Dynamic drying transition via free-surface cusps

Dynamic drying transition via free-surface cusps

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 t...

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Bibliographic Details
Published in:Journal of fluid mechanics 2019-01, Vol.858, p.760-786
Main Authors: Kamal, Catherine, Sprittles, James E., Snoeijer, Jacco H., Eggers, Jens
Format: Article
Language:eng
Subjects:
Air
Air entrainment
Air flow
Bifurcations
Contact angle
Corrections
Cusps
Dimensionless numbers
Drying
Entrainment
Experiments
Free surfaces
JFM Papers
Radius of curvature
Reynolds number
Simulation
Slip
Thin films
Vapor phases
Viscosity
Viscosity ratio
Wetting
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Summary: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.
ISSN:0022-1120
1469-7645