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Dynamic drying transition via free-surface cusps

  • Catherine Kamal (a1), James E. Sprittles (a2), Jacco H. Snoeijer (a3) and Jens Eggers (a1)


We study air entrainment by a solid plate plunging into a viscous liquid, theoretically and numerically. At dimensionless speeds $Ca=U\unicode[STIX]{x1D702}/\unicode[STIX]{x1D6FE}$ of order unity, a near-cusp forms due to the presence of a moving contact line. The radius of curvature of the cusp’s tip scales with the slip length multiplied by an exponential of $-Ca$ . The pressure from the air flow drawn inside the cusp leads to a bifurcation, at which air is entrained, i.e. there is ‘wetting failure’. We develop an analytical theory of the threshold to air entrainment, which predicts the critical capillary number to depend logarithmically on the viscosity ratio, with corrections coming from the slip in the gas phase.

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Present address: School of Engineering and Materials Science, Queen Mary, University of London, Mile End Road, London E1 4NS, UK



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