Why Sediments Are So Uniform
Sedimentation is the process by which small solid particles settle out of a liquid suspension. New calculations show that irregularly shaped particles can display novel behavior during sedimentation that does not occur for more symmetric objects. Such particles can drift laterally so as to smooth out density variations that occur during settling, a result that potentially resolves a long-standing discrepancy between theory and experiment over the magnitude of such variations. The theory may help explain the progress of sedimentation in both natural and industrial contexts.
Sedimentation is important in water treatment and industrial processes that rely on dense suspensions flowing as fluids, and it also influences the paths of rivers and the accumulation of geological deposits. Variations from place to place in the concentration of particles affect the progress of sedimentation. A volume with fewer particles will have greater overall buoyancy than an equal volume containing more particles, so the denser volume will fall faster. For a random distribution, fluctuations in the number of particles grow with the volume, leading to a theoretical prediction 30 years ago that vertical velocity fluctuations in a sediment should depend on the size of the sedimenting system rather than on intrinsic properties of the sediment itself [1]. Most experimental and observational evidence contradicts this prediction.
Tomer Goldfriend and Haim Diamant of Tel Aviv University and Thomas Witten of the University of Chicago now suggest a resolution of this discrepancy. They point out that studies of sedimentation have assumed particles that are spherical or at least have sufficient symmetry that their center of mass coincides with their geometrical center—for example, a rod of uniform density. Such objects have no preferred orientation in a gravitational field. In reality, the researchers say, sedimenting particles will most likely have irregular shapes that orient in a specific direction as they fall under gravity. That additional detail turns out to have important consequences.
The researchers consider a sedimentary flow whose density varies in the horizontal direction. The greater downward velocity of a denser region compared to an adjacent, more rarefied region will tip a particle between them out of its preferred alignment. As this misaligned particle drifts down through the liquid, it will develop a small sideways velocity. This lateral motion, the team argues, will depend in a complicated way on the shape and mass distribution of the particle, but in general, the faster the downward motion, the greater the sideways velocity. And this sideways motion could take particles from higher to lower density regions, or vice versa.
In short, misaligned particles will move in such a way that they either reduce or magnify the initial density variations. As a simple example, Witten suggests a grain of rice that is heavier at one end. If the downward flow rate increases as you go from left to right, say, the grain’s heavier bottom end will tilt to the left. Thus tilted, it will tend to glide to the left as it moves down—meaning that it moves toward the region of slower downward flow and lower particle density. In this case, sideways motion acts to diminish the variations in particle density.
The researchers back up this qualitative picture with calculations using the method of fluctuating hydrodynamics, in which the flow velocity at any time and location is treated not as a single value but as a statistical quantity, with some mean and variation. The method makes it possible to relate the flow rates of sedimenting particles to local variations in their density and confirms that self-aligning particles can indeed smooth out density variations.
The calculations assume that all of the particles are identical, but the researchers say that in a sediment with a mix of self-aligning and spherical particles, the former will move independently of the latter, so as to erase any overall density variations. Russel Caflisch, a UCLA theorist who was one of the first to point out the problem with velocity fluctuations during sedimentation, says he's "impressed by the results." The researchers add that it should be straightforward to test their proposal experimentally by means of light scattering studies or video microscopy.
This research is published in Physical Review Letters.
–David Lindley
David Lindley is a freelance science writer in Alexandria, Virginia.
References
- R. E. Caflisch and J. H.C. Luke, “Variance in the sedimentation speed of a suspension,” Phys. Fluids 28, 759 (1985); E. J. Hinch, “An averaged-equation approach to particle interactions in a fluid suspension,” J. Fluid Mech. 83, 695 (1977).