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 statistics) physics : the motion of particles on a lattice is constrained by basic conservation laws, such as the conservation of mass and momentum. This enables us to simulate the flow of a fluid obeying the Navier-Stokes equations and can be used to estimate the permeability or the coefficient of diffusion of porous media, in the present paper, we propose lattice gas models containing a suspension to simulate aggregation and filtration processes. The growth of aggregates occurs in many fields, such as in the solidification from a melt including various surface tension effects or the deposition of sediments. We use this model to simulate the filtration of suspensions through a tubutar-type filter.