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by Christopher Ness, Romain Mari, and Michael E. Cates

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1 by Christopher Ness, Romain Mari, and Michael E. Cates
Shaken and stirred: Random organization reduces viscosity and dissipation in granular suspensions by Christopher Ness, Romain Mari, and Michael E. Cates Science Volume 4(3):eaar3296 March 30, 2018 Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY).

2 Fig. 1 Viscosity and dissipation reduction under superimposed primary and oscillatory flows.
Viscosity and dissipation reduction under superimposed primary and oscillatory flows. (A) (i) Simulation snapshot showing primary (blue) and cross shear (red) flow directions. (ii and iii) Example flow paths explored for different values of parameters ωpri and ω (values given in insets) with δ = 0. (B) Contour map showing viscosity in primary flow direction as a function of ωpri and ω, for δ = 0 and φ = (C) Viscosity as a function of oscillation rate at various volume fractions φ with amplitude γ = 1% and ωpri = 0, the SO protocol. (D) Viscosity divergence as a function of φ under steady shear (SS) and high-frequency SO with friction coefficient μs = 1. Inset: Difference between SS and SO viscosities. (E) Viscosity divergences for particles with lower friction coefficient μs show diminishing viscosity reduction. (F) Dissipation per unit strain W (rescaled by the φ-dependent steady shear dissipation WSS) as a function of oscillation rate for the same simulations as in (C), for (i) φ = 0.54 and (ii) φ = 0.57, showing contributions in xy and zy. Green areas in (i) and (ii) highlight the region in which both viscosity and dissipation reduction are achieved. (iii) Dissipation in the (, φ) plane, highlighting in white the region for which dissipation may be reduced by at least 5% with SO. Christopher Ness et al. Sci Adv 2018;4:eaar3296 Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY).

3 Fig. 2 Revealing random organization at work during oscillatory shear.
Revealing random organization at work during oscillatory shear. (A) Origin of the viscosity drop at φ = 0.54 with SO. The contact stress contribution is strongly suppressed with increasing oscillation rate. Inset: Schematic of the SO strain profile. (B) The cumulative pair correlation function G(h) under steady shear and , demonstrating a room-making process. Inset: Around 20 cycles are needed to minimize the number of particle contacts. (C) Proportion of particles following an irreversible trajectory under successive periods of oscillatory shear (in the absence of primary shear) as a function of the number of cycles, starting from presheared configurations at several volume fractions. The steady decrease of the irreversibility is a signature of random organization. Christopher Ness et al. Sci Adv 2018;4:eaar3296 Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY).

4 Fig. 3 Optimizing dissipation reduction using an alternating OCS (AO) protocol.
Optimizing dissipation reduction using an alternating OCS (AO) protocol. (A) Primary viscosity as a function of n, the number of cross shear oscillations per phase of the AO protocol, with γ = Γ = 1% and φ = Inset: Schematic of the AO strain profile. (B) Relative viscosity drop as a function of volume fraction φ, comparing steady shear and AO. (C) Energy dissipation for the cases n = 1, 2, 3, 5, and 10 as a function of the fraction of time spent oscillating α. (D) Dissipation in the (, φ) plane rescaled by the φ-dependent steady shear dissipation, highlighting the region for which dissipation is reduced by at least 5% with AO. Outlined in black is the analogous region from Fig. 1F (iii) for comparison. (E) Comparison of the minimal dissipation obtained with the AO and SO protocols across a range of volume fractions φ. Inset: The ratio between the minimal dissipation rates achievable for AO and SO, and , respectively. Christopher Ness et al. Sci Adv 2018;4:eaar3296 Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY).

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