Abstract The present problem is on the mass transport process through an annular tube, where a chemical species is discharged into a flowing stream driven by a harmonic pressure gradient. The species may undergo linear reversible and irreversible reactions at the outer boundary of the annulus. Also, two non-linear chemical decay are assumed within the bulk flow and at the outer wall. However, the degree of the non-linearity of these reactions are different. The problem is analyzed based on the three-time scale, and thus the homogenization method is utilized to average the two-dimensional mass transport problem. We establish analytical expressions for different transport coefficients in terms of rigorous mathematical calculations. The results exhibit some paradoxical behavior with the radius ratio. The transport coefficients linearly increase with the associated reactions rate but decrease with the wall absorption rate.

中文翻译：

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多重反应对通过环空的脉动流传输系数的影响

摘要 当前的问题是关于通过环形管的传质过程，其中化学物质被排放到由谐波压力梯度驱动的流动流中。物质可以在环的外边界处经历线性可逆和不可逆反应。此外，假设在整体流内和外壁处有两种非线性化学衰变。然而，这些反应的非线性程度不同。该问题基于三个时间尺度进行分析，从而利用均质化方法对二维质量运输问题进行平均。我们根据严格的数学计算建立了不同输运系数的解析表达式。结果显示出一些与半径比存在矛盾的行为。