TY - UNPB

T1 - Evaporation of binary liquids from a capillary tube

AU - Raju, Lijun Thayyil

AU - Diddens, Christian

AU - Rodríguez-Rodríguez, Javier

AU - Linden, Marjolein N. van der

AU - Zhang, Xuehua

AU - Lohse, Detlef

AU - Sen, Uddalok

PY - 2022/11/12

Y1 - 2022/11/12

N2 - 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 one-dimensional simulations show three evaporation regimes characterised by different time 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.

AB - 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 one-dimensional simulations show three evaporation regimes characterised by different time 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.

KW - physics.flu-dyn

KW - cond-mat.soft

U2 - 10.48550/arXiv.2211.06528

DO - 10.48550/arXiv.2211.06528

M3 - Preprint

BT - Evaporation of binary liquids from a capillary tube

PB - ArXiv.org

CY - Ithaca, NY

ER -