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Drop fall-off from pendent rivulets

Published online by Cambridge University Press:  10 May 1997

ALEXANDRA INDEIKINA
Affiliation:
Department of Chemical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
IGOR VERETENNIKOV
Affiliation:
Department of Chemical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
HSUEH-CHIA CHANG
Affiliation:
Department of Chemical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA

Abstract

Drops fall off a viscous pendent rivulet on the underside of a plane when the inclination angle θ, measured with respect to the horizontal, is below a critical value θc. We estimate this θc by studying the existence of finite-amplitude drop solutions to a long-wave lubrication equation. Through a partial matched asymptotic analysis, we establish that fall-off occurs by two distinct mechanisms. For θ>ϕ, where ϕ is the static contact angle, a jet mechanism results when a mean-flow steepening effect cannot provide sufficient axial curvature to counter gravity. This fall-off mechanism occurs if the rivulet width B, which is normalized with respect to the capillary length H=(σ/ρg cosθ)1/2, exceeds a critical value defined by β=−cosB>1/4. For θ<ϕ, the normal azimuthal curvature is the dominant force against fall-off and the azimuthal capillary force. The corresponding critical condition is found to be 1.5β1/6>tanθ/tanϕ. Both criteria are in good agreement with our experimental data.

Type
Research Article
Copyright
© 1997 Cambridge University Press

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