Heating, simulations get the drop on drips

The behavior of dripping fluids may seem of more concern to plumbers than to Ph.D.s. Yet studies of how drops elongate and break loose help scientists understand phenomena ranging from atomic fission to cell division (SN: 7/30/94, p. 79). Drip research also advances droplet-related applications such as ink-jet printing and depositing DNA on biochips. Now, two new studies are extending scientists’ understanding of drips.

A liquid sags into the air beneath it, unless heat from below halts drop formation. Burgess et al.

The simplified computer model reveals an effect seen in experiments but never before simulated. The sequence of drips from a faucet alternates between two sizes. Ambravaneswaran et al.

A new drop-formation experiment in Texas demonstrates a way to prevent dripping when a layer of a dense fluid, such as oil, is placed above a lighter fluid, such as air. The not-yet-published findings demonstrate that a temperature difference can suppress the breakdown of fluid layers into droplets.

Called the Rayleigh-Taylor instability, this heavily studied type of breakdown occurs in such diverse settings as seawater mixing, supernova explosions, and laser-driven nuclear fusion. The new results may also apply to everyday problems such as dripping of industrial coatings or wet ceilings.

In the other study, of dripping faucets rather than ceilings, Indiana researchers have for the first time used a computer to simulate a sequence of hundreds of drips rather than just one drip. From those simulations, they predict that slowly opening a faucet to a certain flow rate produces one dripping pattern. Taking the alternate path–of gradually opening the tap wide and then closing it back down to the same flow rate–may yield a different pattern, the simulations show.

In the Texas study, John M. Burgess and his colleagues at the University of Texas in Austin spread a thin layer of viscous silicone oil on the bottom of a clear, sapphire disk and then suspended the disk above an uncoated disk. They next cooled the top disk and heated the bottom one.

Despite the unstable arrangement of oil over air, no droplets formed as long as a modest temperature difference of about 15ºC was maintained, the scientists report in an upcoming issue of Physical Review Letters (PRL).

Burgess explains that the liquid surface warms wherever gravity pulls it closer to the heat source. Since heat reduces surface tension, the tendency to form a drop grows. However, cold increases surface tension, so thinner, cooler regions quickly draw liquid away from budding drops and reverse the sagging. “Very small changes in surface tension are able to counteract these very small changes in surface shape,” he says.

By examining both gravity and heat, the Texas study “enables us to understand how two important things work together” to affect the Rayleigh-Taylor instability, says Leo P. Kadanoff of the University of Chicago. The findings may also prove useful to “paint designers and lubrication specialists . . . interested in maintaining the thicknesses of their films,” he speculates.

In the other drip study, Bala Ambravaneswaran and his coworkers at Purdue University in West Lafayette made the leap to multiple-drip simulations by sketching individual drips as a line of dots, with each dot carrying certain properties, such as local radius. Simulations of a single, fully rendered drip require a day to compute. The Purdue simplification slashed the time to only a few minutes, says study leader Osman A. Basaran. His team reported its findings in the Dec. 18, 2000 PRL.

Unlike the surprisingly path-dependent patterns produced by the model, periodic variations in drop size and other behaviors that turned up in the simulation had previously been seen in experiments. They indicate the simulations’ validity, Basaran says. Compared with experimental data and more-exact computations, the streamlined computer models are accurate to within 1 percent, he adds.

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