Dissolution morphologies of a disk under finite reaction rates: a conformal mapping approach

Reactive transport governs mineral dissolution in a wide range of geological and engineered systems, where the interplay between advection, diffusion, reaction kinetics and evolving geometry gives rise to complex interface morphologies. Even for simple initial shapes, dissolution under flow can produce asymmetric, time-dependent geometries as the shrinking solid continuously modifies the surrounding flow and concentration fields. In confined environments such as porous media or microfluidic systems, these feedbacks strongly influence transport pathways and reactive surface evolution. In this study, we investigate the coupled morphological and surface-area dynamics of a dissolving mineral using a two-dimensional conformal-mapping framework based on the Polubarinova–Galin equation. The formulation explicitly accounts for finite reaction kinetics and exploits the conformal invariance of potential flow and advection–diffusion transport to directly resolve the evolving solid–fluid interface. By systematically varying the Péclet and Damköhler numbers, we identify distinct advection–diffusion–reaction regimes and quantify their influence on dissolution morphologies. The results demonstrate how transport-reaction competition controls both interface geometry and surface availability, providing insight into experimentally observed dissolution patterns. This work extends previous infinite-reaction-rate models and offers a physically grounded framework for linking pore-scale dissolution dynamics to Darcy-scale reactive transport descriptions.