Frictional interparticle interactions stymie rearrangements, so flow stops at a lower solid fraction of about ϕ = 0.57. But at high stress, the thin lubricating layer is no longer present as the particles are forced into closer contact. Flow therefore persists up to approximately ϕ = 0.66, which corresponds to random close packing-the maximum solid fraction achievable by disordered monodisperse spheres. At low stress, a thin layer of fluid remains between the particles as they slide past each other and rearrange themselves. To understand why the mixture solidifies at different values of ϕ for low- and high-stress mixing, consider how particles interact under those conditions. Three regimes emerged: Below ϕ = 0.55, the suspensions flowed above ϕ = 0.70, permanent granules formed in between, large granules that were present after high-stress mixing relaxed into fluids following low-stress vortexing. The top row shows each sample after high-stress mixing with an impeller, and the bottom row shows the same samples after subsequent low-stress mixing with a vortexer. The samples in the figure were made by combining glycerol with 10-µm-diameter glass particles at a range of solid-volume fractions ϕ. Their results point to jamming as the primary mechanism behind the transition between fluid and granular phases.
Now Daniel Hodgson and Wilson Poon at the University of Edinburgh in the UK and their collaborators have developed a model that quantifies the transition between the two ends of the spectrum. In the mixing of cement, on the other hand, the desired product is a high-solid-content dispersion, like on the left side of the figure, that can be poured.īoth of those examples are liquid–powder mixtures, yet physical systems at the two ends of the wetness spectrum have previously been treated as distinct. The applications typically fall at the far ends of the wetness spectrum: Production of powdered laundry detergent, for example, employs so-called wet granulation-in which a small amount of added liquid binds microscopic particles together in small clumps, or granules, like those on the right side of the figure.
Incorporating liquids into powders is also common in industrial materials processing. But just the right amount makes a smooth, flowing batter. Adding just the right amount of moisture is critical to making the batter: Not enough liquid results in dry clumps, whereas too much produces a watery mess. Rheol., in press, Ĭake recipes typically instruct bakers to add wet ingredients to a powdery flour mixture.