Multiscale Hybrid Modeling of Film Deposition Within Porous Substrates

A multiscale, hybrid computational framework for the deposition of films within porous substrates, is developed and applied to a prototype deposition reaction in the opposed reactant flow geometry. The developed model captures transport of reactants through the pores, homogeneous reaction of reagents producing an intermediate species, nucleation, and growth of the film as a moving boundary problem. The pore evolution is described using a capillary model. Adaptive mesh refinement is used to resolve length scales varying from nanometers to one millimeter. Nucleation is treated stochastically at the finest level, whereas transport and reaction at coarser levels are treated deterministically. Transport parameters chosen for these simulations correspond to the deposition of Pd films in porous alumina under supercritical CO ₂ conditions. The numerical results provide insight into the strategies that could be used to control their thickness, including confining thin films within substrates. For example, it has been found that the location of the deposit within the porous substrate is essentially determined by the relative concentrations of reagents on either side of the porous substrate, and the startup of the process. In addition, it is shown that the interplay of nucleation and growth kinetics determines the morphology and roughness of the deposit at short time scales.