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Enhanced dip coating on a soft substrate

Vincent Bertin1,2,3,*, Jacco H. Snoeijer3, Elie Raphaël2, and Thomas Salez1

  • 1Université Bordeaux, CNRS, LOMA, UMR 5798, 33405 Talence, France
  • 2UMR CNRS Gulliver 7083, ESPCI Paris, PSL Research University, 75005 Paris, France
  • 3Physics of Fluids Group, Faculty of Science and Technology, and Mesa+ Institute, University of Twente, 7500AE Enschede, The Netherlands

  • *v.l.bertin@utwente.nl

Phys. Rev. Fluids 7, L102002 – Published 24 October, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.L102002

Abstract

A solid, withdrawn from a wetting liquid bath, entrains a thin liquid film. This simple process, first described by Landau, Levich, and Derjaguin (LLD), is commonly observed in everyday life. It also plays a central role in liquid capture by animals, and is widely used for surface-coating purposes in industry. Motivated by the emerging interest in the mechanics of very soft materials, and in particular the resulting elastocapillary coupling, we develop a dip-coating model that accounts for the additional presence of a soft solid layer atop the rigid plate. The elastic response of this soft layer is described by a Winkler's foundation. Using a combination of numerical, scaling, and asymptotic-matching methods, we find a new softness-dependent power-law regime for the thickness of entrained liquid at a small capillary number, which corresponds to a modified physics at play in the dynamic meniscus. The crossover between this regime and the classical dip-coating one occurs when the substrate's deformation is comparable to the thickness of the entrained liquid film.

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