The effective diffusion of a solute in a rectangular two-dimensional channel is experimentally studied. We experimentally examine the effective diffusion of Rhodamine B dissolved in water oscillating in a rectangular Hele–Shaw cell. The concentration of Rhodamine B in water is measured by the intensity of its fluorescence emission. In particular, we consider two problems: (i) effective diffusion of solute in water oscillating in a two-dimensional rectangular channel (Hele–Shaw cell) and (ii) effective diffusion of solute in pores between monosized hard spheres randomly packed in a rectangular Hele–Shaw cell. It is revealed that the rate of solute mass transfer exceeds the molecular diffusion rate in both cases. It has been demonstrated that when water oscillates between parallel walls, diffusion is accelerated by Taylor dispersion with the effective diffusion coefficient Deff exceeding the molecular diffusion coefficient Dm by 1–2 orders of magnitude. The effective diffusion coefficient Deff depends only on the relative amplitude but not on the frequency of the fluid oscillations in the studied range of frequencies and amplitudes. When the fluid oscillates in the pores of the porous medium, solute transport is faster than in the case of Taylor dispersion. Here, the effective diffusion coefficient depends on both the frequency and amplitude of oscillations. The analysis shows that the experimental data obtained at various frequencies and amplitudes of oscillations are consistent with the relation Deff/Dm∼Pe2 (Pe is the Peclet number). We suggest that the enhanced solute mass transfer is associated with the time-averaged fluid flows that arise due to spatial heterogeneity of the amplitude of water oscillations in the pores between randomly packed hard spheres.

中文翻译：

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二维通道内振荡流中溶质的传质

通过实验研究了溶质在矩形二维通道中的有效扩散。我们通过实验检查了溶解在矩形 Hele-Shaw 池中振荡的水中的罗丹明 B 的有效扩散。水中罗丹明 B 的浓度通过其荧光发射的强度来测量。特别是，我们考虑两个问题：（i）二维矩形通道（Hele-Shaw cell）中振荡的水中溶质的有效扩散和（ii）随机填充在矩形中的单一尺寸硬球之间的孔隙中溶质的有效扩散赫勒-肖氏细胞。结果表明，在两种情况下，溶质传质速率都超过了分子扩散速率。研究表明，当水在平行壁之间振荡时，泰勒色散会加速扩散，有效扩散系数Deff超过分子扩散系数Dm 1~2个数量级。有效扩散系数 Deff 仅取决于相对振幅，而不取决于研究的频率和振幅范围内的流体振荡频率。当流体在多孔介质的孔隙中振荡时，溶质传输比泰勒色散的情况更快。这里，有效扩散系数取决于振荡的频率和幅度。分析表明，在不同频率和振荡幅度下获得的实验数据符合关系式Deff/Dm∼Pe2（Pe为佩克莱特数）。我们认为，增强的溶质传质与时间平均流体流动有关，而时间平均流体流动是由于随机填充的硬球之间的孔隙中水振荡幅度的空间异质性而产生的。