Falling of a viscous jet onto a moving surface
  We analyze the stationary flow of a jet of Newtonian fluid that is drawn by gravity onto a moving surface. The situation is modeled by a third-order ODE on a domain of unknown length and with an additional integral condition; by solving part of the equation explicitly we can reformulate the problem as a first-order ODE, again with an integral constraint. We show that there are two flow regimes, and characterize the associated regions in the three-dimensional parameter space in terms of an easily calculable quantity. In a qualitative sense the results from the model are found to correspond with experimental observations. 
A. Hlod, A.C.T. Aarts, and A.A.F. Van De Ven, M.A. Peletier