Marangoni circulation in evaporating droplets in the presence of soluble surfactants

R T van Gaalen; C Diddens; H M A Wijshoff; J G M Kuerten

doi:10.1016/j.jcis.2020.10.057

Marangoni circulation in evaporating droplets in the presence of soluble surfactants

J Colloid Interface Sci. 2021 Feb 15:584:622-633. doi: 10.1016/j.jcis.2020.10.057. Epub 2020 Oct 21.

Authors

R T van Gaalen¹, C Diddens², H M A Wijshoff³, J G M Kuerten⁴

Affiliations

¹ Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, the Netherlands.
² 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.
³ 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.
⁴ Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, the Netherlands. Electronic address: J.G.M.Kuerten@tue.nl.

PMID: 33129516
DOI: 10.1016/j.jcis.2020.10.057

Abstract

Hypothesis: 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.

Simulations: 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.

Findings: 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.

Keywords: Droplets; Evaporation; Lubrication approximation; Marangoni flow; Soluble surfactants.