Reactive Flow around Spherically Evolving Particles in Critical and Supercritical Dilute Regimes
Abstract
We study a coupled Stokes-reaction-diffusion-advection system in a three dimensional domain perforated by a large number of evolving spherical inclusions with radii of order εα for α∈(1,3]. Their centers are separated on the order of ε but are not assumed to form a periodic lattice. The inclusions grow or shrink through an interfacial adsorption-desorption mechanism, so that the evolution of the geometry is coupled to the Stokes-reaction-diffusion-advection system. We first establish well-posedness on arbitrary large time intervals for sufficiently small ε. We then derive quantitative homogenization limits in terms of the limiting empirical measure describing the spatial distribution and size of the inclusions. Its evolution is governed by a continuity equation in the radius variable, and the convergence of the empirical measures is controlled in the $2$-Wasserstein distance. In the critical case, α=3, the Stokes system converges to a Brinkman system, while non-vanishing concentration boundary layers modify the microscopic exchange law for the reaction-diffusion-advection equation. For α∈(1,3), the limit is of Darcy type and the original exchange law is retained. The homogenization results are quantitative and provide explicit error estimates.
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BibTeX
@misc{eden2026reactive,
title = {{Reactive Flow around Spherically Evolving Particles in Critical and Supercritical Dilute Regimes}},
author = {Michael Eden and Richard M. Höfer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.28489},
eprint = {2608.28489},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28489},
}
RIS
TY - UNPB
TI - Reactive Flow around Spherically Evolving Particles in Critical and Supercritical Dilute Regimes
AU - Michael Eden
AU - Richard M. Höfer
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2608.28489
UR - https://arxiv.org/abs/2608.28489
AB - We study a coupled Stokes-reaction-diffusion-advection system in a three dimensional domain perforated by a large number of evolving spherical inclusions with radii of order ε^α for α∈(1,3]. Their centers are separated on the order of ε but are not assumed to form a periodic lattice. The inclusions grow or shrink through an interfacial adsorption-desorption mechanism, so that the evolution of the geometry is coupled to the Stokes-reaction-diffusion-advection system. We first establish well-posedness on arbitrary large time intervals for sufficiently small ε. We then derive quantitative homogenization limits in terms of the limiting empirical measure describing the spatial distribution and size of the inclusions. Its evolution is governed by a continuity equation in the radius variable, and the convergence of the empirical measures is controlled in the $2$-Wasserstein distance. In the critical case, α=3, the Stokes system converges to a Brinkman system, while non-vanishing concentration boundary layers modify the microscopic exchange law for the reaction-diffusion-advection equation. For α∈(1,3), the limit is of Darcy type and the original exchange law is retained. The homogenization results are quantitative and provide explicit error estimates.
ER -