Dynamic wetting failure in curtain coating by the Volume-of-Fluid method
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part of Springer Nature, 2020 https://doi.org/10.1140/epjst/e2020-000004-0
THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS
Regular Article
Dynamic wetting failure in curtain coating by the Volume-of-Fluid method Volume-of-Fluid simulations on quadtree meshes Tomas Fullanaa , St´ephane Zaleski, and St´ephane Popinet Sorbonne Universit´e, CNRS, Institut Jean le Rond d’Alembert, UMR 7190, 75005 Paris, France Received 15 January 2020 / Accepted 6 July 2020 Published online 14 September 2020 Abstract. In this paper, we investigate dynamic wetting in the curtain coating configuration. The two-phase Navier–Stokes equations are solved by a Volume-of-Fluid method on an adaptive Cartesian mesh. We introduce the Navier boundary condition to regularize the solution at the triple point and remove the implicit numerical slip induced by the cell-centered interface advection. We use a constant contact angle to describe the dynamic contact line. The resolution of the governing equations allows us to predict the substrate velocity at which wetting failure occurs. The model predictions are compared with prior computations of Liu et al. [C.Y. Liu, E. Vandre, M. Carvalho, S. Kumar, J. Fluid Mech. 808, 290 (2016); C.Y. Liu, M. Carvalho, S. Kumar, Chem. Eng. Sci. 195, 74 (2019)] and experimental observations of Blake et al. [T. Blake, M. Bracke, Y. Shikhmurzaev, Phys. Fluids 11, 1995 (1999)] and Marston et al. [J. Marston, V. Hawkins, S. Decent, M. Simmons, Exp. Fluids 46, 549 (2009)].
1 Introduction The motion of the contact line poses, since Huh et al. [1,2], a remarkable problem because of the contradiction between the no-slip condition on the substrate and the motion of the contact line. The slip length theory, expressed as a Navier boundary condition (NBC), is often used as a regularisation of the no-slip paradox at the triple point [3–5]. In this paper, we will present a numerical model for the dynamic contact line that allows us to accurately represent the physics of the coating of a free surface. We will investigate different curtain coating configurations by carrying out two-dimensional Volume-of-Fluid (VOF) simulations. In the curtain coating system (Fig. 1), a liquid is falling with a velocity V on a plate moving at velocity U . When the liquid reaches the solid substrate, it starts coating the free surface, as shown in the time series example (Fig. 2). A steady-state solution is only obtained for given sets of physical parameters and the onset of wetting failure can be predicted by studying a range of capillary and Reynolds numbers by varying U and V . We a
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The European Physical Journal Special Topics
Fig. 1. Schematic of the curtain coating configuration. The system parameters are: hc the curtain height, dc the curtain width, ρl , ρg and µl , µg the densities and viscosities of the liquid phase and the gas phase respectively, U the substrate velocity, V the feed flow velocity and θm the imposed contact angle. The inflexion point noted IP corresponds to the point at which the curvature o
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