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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.

A stationary viscous jet falling from an oriented nozzle onto a moving surface is studied, both theoretically and experimentally. We distinguish three flow regimes and classify them by the convexity of the jet shape (concave, vertical and convex). The fluid is modeled as a Newtonian fluid, and the model for the flow includes viscous effects, inertia and gravity. By studying the characteristics of the conservation of momentum for a dynamic jet, the boundary conditions for each flow regime are derived, and the flow regimes are characterized in terms of the process and material parameters. The model is solved by a transformation into an algebraic equation. We make a comparison between the model and experiments, and obtain qualitative agreement.

The Poiseuille flow of a KBKZ-fluid, being a nonlinear viscoelastic model for a polymeric fluid, is studied. The flow starts from rest and especially the transient phase of the flow is considered. It is shown that under certain conditions the steady flow equation has three different equilibrium points. The stability of these points is investigated. It is proved that two points are stable, whereas the remaining one is unstable, leading to several peculiar phenomena such as discontinuities in the velocity gradient near the wall of the pipe ('spurt') and hysteresis. Our theoretical results are confirmed by numerical calculations of the velocity gradient.

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In this article, deflections of a viscous filament in a classical fiber spinning set-up are analyzed. The deflections are considered in a direction perpendicular to the vertical equilibrium state of the spin line. The result is a traveling wave equation with non-uniform coefficients representing the non-uniform filament velocity and non-uniform tension in the spin line. Under neglect of air drag, the system is conservative with respect to an energy functional, so that its eigenmodes have purely imaginary characteristic values. A numerical analysis of the eigenmodes of the system reveals that deflections propagate from take-up wheel to spinneret, with frequencies being multiples of a basic frequency and amplitudes sinus shaped with the maximum being shifted toward the spinneret. From the numerical results, a formula is derived, which approximates the basic frequency and traveling wave velocity directly in terms of the spinning process parameters.

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