Fully coupled free-boundary evolution driven by local interfacial reaction

Develop a fully coupled free-boundary evolution for spherical inclusions in which the local normal velocity is determined directly by the interfacial reaction rather than by an averaged reaction law.

Background

The paper studies spherical inclusions whose radii evolve through an averaged adsorption–desorption law, while the fluid flow and concentration satisfy a coupled Stokes–reaction–diffusion–advection system. The authors note that their framework could accommodate more general finite-dimensional shape parameters, but a genuinely free-boundary formulation would require resolving the interfacial reaction pointwise and coupling it directly to the local normal velocity.

Such a formulation would go beyond scalar radius dynamics and would introduce substantially more complicated geometric and analytical effects, including fully coupled shape evolution and possible changes in the fluid domain topology. The authors identify this general problem as currently beyond the reach of their approach.