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Film deposition and transition on a partially wetting plate in dip coating

Published online by Cambridge University Press:  22 February 2016

Peng Gao ,
Lei Li ,
James J. Feng ,
Hang Ding  and
Xi-Yun Lu
Peng Gao*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
Lei Li
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
James J. Feng
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, British Columbia V6T 1Z3, Canada
Hang Ding
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
Xi-Yun Lu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
*
†Email address for correspondence: gaopeng@ustc.edu.cn
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Abstract

We investigate the entrainment of liquid films on a partially wetting plate vertically withdrawn from a reservoir of viscous liquid using a combination of diffuse-interface numerical simulation and lubrication analysis. So far available theoretical investigations were commonly conducted by focusing on separate parameter regions, and a complete description of the flow regimes with increasing plate speed is still missing. By solving the full Stokes equations, we present a complete scenario of film transition in the presence of moving contact line. With increasing plate speed, we identify numerically four successive flow regimes in terms of the interfacial morphologies: (1) a stationary meniscus, (2) a speed-independent thick film connected to the liquid bath through a stationary dimple, (3) coexistence of a thick film and the classical Landau–Levich–Derjaguin (LLD) film connected by a propagating capillary shock and (4) a film with a monotonically varying thickness. The characteristics of the film profiles in different regions of the interfaces are analysed with lubrication theory as applicable, and satisfactory agreements with the numerical results are obtained. In particular, we confirm that the onset of film deposition occurs at a vanishing apparent contact angle, consistent with the predictions of lubrication theory. Numerical results suggest that the critical capillary number for the onset of film deposition is smaller than that for the onset of LLD film despite the fact that it is higher than the experimentally observed one, showing that the thick film can be realized in the two-dimensional model. We also demonstrated that the LLD film is triggered by the bifurcation of the stationary dimple, which is found to admit multiple branches of stable and unstable solutions.

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Contact lines Interfacial Flows (free surface): Thin films

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Papers
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Journal of Fluid Mechanics , Volume 791 , 25 March 2016 , pp. 358 - 383
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© 2016 Cambridge University Press 

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