Steady moving contact line of water over a no-slip substrate
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https://doi.org/10.1140/epjst/e2020-900280-9
THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS
Regular Article
Steady moving contact line of water over a no-slip substrate Challenges in benchmarking phase-field and volume-of-fluid methods against molecular dynamics simulations Uˇgis L¯acis1,a , Petter Johansson2 , Tomas Fullana3 , Berk Hess2 , Gustav Amberg1,4 , Shervin Bagheri1 , and Stephan´e Zaleski1,3 1
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FLOW Centre, Department of Engineering Mechanics KTH, 100 44 Stockholm, Sweden Swedish e-Science Research Centre, Science for Life Laboratory, Department of Applied Physics KTH, 100 44 Stockholm, Sweden Sorbonne Universit´e and CNRS, Paris, France S¨ odertorn University, Stockholm, Sweden Received 19 December 2019 / Accepted 6 July 2020 Published online 14 September 2020 Abstract. The movement of the triple contact line plays a crucial role in many applications such as ink-jet printing, liquid coating and drainage (imbibition) in porous media. To design accurate computational tools for these applications, predictive models of the moving contact line are needed. However, the basic mechanisms responsible for movement of the triple contact line are not well understood but still debated. We investigate the movement of the contact line between water, vapour and a silica-like solid surface under steady conditions in low capillary number regime. We use molecular dynamics (MD) with an atomistic water model to simulate a nanoscopic drop between two moving plates. We include hydrogen bonding between the water molecules and the solid substrate, which leads to a sub-molecular slip length. We benchmark two continuum methods, the Cahn–Hilliard phase-field (PF) model and a volume-of-fluid (VOF) model, against MD results. We show that both continuum models reproduce the statistical measures obtained from MD reasonably well, with a trade-off in accuracy. We demonstrate the importance of the phase-field mobility parameter and the local slip length in accurately modelling the moving contact line.
1 Introduction The motion of a two-fluid interface contacting a flat solid surface poses a particularly difficult problem of continuum fluid mechanics. If the traditional point of view of a no-slip wall – a sharp transition between the phases and constant surface tension a
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The European Physical Journal Special Topics
– is to be believed, then a contradiction ensues since at the triple point or contact line the velocity is both zero and non zero [1]. Attempts to solve this paradox and make progress on the issue abound [2–4]. One of the most popular is the assumption of Navier slip [5], but in general all solutions to the paradox amount to the introduction of a small length scale lµ below which the continuum model ceases to be valid as discussed by Voinov [6]. Cox [7] extended Voinov’s theory to arbitrary viscosity ratios and contact angles. Since then, many theoretical endeavours has been directed towards solving this problem [8–17] and the effort continues. Nevertheless, the microscopic scale physi
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