Cake recipes typically instruct bakers to add wet ingredients to a powdery flour mixture. 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. But just the right amount makes a smooth, flowing batter.
Incorporating liquids into powders is also common in industrial materials processing. 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. 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.
Both of those examples are liquid–powder mixtures, yet physical systems at the two ends of the wetness spectrum have previously been treated as distinct. 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. Their results point to jamming as the primary mechanism behind the transition between fluid and granular phases.
The samples in the figure were made by combining glycerol with 10-µm-diameter glass particles at a range of solid-volume fractions ϕ. 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. 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.
To understand why the mixture solidifies at different values of ϕ for low- and high-stress mixing, consider how particles interact under those conditions. At low stress, a thin layer of fluid remains between the particles as they slide past each other and rearrange themselves. Flow therefore persists up to approximately ϕ = 0.66, which corresponds to random close packing—the maximum solid fraction achievable by disordered monodisperse spheres. But at high stress, the thin lubricating layer is no longer present as the particles are forced into closer contact. Frictional interparticle interactions stymie rearrangements, so flow stops at a lower solid fraction of about ϕ = 0.57. That’s the point at which the particles trying to rearrange get stuck, a process known as jamming. (See the Quick Study by Jasna Brujic, Physics Today, November 2010, page 64.)
Based on their model, the researchers have derived a formula for a liquid–powder mixture’s average granule size as a function of particle size, solid-volume fraction, and the stress at which jamming begins. Their predictions for both granule size and the onset of flow—indicated by a diverging granule radius—were consistent with their measurements. The physical insights from the model provide the basis for a quantitative approach to tuning such processes as conching: the mixing of powdered cocoa, sugar, and milk with cocoa butter to produce chocolate’s distinctive flavor and smooth texture. (D. J. M. Hodgson et al., J. Rheol., in press, https://arxiv.org/abs/1907.10980.)
"flow" - Google News
July 27, 2022 at 08:57PM
https://ift.tt/xpe3g7V
Jamming links granulation and flow - Physics Today
"flow" - Google News
https://ift.tt/Wjqvsb9
https://ift.tt/c9JWe7T
Bagikan Berita Ini
0 Response to "Jamming links granulation and flow - Physics Today"
Post a Comment