Evaporation of binary liquids from a capillary tube

TL;DR

This study investigates the evaporation dynamics of aqueous glycerol solutions in capillary tubes, identifying three regimes and developing an analytical model that captures the complex interplay of diffusion and advection effects.

Contribution

The paper introduces a simplified analytical model for evaporation in capillaries that accounts for different regimes and finite length effects, advancing understanding of multi-component liquid evaporation.

Findings

Identified three distinct evaporation regimes with different Sherwood number behaviors.

Developed an analytical expression relating Sherwood number to normalized time, matching observed regimes.

Extended the model to include advection effects, clarifying their significance in evaporation dynamics.

Abstract

Evaporation of multi-component liquid mixtures in confined geometries, such as capillaries, is crucial in applications such as microfluidics, two-phase cooling devices, and inkjet printing. Predicting the behaviour of such systems becomes challenging because evaporation triggers complex spatio-temporal changes in the composition of the mixture. These changes in composition, in turn, affect evaporation. In the present work, we study the evaporation of aqueous glycerol solutions contained as a liquid column in a capillary tube. Experiments and direct numerical simulations show three evaporation regimes characterised by different temporal evolutions of the normalised mass transfer rate (or Sherwood number, $Sh$), namely $Sh (\tilde{t}) = 1$, $Sh \sim 1/\sqrt{\tilde{t}}$, and $Sh \sim \exp\left(-\tilde{t}\right)$. Here $\tilde{t}$ is a normalised time. We present a simplistic analytical model which shows that the evaporation dynamics can be expressed by the classical relation $Sh = \exp \left( \tilde{t} \right) \mathrm{erfc} \left( \sqrt{\tilde{t}}\right)$. For small and medium $\tilde{t}$, this expression results in the first and second of the three observed scaling regimes, respectively. This analytical model is formulated in the limit of pure diffusion and when the penetration depth $\delta(t)$ of the diffusion front is much smaller than the length $L(t)$ of the liquid column. When $\delta \approx L$, finite length effects lead to $Sh \sim \exp\left(-\tilde{t}\right)$, i.e. the third regime. Finally, we extend our analytical model to incorporate the effect of advection and determine the conditions under which this effect is important. Our results provide fundamental insight into the physics of selective evaporation from a multi-component liquid column.