Dripping faucet and bubbling faucet: An analogy

Abstract

A generic analogy is established between the subsequent formation of bubbles from an orifice on a perforated plate and the formation of drops from a needle. The bubble formation was described recently with a model based on the liquid piston oscillating inside the orifice. The drop formation was described about 25 years ago and became known as the ‘dripping faucet’. It is shown here that these two different cases share a common physical basis: an open mechanical system is continuously fed with mass that is then released stepwise upon reaching a threshold condition. The discontinuous nature of the process together with the strong coupling between the end of one cycle and the beginning of the next cycle endows this basically linear system with interesting nonlinear dynamical effects. It is further shown here that the model governing equations describing both cases can be reduced to a common limit. The analogy thus established is to encourage our efforts aimed at looking for the generic similarities between different multiphase flow systems, rather than to lament over the overwhelming diversity of manifestations they maliciously tend to display to us.