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Mathematical model of falling of a viscous jet onto a moving surface. (English) Zbl 1129.76018

Summary: We analyze the stationary jet of Newtonian fluid that is drawn by gravity onto a moving surface. 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 in 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.

MSC:

76D25 Wakes and jets
35Q35 PDEs in connection with fluid mechanics
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