Abstract Catalytic membranes can degrade gaseous pollutants to clean gas via a catalytic reaction to achieve green emissions. A catalytic membrane is a three scale porous medium. Membranes used in catalytic filters usually have thickness centimeters or millimeters, and consist of active (washcoat) particles, inert material and microscale, micron size, pores. The washcoat particles are porous material with nanoscale pores. The catalytic reactions are heterogeneous (surface reactions) and they occur on the surface of the nanopores. Obviously, simulations at fully resolved pore scale are not feasible, and upscaling techniques have to be applied. It is known that the same microscale problem can be upscaled to different macroscale equations depending on the characteristic numbers. In this paper we study the homogenization of reactive flow in the presence of strong absorption in the washcoat particles. Two reactive transport regimes are studied, in both the reaction dominates over the convection and the diffusion. Peclet’s number in the first one is of order 1, and in the second one it is proportional to the ratio of the thickness of the catalytic membrane and the characteristic length of the microscale pores. Two different upscaled equations are obtained, respectively. Direct numerical simulation at microscale is used to validate these derived macroscale equations.

中文翻译：

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通过具有壁集成催化剂的微粒过滤器的反应流放大的均化方法

摘要 催化膜可通过催化反应将气态污染物降解为清洁气体，实现绿色排放。催化膜是一种三级多孔介质。催化过滤器中使用的膜通常具有厘米或毫米的厚度，由活性（涂层）颗粒、惰性材料和微米级、微米级、孔组成。修补基面涂层颗粒是具有纳米级孔隙的多孔材料。催化反应是多相的（表面反应），它们发生在纳米孔的表面。显然，完全解析孔隙尺度的模拟是不可行的，必须应用放大技术。众所周知，相同的微观问题可以根据特征数升级为不同的宏观方程。在本文中，我们研究了在涂层颗粒中存在强吸收的情况下反应流的均质化。研究了两种反应传输机制，反应在对流和扩散中均占主导地位。第一个中的 Peclet 数为 1，第二个中它与催化膜的厚度和微孔特征长度的比值成正比。分别得到两个不同的放大方程。微观尺度的直接数值模拟用于验证这些导出的宏观方程。在第二个中，它与催化膜的厚度和微孔特征长度的比值成正比。分别得到两个不同的放大方程。微观尺度的直接数值模拟用于验证这些导出的宏观方程。在第二个中，它与催化膜的厚度和微孔特征长度的比值成正比。分别得到两个不同的放大方程。微观尺度的直接数值模拟用于验证这些导出的宏观方程。