# A unified framework for non-Brownian suspension flows and soft amorphous solids

@article{Lerner2012AUF, title={A unified framework for non-Brownian suspension flows and soft amorphous solids}, author={Edan Lerner and Gustavo D{\"u}ring and Matthieu Wyart}, journal={Proceedings of the National Academy of Sciences}, year={2012}, volume={109}, pages={4798 - 4803} }

While the rheology of non-Brownian suspensions in the dilute regime is well understood, their behavior in the dense limit remains mystifying. As the packing fraction of particles increases, particle motion becomes more collective, leading to a growing length scale and scaling properties in the rheology as the material approaches the jamming transition. There is no accepted microscopic description of this phenomenon. However, in recent years it has been understood that the elasticity of simple…

## 110 Citations

Length scales and self-organization in dense suspension flows.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2014

The microscopic mechanism governing dissipation and its connection to the observed correlation length is developed, and it is found that this proximity causes a decoupling between viscosity and the correlation length of velocities ξ.

Disentangling glass and jamming physics in the rheology of soft materials

- Physics
- 2013

The shear rheology of soft particle systems becomes complex at large density because crowding effects may induce a glass transition for Brownian particles or a jamming transition for non-Brownian…

Dynamical behavior of disordered spring networks

- Physics
- 2013

We study the dynamical rheology of spring networks with a percolation model constructed by bond dilution in a two-dimensional triangular lattice. Hydrodynamic interactions are implemented by a…

Characterizing the nature of the rigidity transition

- PhysicsPhysical Review E
- 2018

Particulate matter, such as foams, emulsions, and granular materials, attain rigidity in a dense regime: the rigid phase can yield when a threshold force is applied. The rigidity transition in…

Interparticle Friction Leads to Nonmonotonic Flow Curves and Hysteresis in Viscous Suspensions

- Materials Science, PhysicsPhysical Review X
- 2019

Hysteresis is a major feature of the solid-liquid transition in granular materials. This property, by allowing metastable states, can potentially yield catastrophic phenomena such as earthquakes or…

Oscillatory rheology of dense, athermal suspensions of nearly hard spheres below the jamming point.

- Materials Science, MedicineSoft matter
- 2017

It is shown that oscillatory shear may serve as a diagnostic tool to isolate specific stress contributions in dense suspensions, and more generally in those materials whose rheology has contributions with both hydrodynamic and non-hydrodynamic origin.

Shear thickening, frictionless and frictional rheologies in non-Brownian suspensions

- Physics
- 2014

Particles suspended in a Newtonian fluid raise the viscosity and also generally give rise to a shear-rate dependent rheology. In particular, pronounced shear thickening may be observed at large solid…

Rheology of granular flows across the transition from soft to rigid particles

- Materials Science, Physics
- 2017

The rheology of dense granular flows is often seen as dependent on the nature of the energy landscape defining the modes of energy relaxation under shear. We investigate numerically the transition…

Critical scaling of compression-driven jamming of athermal frictionless spheres in suspension.

- Physics, MedicinePhysical review. E
- 2021

It is found for compression-driven jamming that pressure obeys a critical scaling relation as a function of packing fraction ϕ and compression rate, and that the bulk viscosity p/ε[over ̇] diverges upon jamming.

Universality of jamming of nonspherical particles

- Physics, MedicineProceedings of the National Academy of Sciences
- 2018

A general theory of hypostatic amorphous packings and the associated jamming transition is proposed and a generalized perceptron model is introduced which can be solved analytically by the replica method and predicts critical exponents in the same Hypostatic jamming universality class.

## References

SHOWING 1-10 OF 45 REFERENCES

What do dry granular flows tell us about dense non-Brownian suspension rheology?

- Physics
- 2009

Recent years have seen significant progress in our understanding of the rheology of dry granular materials. A scale invariance of equations of motion in the rigid grain limit has helped identifying…

Superdiffusive, heterogeneous, and collective particle motion near the fluid-solid transition in athermal disordered materials

- Materials Science, Physics
- 2010

We use computer simulations to study the microscopic dynamics of an athermal assembly of soft particles near the fluid-to-solid jamming transition. Borrowing tools developed to study dynamic…

Scaling of phononic transport with connectivity in amorphous solids

- Physics
- 2009

The effect of coordination on transport is investigated theoretically using random networks of springs as model systems. An effective medium approximation is made to compute the density of states of…

Critical scaling of shear viscosity at the jamming transition.

- Physics, MedicinePhysical review letters
- 2007

The results support the assertion that jamming is a true second-order critical phenomenon.

A constitutive law for dense granular flows

- Physics, MedicineNature
- 2006

The results support the idea that a simple visco-plastic approach can quantitatively capture granular flow properties, and could serve as a basic tool for modelling more complex flows in geophysical or industrial applications.

Jamming transition as probed by quasistatic shear flow.

- Materials Science, PhysicsPhysical review letters
- 2009

It is proposed that long-range correlations observed below the transition are dominated by this isostatic point, while those that are observed above the Transition are characteristic of dense, disordered elastic media.

Scaling Properties of Granular Rheology near the Jamming Transition(General)

- Physics
- 2008

Rheological properties of a dense granular material consisting of frictionless spheres are investigated. It is found that the shear stress, the pressure, and the kinetic temperature obey critical…

The effect of Brownian motion on the bulk stress in a suspension of spherical particles

- Physics
- 1977

The effect of Brownian motion of particles in a statistically homogeneous suspension is to tend to make uniform the joint probability density functions for the relative positions of particles, in…

Jamming at zero temperature and zero applied stress: the epitome of disorder.

- Mathematics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003

The results provide a well-defined meaning for "random close packing" in terms of the fraction of all phase space with inherent structures that jam, and suggest that point J is a point of maximal disorder and may control behavior in its vicinity-perhaps even at the glass transition.

The jamming scenario - an introduction and outlook

- Physics
- 2010

The jamming scenario of disordered media, formulated about 10 years ago, has in recent years been advanced by analyzing model systems of granular media. This has led to various new concepts that are…