Kinetics of multilayer adsorption: Monte Carlo studies of models without screening

New 1D and 2D lattice models are introduced to study irreversible multilayer adsorption processes observed in recent experiments in colloid systems. Kinetics of deposition without screening (with no overhangs) is investigated by Monte Carlo simulations. The approach to the jamming coverage in each layer is asymptotically exponential. The jamming coverages approach the infinite-layer limiting value according to a power law, reminiscent of critical phenomena, with no length scale, and with exponent universality within the accuracy of the numerical data.