论文标题
从毛细管中蒸发二元液体
Evaporation of binary liquids from a capillary tube
论文作者
论文摘要
在诸如毛细血管等密闭几何形状中多组分液体混合物的蒸发在诸如微流体,两阶段冷却设备和喷墨打印等应用中至关重要。预测这种系统的行为变得具有挑战性,因为蒸发会触发混合物组成的复杂时空变化。这些成分的变化反过来影响蒸发。在目前的工作中,我们研究了毛细管中包含的甘油溶液的蒸发。实验和直接数值模拟显示了三个蒸发方案,其特征是归一化质量转移率(或舍伍德号,$ sh $)的不同时间变化,即$ sh(\ tilde {t})= 1 $,$ sh \ sim \ sim \ sim 1/\ sqrt {\ sqrt { \ exp \ left( - \ tilde {t} \ right)$。这里$ \ tilde {t} $是标准化时间。我们提出了一个简单的分析模型,该模型表明蒸发动力学可以通过经典关系$ sh = \ exp \ left(\ tilde {t} \ right)\ mathrm {erfc} \ left(\ sqrt {\ sqrt {\ tilde {\ tilde {tilde {tilde {tilde {t}} \ right)$。对于中小型$ \ tilde {t} $,此表达式分别导致三个观察到的缩放制度中的第一和第二。该分析模型以纯扩散的极限为准,当扩散前界的渗透深度$δ(t)$比液体柱的长度$ l(t)$小得多。当$δ\大约l $时,有限长度效应会导致$ sh \ sim \ exp \ left( - \ tilde {t} \ right)$,即第三条制度。最后,我们扩展了分析模型以纳入对流的效果,并确定这种效果重要的条件。我们的结果提供了从多组分液体柱中选择性蒸发物理学的基本见解。
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 $δ(t)$ of the diffusion front is much smaller than the length $L(t)$ of the liquid column. When $δ\approx L$, 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.