Open Access

ARTICLE

Diffusive Transfer between a Droplet and an Immiscible Oscillating Liquid in a Radial Hele-Shaw Cell

Ivan Karpunin^*, Denis Polezhaev

Laboratory of Vibrational Hydromechanics, Perm State Humanitarian Pedagogical University, Perm, 614990, Russia

* Corresponding Author: Ivan Karpunin. Email:

(This article belongs to the Special Issue: Non-Equilibrium Processes in Continuous Media)

Fluid Dynamics & Materials Processing 2025, 21(3), 543-553. https://doi.org/10.32604/fdmp.2025.061163

Received 18 November 2024; Accepted 23 January 2025; Issue published 01 April 2025

Abstract

An experimental study of the diffusive mass transfer between a droplet and an oscillating immiscible liquid in a horizontal axisymmetric Hele-Shaw cell is carried out. The liquid oscillates radially in the cell. The transverse size of the droplet exceeds the cell thickness. The viscosities of the droplet and the surrounding liquid are comparable. Relevant effort is provided to design and test an experimental setup and validate a protocol for determining the mass transfer rate of a solute in a two-liquid system. In particular, fluorescent dye Rhodamine B is considered as the solute. A critical comparison of the situations with and without oscillation is implemented. A procedure is introduced and validated to determine the molecular and effective diffusion coefficients through evaluation of the growth of the diffusion zone width over time. It is shown that, in the presence of the liquid oscillations, there is a significant increase in the width of the zone in which Rhodamine B is present compared to the reference case with no oscillations. The oscillatory flow leads to an intensification of the solute diffusion due to intense time-averaged flows inside the droplet and the surrounding liquid and oscillations of the drop itself. The study is of significant practical interest with particular relevance to typical processes for liquid-liquid extraction.

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