van Gaalen R T, Diddens C, Wijshoff H M A, Kuerten J G M
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; Faculty of Science and Technology (TNW), University of Twente, P.O. Box 217, 7500 AE Enschede, the Netherlands.
J Colloid Interface Sci. 2021 Feb 15;584:622-633. doi: 10.1016/j.jcis.2020.10.057. Epub 2020 Oct 21.
Soluble surfactants in evaporating sessile droplets can cause a circulatory Marangoni flow. However, it is not straightforward to predict for what cases this vortical flow arises. It is hypothesized that the occurrence of Marangoni circulation can be predicted from the values of a small number of dimensionless parameters.
A numerical model for the drop evolution is developed using lubrication theory. Surfactant transport is implemented by means of convection-diffusion-adsorption equations. Results are compared to literature.
It is shown that stronger evaporation, slower adsorption kinetics and lower solubility of the surfactants all tend to increasingly suppress Marangoni circulation. These results are found to be consistent with both experimental and numerical results from literature and can explain qualitative differences in flow behavior of surfactant-laden droplets. Furthermore, diffusion also tends to counteract Marangoni flow, where bulk diffusion has a more significant influence than surface diffusion. Also, the formation of micelles is found to slightly suppress Marangoni circulation. Experimental results from literature, however, show that in some cases circulatory behavior is enhanced by micelles, possibly even resulting in qualitative changes in the flow. Potential explanations for these differences are given and extensions to the model are suggested to improve its consistency with experiments.
蒸发的固着液滴中的可溶性表面活性剂会导致循环性的马兰戈尼流。然而，预测这种涡旋流在何种情况下出现并非易事。据推测，马兰戈尼循环的发生可以根据少数无量纲参数的值来预测。
利用润滑理论建立了液滴演化的数值模型。表面活性剂的传输通过对流 - 扩散 - 吸附方程来实现。将结果与文献进行比较。
结果表明，更强的蒸发、更慢的吸附动力学以及表面活性剂更低的溶解度都倾向于越来越多地抑制马兰戈尼循环。这些结果与文献中的实验和数值结果一致，并且可以解释含表面活性剂液滴流动行为的定性差异。此外，扩散也倾向于抵消马兰戈尼流，其中体扩散比表面扩散的影响更显著。而且，发现胶束的形成会略微抑制马兰戈尼循环。然而，文献中的实验结果表明，在某些情况下，胶束会增强循环行为，甚至可能导致流动的定性变化。给出了这些差异的潜在解释，并建议对模型进行扩展以提高其与实验的一致性。
