The puzzling success of an empirical model

When snakes and lizards, like the sandfish skink shown in the photograph, wriggle on or in granular environments, their movements often resemble swimming . Granular resistive force theory (RFT) asserts that the forces on any small segment of such a creature are independent of the motions of other segments. (See the Quick Study by Yang Ding, Chen Li, and Daniel Goldman, Physics Today, November 2013, page 68 .)

First proposed in the 1950s to calculate speeds of sea-urchin spermatozoa swimming in seawater (J. Gray, G. H. Hancock, J. Exp. Biol. 32, 802, 1955), RFT approximates locomotion in viscous fluids relatively well. But for granular media, it’s bafflingly spot on. To figure out why, Ken Kamrin of MIT and his postdoc Hesam Askari (now at the University of Rochester) devised the simplest continuum-mechanical equations that could describe granular flow around an intruding object and fed the equations into numerical simulations. The only inputs to their model were the medium’s internal friction coefficient and density.

The predicted force profiles and other properties that Kamrin and Askari derived from their continuum formulation turned out to be strikingly similar to what RFT produces. Furthermore, their analysis revealed that RFT’s success is a natural consequence of how granular media deform in response to intruder motion. Kamrin and Askari suggest their method could identify other materials ripe for RFT—for instance, they predict that it should work for mud, paste, and other cohesive media. (H. Askari, K. Kamrin, Nat. Mater., in press .)