Periodically driven flows are known to generate nonzero, time-averaged fluxes of heat or solute species, due to the interactions of out-of-phase velocity and temperature/concentration fields, respectively. Herein, we investigate such transport (a form of the well-known Taylor-Aris dispersion) in the gap between two parallel plates, one of which oscillates vertically, generating a time-periodic squeeze flow of either a Newtonian or a Maxwell fluid. Using the method of multiple time-scale homogenization, the mass/heat balance equation describing transport in this flow is reduced to a one-dimensional advection-diffusion-reaction equation. This result indicates three effective mechanisms in the mass/heat transfer in the system: an effective diffusion that spreads mass/heat along the concentration/temperature gradient, an effective advective flux, and an effective reaction that releases or absorbs mass/heat—in the time-averaged frame. Our results demonstrate that there exist resonant modes under which the velocity peaks when the dimensionless plate oscillation frequency (embodied by the Womersley number, the ratio of the transient inertia to viscous forces) approaches specific values. As a result, transport in this flow is significantly influenced by the dimensionless frequency. On the one hand, the effective, time-averaged dispersion coefficient is always larger than the molecular diffusivity and is sharply enhanced near resonance. The interaction between the fluid elasticity and the oscillatory forcing enhances the efficiency of transport in the system. On the other hand, the identified effective advection and reaction mechanisms may transport mass/heat from regions of high concentration/temperature to those of low concentration/temperature, or vice versa, depending on the value of the dimensionless frequency. Ultimately, it is shown that the oscillatory squeeze flow can either enhance or diminish transport, depending on the interplay of these three effective (homogenized) mechanisms.

中文翻译：

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粘弹性流体的振荡挤压流中的时间平均传输

已知由于分别异相速度和温度/浓度场的相互作用，周期性驱动的流会生成非零时均热或溶质物种通量。本文中，我们研究了在两个平行板之间的间隙中的这种传输（众所周知的泰勒-阿里斯色散的一种形式），其中一个平行板垂直振荡，产生牛顿流体或麦克斯韦流体的时间周期挤压流。使用多重时标均质化方法，描述该流中传输的质/热平衡方程式简化为一维对流扩散反应方程式。该结果表明了系统中质量/热传递的三个有效机制：沿浓度/温度梯度扩散质量/热的有效扩散，有效对流，以及在时间平均框架内释放或吸收质量/热量的有效反应。我们的结果表明，当无量纲板的振动频率（由Womersley数表示，瞬态惯性与粘性力之比）接近特定值时，存在共振模式，速度达到峰值。结果，该流中的传输受到无量纲频率的显着影响。一方面，有效的时间平均色散系数始终大于分子扩散系数，并且在共振附近会急剧增强。流体弹性和振荡力之间的相互作用增强了系统中的传输效率。另一方面，取决于无量纲频率的值，所识别的有效对流和反应机理可以将质量/热量从高浓度/温度的区域传输到低浓度/温度的区域，反之亦然。最终，根据这三种有效（均质）机制的相互作用，表明了振荡挤压流可以增强或减少运输。