Hydrodynamical models for the chaotic dripping faucet
Original Entry by Michelle Borkin, AP225 Fall 2009
P. Coullet, L. Mahadevan and C. Riera, Journal of Fluid Mechanics, 526, 1-17, 2005.
surface tension, capillary force, chaos, hydrodynamics
This paper presents a series of mathematical models describing the chaotic dripping of a facet. First, a static droplet of water hanging at the end of a facet is discussed, then time dependence is examined with a lubrication model, chaotic behavior is investigated using a proper orthogonal decomposition (POD) resulting in a simplified model, and finally a mechanical description encompassing the main features of these detailed fluid models is presented. The mathematical models presented importantly include and explain features of the dripping faucet such as the time between drips, chaotic dripping (i.e. drip-drop behavior), and the critical point between dripping and jetting.