Scaling analysis of coating of a plate or a fiber

The problem of coating a plate or a fiber through their withdrawal from a large reservoir was treated in the literature in various limiting cases. In the present paper, interpolation expressions are derived by scaling for Newtonian, Bingham, and viscoelastic fluids. The scaling analysis was also employed to explain the sharp increase in film thickness produced by inertia and the occurrence of a maximum thickness for an optimum velocity. It is also shown that, for a viscoelastic fluid, the film thickness tends to a finite value at very large withdrawal rates. An explanation is also provided for the existence of a maximum film thickness for an optimum surfactant concentration.