Many structures are the result of complex interactions between various
components. A simple way to simulate these interactions is to build a
physical model such as the lattice gas proposed in statistical physic
s : the motion of particles on a lattice is constrained by basic conse
rvation laws, such as the conservation of mass and momentum. This enab
les us to simulate the flow of a fluid obeying the Navier-Stokes equat
ions and can be used to estimate the permeability or the coefficient o
f diffusion of porous media. In the present paper, we propose lattice
gas models containing a suspension to simulate aggregation and filtrat
ion processes. The growth of aggregates occurs in many fields, such as
in the solidification from a melt including various surface tension e
ffects or the deposition of sediments. We use this model to simulate t
he filtration of suspensions through a tubular-type filter.