We probe flows of soft, viscous spheres near the jamming point, which acts as a critical point for static soft spheres. Starting from energy considerations, we find nontrivial scaling of velocity fluctuations with strain rate. Combining this scaling with insights from jamming, we arrive at an analytical model that predicts four distinct regimes of flow, each characterized by rational-valued scaling exponents. Both the number of regimes and values of the exponents depart from prior results. We validate predictions of the model with simulations.PACS numbers: 47.57. Bc, 83.50.Rp, 83.80.Iz The past few years have seen enormous progress towards understanding the static, "jammed" state that occurs when soft athermal particles are packed sufficiently densely that they attain a finite rigidity [1][2][3]. Such systems may flow when shear stresses are applied, and in seminal work, Olsson and Teitel addressed the relation between strain rate, shear stress and packing fraction in a simplified numerical model for the flow of soft viscous spheres [4]. When rescaled appropriately, the data for strain rateγ, shear stress σ and packing fraction φ were found to collapse to two curves, reminiscent of second order-like scaling functions, and a large length scale was found to emerge near jamming. Since then, qualitatively similar results have been obtained in simulations of a number of flowing systems [5][6][7][8][9], but there is little agreement on the actual value of scaling exponents, nor on the relation to jamming in static systems.Here we describe an analytical model that connects the scaling of static systems to the scaling of both the velocity fluctuations and the shear stress of flowing systems near jamming. The model is built around a "viscoplastic" effective strain γ eff = γ y + γ dyn , where γ dyn is a dynamic contribution set by the strain rate, and γ y stems from the (dynamical) yield stress and is controlled by the distance to jamming. We show that steady state power balance dictates nontrivial scaling of γ dyn with strain rate, and propose a nonlinear stress-strain relation that leads to a closed set of equations predicting a rich scaling scenario for flows near jamming. We verify central ingredients of the model and our predictions for the rheology numerically in Durian's bubble model for foams [11]. Our simple model captures and predicts the rheology and fluctuations starting from the microscopic interactions; it also indicates the need for, and provides, new ways to present and analyze rheological data near jamming.Numerical Model -The two-dimensional Durian bubble model stipulates overdamped dynamics in which the sums of elastic and dissipative forces on each bubble, represented by a disk, balance at all times [11]. Forces are pairwise and occur only between contacting bubbles. Elastic interaction forces are proportional to the disk overlap, f el ij = k(R i + R j − r ij ) α el , where r ij := r j − r i points from one bubble center to another and R i labels the radius of disk i. In the full model that we focus...

Fluctuations in flows near jammingWoldhuis, E.; Chikkadi, V.; van Deen, M.S.; Schall, P.; van Hecke, M. Published in: Soft Matter DOI:10.1039/c5sm01592hLink to publication Citation for published version (APA):Woldhuis, E., Chikkadi, V., van Deen, M. S., Schall, P., & van Hecke, M. (2015). Fluctuations in flows near jamming. Soft Matter, 11(35), 7024-7031. DOI: 10.1039/c5sm01592h 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. Bubbles, droplets or particles in flowing complex media such as foams, emulsions or suspensions follow highly complex paths, with the relative motion of the constituents setting the energy dissipation rate.What is their dynamics, and how is this connected to the global rheology? To address these questions, we probe the statistics and spatio-temporal organization of the local particle motion and energy dissipation in a model for sheared disordered materials. We find that the fluctuations in the local dissipation vary from nearly Gaussian and homogeneous at low densities and fast flows, to strongly intermittent for large densities and slow flows. The higher order moments of the relative particle velocities reveal strong evidence for a qualitative difference between two distinct regimes which are nevertheless connected by a smooth crossover. In the critical regime, the higher order moments are related by novel multiscaling relations. In the plastic regime the relations between these moments take on a different form, with higher moments diverging rapidly when the flow rate vanishes. As these velocity differences govern the energy dissipation, we can distinguish two qualitatively different types of flow: an intermediate density, critical regime related to jamming, and a large density, plastic regime.

-Via simulations of flowing foam, we connect the high and intermediate density regimes of complex fluid flows into a consistent microscopic picture of deformation. While at and above the jamming transition, elastic correlations lead to strong spatial organization of the flow field, below jamming, the slowly diminishing elastic correlation length leads to slowly ceasing spatial organization, which is nevertheless still present down to densities far below jamming. We show that the long-range correlated flow field arises from the superposition of quadrupolar strain fields of shear zones with highly correlated positions, strengths and orientation. These interactions are still pertinent below jamming, where they systematically weaken with the slowly diminishing elastic correlation length. These results demonstrate the ubiquity and importance of elastic correlations in the flow of complex fluids even below the jamming transition, and motivate a scale-bridging description of their flow over wide ranges of density from solid to fluid.Disordered packings of foams, emulsions, colloidal suspensions and granular particles all exhibit a rigidity transition to jammed solids when packed densely [1][2][3][4][5][6]. This rigidity vanishes at the jamming transition, where the packing approaches its stability limit: the average number of contacts with neighboring particles approaches a critical stability limit, and the shear moduli vanish with well-known scaling relations [4,5]. Concomitantly with the loss of elasticity, non-affine fluctuations become increasingly important, and floppy modes indicate the increasing susceptibility of the material to applied stress [6][7][8][9][10]. At unjamming the elastic moduli of the static packing vanish and the material is irreversibly affected by the smallest applied force [4,5,10].The situation changes qualitatively when the material is subjected to flow. In steady-state flow, particle contacts are constantly broken and reformed, leading to a dynamic scenario of continuously changing, transient particle contacts [11]. At the same time, the structural rearrangements have to be relaxed to the boundaries by some longrange displacement field. The nature of these fields as the density decreases near to and below the static jamming transition remains unclear. In the deeply jammed state, the material exhibits pronounced elasticity that causes correlations in the flow, and provides the long-range field that transfers the local relaxation. In this regime, simulations as well as experiments have established that the flow of dense foams, emulsions and suspensions is governed by local shear transformation zones [12][13][14] surrounded by a long-range quadrupolar elastic strain field [15]. While this long-range elastic field -an essential feature of elastic materials -provides interactions between transformation zones and leads to strongly correlated flow, it is unclear what happens near jamming, and how the flow ultimately crosses over to the Newtonian regime far below jamming. Despite its cent...

The spot model has been developed by Bazant and co-workers to describe quasistatic granular flows. It assumes that granular flow is caused by the opposing flow of so-called spots of excess free volume, with spots moving along the slip lines of Mohr-Coulomb plasticity. The model is two-dimensional and has been successfully applied to a number of different geometries. In this paper we investigate whether the spot model in its simplest form can describe the wide shear zones observed in experiments and simulations of a Couette cell with split bottom.We give a general argument that is independent of the particular description of the stresses, but which shows that the present formulation of the spot model in which diffusion and drift terms are postulated to balance on length scales of order of the spot diameter, i.e. of order 3-5 grain diameters, is difficult to reconcile with the observed wide shear zones. We also discuss the implications for the spot model of co-axiality of the stress and strain rate tensors found in these wide shear flows, and point to possible extensions of the model that might allow one to account for the existence of wide shear zones.