Kolliopoulos Panayiotis, Jochem Krystopher S, Lade Robert K, Francis Lorraine F, Kumar Satish
Department of Chemical Engineering and Materials Science , University of Minnesota , Minneapolis , Minnesota 55455 , United States.
Langmuir. 2019 Jun 18;35(24):8131-8143. doi: 10.1021/acs.langmuir.9b00226. Epub 2019 May 28.
Numerous applications rely upon capillary flow in microchannels for successful operation including lab-on-a-chip devices, porous media flows, and printed electronics manufacturing. Open microchannels often appear in these applications, and evaporation of the liquid can significantly affect its flow. In this work, we develop a Lucas-Washburn-type one-dimensional model that incorporates the effects of concentration-dependent viscosity and uniform evaporation on capillary flow in channels of a rectangular cross section. The model yields predictions of the time evolution of the liquid front down the length of the microchannel. For the case where evaporation is absent, prior studies have demonstrated better agreement between model predictions and experimental observations in low-viscosity liquids when using a no-slip rather than a no-stress boundary condition at the upper liquid-air interface. However, flow visualization experiments conducted in this work suggest the absence of a rigidified liquid-air interface. The use of the no-stress condition results in overestimation of the time evolution of the liquid front, which appears to be due to underestimation of the viscous forces from (i) the upper and front meniscus morphology, (ii) dynamic contact angle effects, and (iii) surface roughness, none of which are accounted for in the model. When high-viscosity liquids are considered, the large bulk viscosity is found to suppress these factors, resulting in better agreement between model predictions using the no-stress condition and experiments. Model predictions are also compared to prior experiments involving poly(vinyl alcohol) in the presence of evaporation by using the evaporation rate as a fitting parameter. Scaling relationships obtained from the model for the dependence of the final liquid-front position and total flow time on the channel dimensions and rate of uniform evaporation are found to be in good agreement with experimental observations.
许多应用的成功运行都依赖于微通道中的毛细流动，包括芯片实验室设备、多孔介质流动和印刷电子制造。这些应用中经常会出现开放微通道，液体的蒸发会显著影响其流动。在这项工作中，我们开发了一种卢卡斯-沃什伯恩型一维模型，该模型考虑了浓度依赖性粘度和均匀蒸发对矩形横截面通道中毛细流动的影响。该模型能够预测微通道长度方向上液面前沿的时间演化。对于不存在蒸发的情况，先前的研究表明，在低粘度液体中，当在上部液-气界面使用无滑移而非无应力边界条件时，模型预测与实验观测结果之间的一致性更好。然而，本工作中进行的流动可视化实验表明不存在固化的液-气界面。使用无应力条件会导致对液面前沿时间演化的高估，这似乎是由于（i）上部和前沿弯月面形态、（ii）动态接触角效应以及（iii）表面粗糙度所产生的粘性力被低估，而模型中并未考虑这些因素。当考虑高粘度液体时，发现较大的体粘度会抑制这些因素，从而使使用无应力条件的模型预测与实验结果之间的一致性更好。通过将蒸发速率作为拟合参数，还将模型预测与先前涉及聚乙烯醇在有蒸发情况下的实验进行了比较。从模型中获得的最终液面前沿位置和总流动时间对通道尺寸和均匀蒸发速率的依赖性的标度关系与实验观测结果高度一致。
