Mass transfer of solute in an oscillating flow in a two-dimensional channel

Abstract

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.