Inertial capillarity

– We present new results on an old problem (capillary rise). A small tube is put in contact with a liquid of low viscosity. It is found that 1) the early stage of the rise is described by a linear law for the position of the meniscus vs. time; 2) oscillations around the equilibrium occur if the liquid viscosity is low enough. A simple analytical model allows us to understand these behaviours. Usual capillary rise. – If a small tube (radius r smaller than the capillary length) is put into contact with a bath of a wetting liquid (of surface tension γ, density ρ and viscosity η), liquid rises in the tube up to a height which is generally of order 1 cm for a tube of inner diameter 1 mm. This venerable effect was experimentally studied by Newton (1704) and Jurin (1712) and explained by Laplace (1805). The final static height z0 is obtained by balancing the capillary force (F = 2πrγ) with the weight of the liquid column (Mg = πrz0ρg):