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Droplet formation and scaling in dense suspensions
Marc Z. Miskin and Heinrich M. Jaeger
Proceedings of the National Academy of Sciences of the United States of America
Vol. 109, No. 12 (March 20, 2012), pp. 4389-4394
Published by: National Academy of Sciences
Stable URL: http://www.jstor.org/stable/41585503
Page Count: 6
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When a dense suspension is squeezed from a nozzle, droplet detachment can occur similar to that of pure liquids. While in pure liquids the process of droplet detachment is well characterized through self-similar profiles and known scaling laws, we show here the simple presence of particles causes suspensions to break up in a new fashion. Using high-speed imaging, we find that detachment of a suspension drop is described by a power law; specifically we find the neck minimum radius, rm, scales like τ⅔ near breakup at time τ = 0. We demonstrate data collapse in a variety of particle/liquid combinations, packing fractions, solvent viscosities, and initial conditions. We argue that this scaling is a consequence of particles deforming the neck surface, thereby creating a pressure that is balanced by inertia, and show how it emerges from topological constraints that relate particle configurations with macroscopic Gaussian curvature. This new type of scaling, uniquely enforced by geometry and regulated by the particles, displays memory of its initial conditions, fails to be self-similar, and has implications for the pressure given at generic suspension interfaces.
Proceedings of the National Academy of Sciences of the United States of America © 2012 National Academy of Sciences