Two-dimensional, unsteady flow of a two-layer fluid in a tank is considered. Each fluid is inviscid and flows irrotationally. The lower, denser fluid flows with constant speed out through a drain hole of finite width in the bottom of the tank. The upper, lighter fluid is recharged at the top of the tank, with an input volume flux that matches the outward flux through the drain. As a result, the interface between the two fluids moves uniformly downwards, and is eventually withdrawn through the drain hole. However, waves are present at the interface, and they have a strong effect on the time at which the interface is first drawn into the drain. A linearized theory valid for small extraction rates is presented. Fully nonlinear, unsteady solutions are computed by means of a novel numerical technique based on Fourier series. For impulsive start of the drain, the nonlinear results are found to agree with the linearized theory initially, but the two theories differ markedly as the interface approaches the drain and nonlinear effects dominate. For wide drains, curvature singularities appear to form at the interface within finite time. © 2007 American Institute of Physics.

Item Type:	Refereed Article
Research Division:	Engineering
Research Group:	Fluid mechanics and thermal engineering
Research Field:	Microfluidics and nanofluidics
Objective Division:	Expanding Knowledge
Objective Group:	Expanding knowledge
Objective Field:	Expanding knowledge in the physical sciences
UTAS Author:	Forbes, LK (Professor Larry Forbes)
ID Code:	46407
Year Published:	2007
Funding Support:	Australian Research Council (DP0450225)
Web of Science® Times Cited:	17
Deposited By:	Mathematics
Deposited On:	2007-08-01
Last Modified:	2011-11-24
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