Homogenization-Based Modeling of a Dissolving Porous Medium Experiencing Both Microstructural and Macroscale Evolution

Abstract. Control of chemical release from soluble, or partially soluble, porous systems is important in a variety of applications, including drug release from pharmaceutical tablets. The underlying process involves complex interactions between dissolvable microparticles in the structure and a solvent, governed by factors like solute diffusion, dissolution reaction kinetics, and matrix porosity. We use asymptotic homogenization to develop a tractable model for chemical release from a three-dimensional porous domain consisting of soluble spherical microparticles. The effect of the evolving microstructure on release is captured in systematically-derived macroscale bulk diffusion and reaction terms. The model is analyzed and applied to a radially-symmetric spherical tablet. When drug particles near the tablet boundary dissolve completely, the tablet shrinks, initiating a moving boundary at the macroscale. A differential equation is derived to track the evolution of this boundary over time. We investigate how the physicochemical properties of a tablet affect its internal drug transport dynamics, mass release through its surface, and the time required to achieve complete dissolution. This study lays the groundwork to model more complex microstructural geometries and partially soluble systems, offering a promising framework to optimize release profiles from real drug delivery devices.