In the talk we present recently published results (with F.P. Medina) on a 2x2 system of conservation laws which we prove to be strictly hyperbolic. Usually the data for such a system, i.e., two nonlinear functions called adsorption isotherms, are given as algebraic expressions, but this approach has several limitations which we will overview. In our approach we find the isotherms using computational (lattice) models from statistical mechanics: either following a Mean Field approximation or using the Metropolis algorithm. This approach, originally proposed by Monson et al, is self-consistent, but the challenge, beside the implementation, is to analyze the qualitative properties of the resulting bivariate isotherms. As part of the talk we will show also some animations and movies demonstrating the porescale and lattice computations.