Unified theory of inertial granular flows and non-Brownian suspensions

Abstract

Unified theory of inertial granular flows and non-Brownian suspensionsDeGiuli, E.; Düring, G.; Lerner, E.; Wyart, M. Published in:Physical Review E DOI:10.1103/PhysRevE.91.062206 Link to publication Citation for published version (APA):DeGiuli, E., Düring, G., Lerner, E., & Wyart, M. (2015). Unified theory of inertial granular flows and non-Brownian suspensions. Physical Review E, 91(6), [062206]. DOI: 10.1103/PhysRevE.91.062206 General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Rheological properties of dense flows of hard particles are singular as one approaches the jamming threshold where flow ceases both for aerial granular flows dominated by inertia and for over-damped suspensions. Concomitantly, the length scale characterizing velocity correlations appears to diverge at jamming. Here we introduce a theoretical framework that proposes a tentative, but potentially complete, scaling description of stationary flows. Our analysis, which focuses on frictionless particles, applies both to suspensions and inertial flows of hard particles. We compare our predictions with the empirical literature, as well as with novel numerical data. Overall, we find a very good agreement between theory and observations, except for frictional inertial flows whose scaling properties clearly differ from frictionless systems. For overdamped flows, more observations are needed to decide if friction is a relevant perturbation. Our analysis makes several new predictions on microscopic dynamical quantities that should be accessible experimentally.

Unifying Suspension and Granular flows near Jamming

“…(1), the kick of amplitude δμ opens a fraction δz ≡ z c − z of the contacts, allowing collective motions of the particles for which particles do not overlap, but simply stay in contact, the so-called called floppy modes. Using a virtual work theorem to compute the work done after a contact is opened, we find [25] that the lever amplitude is directly related to the density of floppy modes δz, in particular…”

“…This equation can also be derived formally, see [25]. In inertial flow, unbalanced forces are proportional to accelerations, F = pI 2 dL/d , which leads to…”

“…To achieve this goal, we make the assumption that the contact network of configurations in flow is similar to that of jammed configurations at μ c immediately after increasing the stress ratio by δμ > 0. The detailed arguments in this section are presented in [25]; here we discuss the physical ingredients of each argument and summarize the results. The coordination z of the network of contacts is a key microscopic quantity that distinguishes flowing from jammed configurations.…”

“…They seem not to depend on dimension, which we thus did not report in our Viscous δμ ∼ J γ μ γ μ = 0.35 0.38 [27], 0.5 [5] 0.42 [27,28] 0.37 [16], 0.25 [23], 0.32 [25] 0.5 [12] δz ∼ J γ z γ z = 0.30 0.30 [25] …”

“…In this work we review a framework to de- scribe flow in such situations. The detailed arguments are presented in [25]; here we discuss the essential ingredients of the theory, and focus on the effect of friction, discussed in more detail in [20,26].…”