Scholarlink

<p>The diffusion of a species undergoing a linear heterogeneous reaction at the solid–fluid interface in a porous medium leads, at the macroscopic scale, to a diffusion law characterized by an effective diffusion coefficient and a reactive source term. These macroscopic quantities can be rigorously derived using upscaling techniques such as the periodic homogenization technique or the volume averaging method. In both approaches, the effective diffusion coefficient and the reactive term can be obtained by solving closure problems defined within a representative unit cell of the porous structure. A discrepancy between the two approaches was reported in Bourbatache et al. (Acta Mech 231:2011–2031, 2020) and Valdés-Parada and Lasseux (Acta Mech 236:1697–1717, 2025), specifically regarding how the effective diffusion coefficient evolves with the reaction rate. In this work, we propose an alternative method to compute these coefficients, based on Brownian random walks of particles that interact with solid surfaces according to a prescribed reaction rate. Starting from a given particle distribution, the method of moments is applied to extract the effective diffusion coefficient appearing in the macroscopic model. Numerical results show excellent agreement with those obtained from the homogenization technique, confirming the predicted dependence of the effective diffusion coefficient on the reaction rate.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Diffusion/heterogeneous reaction in porous media: Brownian random walk approach

  • 期刊论文

  • 发表日期：

    2026年4月10日

查看全文
  • Christian Moyne,
  • Tien Dung Le,
  • Mohamed Khaled Bourbatache,
  • Olivier Millet

摘要

The diffusion of a species undergoing a linear heterogeneous reaction at the solid–fluid interface in a porous medium leads, at the macroscopic scale, to a diffusion law characterized by an effective diffusion coefficient and a reactive source term. These macroscopic quantities can be rigorously derived using upscaling techniques such as the periodic homogenization technique or the volume averaging method. In both approaches, the effective diffusion coefficient and the reactive term can be obtained by solving closure problems defined within a representative unit cell of the porous structure. A discrepancy between the two approaches was reported in Bourbatache et al. (Acta Mech 231:2011–2031, 2020) and Valdés-Parada and Lasseux (Acta Mech 236:1697–1717, 2025), specifically regarding how the effective diffusion coefficient evolves with the reaction rate. In this work, we propose an alternative method to compute these coefficients, based on Brownian random walks of particles that interact with solid surfaces according to a prescribed reaction rate. Starting from a given particle distribution, the method of moments is applied to extract the effective diffusion coefficient appearing in the macroscopic model. Numerical results show excellent agreement with those obtained from the homogenization technique, confirming the predicted dependence of the effective diffusion coefficient on the reaction rate.