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首页> 外文期刊>Annali dell'Universita di Ferrara >Rigorous upscaling of the infinite adsorption rate reactive flow under dominant Peclet number through a pore
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Rigorous upscaling of the infinite adsorption rate reactive flow under dominant Peclet number through a pore

机译：在主要Peclet数下通过孔的无限吸附速率反应流的严格提升

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摘要

In this paper we present a rigorous derivation of the effective model for enhanced diffusion through a narrow and long 2D pore. The analysis uses the anisotropic singular perturbation technique. Starting point is a local pore scale model describing the transport by convection and diffusion of a reactive solute. The solute particles undergo an adsorption process at the lateral tube boundary, with high adsorption rate. The transport and reaction parameters are such that we have large, dominant Peclet number with respect to the ratio of characteristic transversal and longitudinal lengths (the small parameter ). We give a formal derivation of the model using the anisotropic multiscale expansion with respect to . Error estimates for the approximation of the physical solution, by the upscaled one, are presented in the energy norm as well as in L ∞ and L 1 norms with respect to the space variable. They give the approximation error as a power of and guarantee the validity of the upscaled model through the rigorous mathematical justification of the effective behavior for small .
机译：在本文中，我们提出了一个有效模型的严格推导，该模型用于增强通过狭窄和较长的二维孔的扩散。分析使用各向异性奇异摄动技术。起始点是局部孔隙尺度模型，描述了反应性溶质通过对流和扩散的迁移。溶质颗粒在侧管边界处以高吸附速率经历吸附过程。传输和反应参数使得相对于特征性横向长度和纵向长度之比，我们具有大的占主导地位的Peclet数（小的参数）。我们使用各向异性多尺度展开式相对于给出模型的形式推导。对于能量解以及关于空间的L ∞和L 1 范数，提出了按比例放大的物理解近似值的误差估计。变量。他们通过严格的数学模型证明了小机器人的有效行为，给出了近似误差的幂，并保证了放大模型的有效性。

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