van Gaalen R T, Wijshoff H M A, Kuerten J G M, Diddens C
Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, the Netherlands.
Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, the Netherlands; Canon Production Printing Netherlands B.V., P.O. Box 101, 5900 MA Venlo, the Netherlands.
J Colloid Interface Sci. 2022 Sep 15;622:892-903. doi: 10.1016/j.jcis.2022.04.146. Epub 2022 Apr 29.
Thermal Marangoni flow in evaporating sessile water droplets is much weaker in experiments than predicted theoretically. Often this is attributed to surfactant contamination, but there have not been any in-depth analyses that consider the full fluid and surfactant dynamics. It is expected that more insight into this problem can be gained by using numerical models to analyze the interplay between thermal Marangoni flow and surfactant dynamics in terms of dimensionless parameters.
Two numerical models are implemented: one dynamic model based on lubrication theory and one quasi-stationary model, that allows for arbitrary contact angles.
It is found that insoluble surfactants can suppress the thermal Marangoni flow if their concentration is sufficiently large and evaporation and diffusion are sufficiently slow. Soluble surfactants, however, either reduce or increase the interfacial velocity, depending on their sorption kinetics. Furthermore, insoluble surfactant concentrations that cause an order 0.1% surface tension reduction are sufficient to reduce the spatially averaged tangential flow velocity at the interface by a factor 100. For larger contact angles and smaller droplets this required concentration is larger (typically <1% surface tension reduction). The numerical models are mutually validated by comparing their results in cases where both are valid.
在实验中，蒸发的静止水滴中的热马兰戈尼流比理论预测的要弱得多。通常这归因于表面活性剂污染，但尚未有任何深入分析考虑完整的流体和表面活性剂动力学。预计通过使用数值模型根据无量纲参数分析热马兰戈尼流与表面活性剂动力学之间的相互作用，可以更深入地了解这个问题。
实现了两个数值模型：一个基于润滑理论的动态模型和一个允许任意接触角的准静态模型。
发现不溶性表面活性剂如果浓度足够大且蒸发和扩散足够慢，就可以抑制热马兰戈尼流。然而，可溶性表面活性剂根据其吸附动力学，要么降低要么增加界面速度。此外，导致表面张力降低0.1%量级的不溶性表面活性剂浓度足以使界面处的空间平均切向流速降低100倍。对于更大的接触角和更小的液滴，所需浓度更大（通常表面张力降低<1%）。通过比较两个数值模型在都有效的情况下的结果，对它们进行了相互验证。
