The effect of weak inertia on the emptying of a tube

We present an extension of the classical axisymmetric Bretherton theory giving the thickness of the liquid film left on the walls of a drained tube, treating the case of weak inertia by a regular perturbation method. The results obtained by numerical integration fit Taylor's [J. Fluid Mech. 10, 161 (1961)] experiments, obtained with viscous fluids (glycerine and strong sucrose solutions), and Aussillous and Quere's [Phys. Fluids 12, 2367 (2000)] experiments with low viscosity liquids (hexamethyldisiloxane and water) when inertia becomes important. The discrepancies observed between the theory and high Reynolds numbers experiments (Re>1000) are commented on. (C) 2002 American Institute of Physics.