临界与超临界稀相区中球形演化颗粒周围的反应流
Reactive Flow around Spherically Evolving Particles in Critical and Supercritical Dilute Regimes
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中文总结 AI 辅助
研究临界与超临界稀相区中大量演化球形颗粒周围的Stokes-反应-扩散-对流耦合系统，建立大时间适定性，推导不同情形下的定量均匀化极限并给出误差估计。
中文摘要 AI 辅助
我们研究三维区域中耦合的Stokes-反应-扩散-对流系统，该区域被大量演化球形包裹体贯穿，当$α\in(1,3]$时，包裹体半径量级为$\varepsilon^α$。包裹体中心间距量级为$\varepsilon$，但不假设其构成周期晶格。包裹体通过界面吸附-解吸机制生长或收缩，因此几何演化与Stokes-反应-扩散-对流系统相耦合。我们首先针对足够小的$\varepsilon$，在任意大的时间区间上建立了适定性。随后，我们借助描述包裹体空间分布与尺寸的极限经验测度，推导了定量均匀化极限。经验测度的演化由半径变量下的连续性方程控制，其收敛性由$2$-Wasserstein距离刻画。在临界情形$α=3$下，Stokes系统收敛为Brinkman系统，而非零浓度边界层会修正反应-扩散-对流方程的微观交换律。当$α\in(1,3)$时，极限为Darcy型，且原交换律得以保留。所得均匀化结果是定量的，给出了显式误差估计。
英文摘要
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 $\varepsilon^α$ for $α\in(1,3]$. Their centers are separated on the order of $\varepsilon$ 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 $\varepsilon$. 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 $α\in(1,3)$, the limit is of Darcy type and the original exchange law is retained. The homogenization results are quantitative and provide explicit error estimates.
发表机构
- University of Regensburg（雷根斯堡大学）
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