Asymptotic modelling of spherical particle dissolution under a uniform flow

The dissolution of solid particles in liquids is commonly modeled as a diffusion-controlled process coupled with a moving boundary. While such models allow for analytical solutions under stationary conditions, they do not account for the effects of fluid motion that commonly arise in practical situations. In the present work, this classical model is extended by incorporating advective transport due to an imposed uniform flow. The dissolution process is formulated as a free boundary problem governed by an advection-diffusion equation in the exterior of the particle, coupled with a Stefan-type condition describing the interface motion. By introducing a non-dimensionalization, the problem is characterized by the Péclet number, which measures the relative importance of advection and diffusion. An asymptotic expansion in the Péclet number is employed to develop semi-analytical asymptotic solutions. The leading-order term recovers the diffusion controlled self-similar behavior, while higher-order corrections reveal how uniform flow modifies the concentration field and increases the dissolution rate. In particular, it is shown that the first non-zero flow-induced correction to the interface motion arises at second order, reflecting the inherently nonlinear nature of advection effects. The analysis provides a mathematically consistent extension of diffusion-only dissolution models and offers new insight into flow-induced dissolution mechanisms.