How vibrating a dense suspension prevents it from jamming

Chocolate paste, cement, and some other industrially important materials consist of particles larger than 10 µm packed closely within a liquid. The particles are sufficiently large and massive that Brownian buffeting is unimportant to their dynamic behavior. What matters is the interplay between hydrodynamic and contact forces.

Like their dry, fluid-free counterparts, wet granular materials can jam when the density of particles is high enough. Stresses above a critical value are needed to unjam them. Vibration works too, as anyone who has sifted flour in a sieve can attest.

How much vibration is needed to unjam a wet suspension? And what is the physical mechanism behind its success? To answer those questions, Chloé Garat of the University of Bordeaux in France and her colleagues conducted a series of experiments.

Their setup (shown here) is based on a cylindrical container atop a shaker that vibrates the container vertically. To characterize the suspensions’ rheological behavior, a six-bladed vane is inserted into the container along the cylinder’s central axis and rotated. Shear stress and shear rate are derived from the torque applied to the vane and its rotation rate. Six vertical baffles on the inside surface of the cylinder prevent what rheologists call wall slip—that is, the sudden release of large gradients at surfaces that lead to anomalously low measurements of shear stress.

Garat and her collaborators chose as their suspension irregularly shaped particles of silica whose average diameter was 30 µm. Water served as the fluid.

At high shear rates—that is, when the vane was rotating quickly—the addition of vibrations made little difference. The wet granular suspension behaved like a viscous, non-Newtonian fluid that flowed only above a certain yield stress. But at low shear rates, vibrations caused the suspension to behave somewhat like a Newtonian fluid. The shear rate at which the transition between the two behaviors occurred depended on the amplitude and frequency of the vibrations and the density of suspension.

Although Brownian motion was irrelevant to the conditions that prevailed in the experiment, it turned out that the effect of the vibrations could be understood in terms of a thermal-like force. In the liquid-like state, the vibrations acted as a source of energy that disrupted the contact forces between the particles and made them effectively frictionless.

A model developed in 2014 by Matthieu Wyart and Michael Cates did not explicitly include vibrations, but Garat and company found that its consideration of two regimes of contact force—lubricated and frictional—could be adapted to account for the behavior revealed in Garat and company’s experiments. (C. Garat et al., J. Rheol. 66, 237, 2022 .)