  A physical model for the simulation ink/paper interaction at the mesoscopic
scale is developed. It is based on the modified Ising model, and is generalized
to consider the restriction of the finite-volume of ink and also its dynamic
seepage. This allows the model to obtain the ink distribution within the paper
volume. At the mesoscopic scale, the paper is modeled using a discretized fiber
structure. The ink distribution is obtained by solving its equivalent
optimization problem, which is solved using a modified genetic algorithm, along
with a new boundary condition and the quasi-linear technique. The model is able
to simulate the finite-volume distribution of ink.
