Particle-to-particle solvent diffusion in compacted granular systems

We develop a particle-to-particle solvent diffusion model for compacted granular systems that addresses long-standing gap in particle-to-particle transport models. The proposed effective mass transfer coefficient is a function of not only the size of the contact interface and the diffusion coefficient of solvent in each particle, but it is also a function of solvent-solid equilibrium mass concentration in each particle, through the equilibrium partition coefficient. The latter dependency being a salient aspect of the model that is sharp contrast to particle-to-particle effective heat transfer coefficients. The efficacy of the proposed method is borne out by studying granular packings with the same composition, namely a 50-50 binary mixture of two monodisperse systems comprised by elasto-plastic spheres with bonding strength, but with microstructures which are topologically different, namely a random packing, a bilayer, and core-shell structures. The method uses the particle mechanics approach to model consolidation and compaction of the granular system under large deformations, and it yields sorption kinetics results, namely solute concentration distributions and directional distribution of effective mass transfer coefficient, that strongly depend not only on mechanotransport properties of each component, but also on the topology of the microstructure formed during compaction of the 50-50 binary mixtures. Therefore, this work showcases that modeling approaches at the particle scale are of paramount relevance to understanding multi-functional, architectured granular material systems.