulation in (2+1) dimension using a bidisperse ballistic deposition model. Particles of two different sizes are deposited randomly creating a porous bulk bounded by a highly irregular upper surface. The structure of the interface is connected to the homogeneity of the bulk produced. In this paper we study the development of the dynamic interface as a function of the proportion of the two types of particles. F is the probability of choosing the larger grains and 1-F that of the smaller grains. In the limit F=0, the model is identical to the random deposition (RD) model whereas in the limit F=1, the model is similar, but not identical to the ballistic deposition (BD) model. For all F values greater than 0, the growth exponent β changes across a transition time tr. tr increases asymptotically from 0 to infinity as F tends to 0, from 1. The roughness and dynamic exponents are also determined as a function of F. We conclude that to simulate a homogeneous medium with a uniform porosity throughout, it is necessary to grow the system for a time t>tr.