Three flow regimes of viscous jet falling onto a moving surface

A stationary viscous jet falling from an oriented nozzle onto a moving surface is studied theoretically. The fluid is modelled as a Newtonian fluid, and the model for the flow includes viscous effects, inertia and gravity. We distinguish three flow regimes, called inertial, viscous-inertial and viscous, according to which effect is dominant in the momentum transfer through the jet cross section. 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. The parameter regions of the three flow regimes, and their boundaries, are confirmed experimentally. Influences of surface tension, bending stiffness and air drag are presented.