Air Entrainment through Free-Surface Cusps

Jens Eggers
Phys. Rev. Lett. 86, 4290 – Published 7 May 2001
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Abstract

In many industrial processes, such as pouring a liquid or coating a rotating cylinder, air bubbles are entrapped inside the liquid. We propose that this is due to air being drawn into the narrow channel of a cusp singularity that generically forms on free surfaces. Since the width of the cusp is exponentially small in the driving strength, even the minute viscosity of air is enough to destroy the stationary solution, and a sheet emanates from the cusp's tip, through which air is entrained. Our analytical theory is confirmed by quantitative comparison with numerical simulations of the flow equations, and is found to be in qualitative agreement with experimental observation.

  • Received 14 November 2000

DOI:https://doi.org/10.1103/PhysRevLett.86.4290

©2001 American Physical Society

Authors & Affiliations

Jens Eggers

  • Universität Gesamthochschule Essen, Fachbereich Physik, 45117 Essen, Germany

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Vol. 86, Iss. 19 — 7 May 2001

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