In this work, we carry out a theoretical analysis of the mass transport rate through a long microcapillary, with a reactive wall, connecting two reservoirs with different concentrations of some electro-neutral solute, caused by an oscillatory electroosmotic flow of a Jeffreys fluid. The mass transport enhancement relative to that caused only by molecular diffusion is found to be a function of the following dimensionless parameters: the angular Reynolds number Rω; the Deborah numbers De1 and De2, associated with the relaxation and retardation times, respectively; the Schmidt number Sc; the Damkohler number Da; the partition number σ; the tidal displacement ΔZ; and the ratio between the radius of the microcapillary and the Debye length κ. We find that for a viscoelastic fluid, there exists a resonant behavior of the mass transfer rate when the angular Reynolds number assumes specific values. In this context, we evidence that the interaction between the fluid elasticity and the oscillatory character of the flow enhances the mass transfer rate up to several orders of magnitude compared with that caused by an oscillatory electroosmotic flow of a Newtonian fluid. We also found that the microcapillary wall’s reactive characteristics, manifested through the Damkohler number and the dimensionless partitioning coefficient, could enhance or diminish the mass transfer rate depending on the interplay of the other dimensionless parameters involved in the analysis.

中文翻译：

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振荡电渗流对具有可逆壁反应的微毛细管中传质过程的流体动力学流变学影响

在这项工作中，我们对通过长微毛细管的质量传输速率进行了理论分析，该微毛细管具有反应壁，连接两个具有不同浓度的一些电中性溶质的水库，由 Jeffreys 流体的振荡电渗流引起。发现相对于仅由分子扩散引起的传质增强是以下无量纲参数的函数：角雷诺数 Rω；Deborah 数 De1 和 De2，分别与弛豫时间和延迟时间相关；施密特数 Sc；Damkohler 数 Da；分区数σ；潮汐位移ΔZ；以及微毛细管半径与德拜长度 κ 之间的比率。我们发现对于粘弹性流体，当角雷诺数取特定值时，存在传质速率的共振行为。在这种情况下，我们证明流体弹性与流动的振荡特性之间的相互作用与由牛顿流体的振荡电渗流引起的传质速率相比，将传质速率提高了几个数量级。我们还发现，通过 Damkohler 数和无量纲分配系数表现出来的微毛细管壁的反应特性可以根据分析中涉及的其他无量纲参数的相互作用来提高或降低传质速率。我们证明，与牛顿流体的振荡电渗流引起的传质速率相比，流体弹性和流动的振荡特性之间的相互作用将传质速率提高了几个数量级。我们还发现，通过 Damkohler 数和无量纲分配系数表现出来的微毛细管壁的反应特性可以根据分析中涉及的其他无量纲参数的相互作用来提高或降低传质速率。我们证明，与牛顿流体的振荡电渗流引起的传质速率相比，流体弹性和流动的振荡特性之间的相互作用将传质速率提高了几个数量级。我们还发现，通过 Damkohler 数和无量纲分配系数表现出来的微毛细管壁的反应特性可以根据分析中涉及的其他无量纲参数的相互作用来提高或降低传质速率。