Dense Suspensions

April 10, 2012

Everyone knows about quicksand, or at least the cinema version of quicksand. Quicksand is a colloid of fine, granular material, usually sand, mixed with clay and water. It's essentially a liquefied soil that can't support any weight, but the screenplay scenes of the bad guy sinking beneath the surface of quicksand are completely wrong.

Normal hydrostatics apply, and since the quicksand is much denser than a human, a human would never sink completely into it. The danger of quicksand is that it's hard to extract oneself from it, since movement is difficult. It is also difficult for another person to extract someone from quicksand. The best course of action is to do anything very slowly, since the viscous forces are less. It might also be possible to float upon quicksand as you would on water.

No dancing allowed? A quicksand warning sign in the Zeeland Province of the Netherlands. Zeeland is a popular venue for German tourists, thus the additional German language warning on the sign. (Via Wikimedia Commons).

Quicksand is a reminder that colloidal mixtures behave in non-intuitive ways. After all, they're not completely liquid, and they're not completely solid. Two physicists, a professor and his graduate student, from the James Franck Institute of the University of Chicago (Chicago, IL) have just published the results of their studies of droplet detachment of dense suspensions from nozzles.[1-2] Dense suspensions are colloids of a liquid and solid granular particles for which the volume fraction of the solid is very high, much like quicksand.

Heinrich Jaeger, the William J. Friedman and Alicia Townsend Friedman Professor in Physics, along with his student, Marc Miskin, examined the drip behavior of such suspensions in which particles were added at more than 50% volume fraction to a variety of pure liquids.[1] Nozzle drip of these mixtures, which are highly viscous, was captured using high speed imaging at a hundred thousand frames per second, or better.[1]

The expectation was that these dense suspensions would drip like other viscous fluids, such as oil and honey. In those cases, the thread formed between the nozzle and the droplet becomes slowly thinner, eventually breaking. For the dense suspensions, however, this thread thins in a non-viscous manner, like water. Although these suspensions are viscous, the viscosity of the mixture doesn't much affect the necking behavior.[1] Not only that, but the viscosity of the suspending liquid is relatively unimportant, another unexpected result.

The presence of the particles is what causes this phenomenon. Said Jaeger, "While the liquid deforms and becomes thinner and thinner at a certain spot, the particles also have to move with that liquid. They are trapped inside the liquid." In effect, the particles get in each other's way. "If you want to make it behave more like a pure non-viscous liquid, you want to make the particles large."[1]

A dense suspension of 850 micrometer zirconia particles in water detaching from a nozzle. The neck gradually thins to a single particle diameter, and then the surrounding liquid ruptures.(University of Chicago Image/Heinrich Jaeger and Marc Miskin).

The Chicago team developed a mathematical model that explains the evolution of the droplet neck. The variables include the viscosity and particle size. They find that the necking radius near the time of detachment scales as the 2/3 power of time.[2] They conclude that this scaling is a consequence of particles deforming the surface of the neck.[2] Such findings can be important to applications such as inkjet printing, combustion of coal-oil slurries, and biochemical analyses involving pipetting into microarrays.[1]

This research was funded by the National Science Foundation, and the Keck Initiative for Ultrafast Imaging at the University of Chicago.[1]

References:

1. Steve Koppes, "Images capture split personality of dense suspensions," March 30, 2012.
2. Marc Z. Miskin and Heinrich M. Jaeger, "Droplet formation and scaling in dense suspensions," Proc. Natl. Acad. Sci., vol. 109 no. 12 (March 20, 2012), pp. 4389-4394.
3. Jaeger Laboratory,