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Mathematical model of falling of a viscous jet onto a moving surface

Published online by Cambridge University Press:  01 December 2007

A. HLOD ,
A. C. T. AARTS ,
A. A. F. van de VEN  and
M. A. PELETIER
A. HLOD
Affiliation:
Center for Analysis, Scientific computing and Applications, Eindhoven University of Technology, Eindhoven, The Netherlands
A. C. T. AARTS
Affiliation:
Center for Analysis, Scientific computing and Applications, Eindhoven University of Technology, Eindhoven, The Netherlands
A. A. F. van de VEN
Affiliation:
Center for Analysis, Scientific computing and Applications, Eindhoven University of Technology, Eindhoven, The Netherlands
M. A. PELETIER
Affiliation:
Center for Analysis, Scientific computing and Applications, Eindhoven University of Technology, Eindhoven, The Netherlands
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Abstract

The stationary flow of a jet of a Newtonian fluid that is drawn by gravity onto a moving surface is analyzed. It is assumed that the jet has a convex shape and hits the moving surface tangentially. The flow is modelled by a third-order ODE on a domain of unknown length and with an additional integral condition. By solving part of the equation explicitly, the problem is reformulated as a first-order ODE with an integral constraint. The corresponding existence region in the three-dimensional parameter space is characterized in terms of an easily calculable quantity. In a qualitative sense, the results from the model are found to correspond with experimental observations.

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Type
Papers
Information
European Journal of Applied Mathematics , Volume 18 , Issue 6 , December 2007 , pp. 659 - 677
Copyright
Copyright © Cambridge University Press 2007

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