Critical scaling of Bagnold rheology at the jamming transition of frictionless two-dimensional disks

Critical scaling of Bagnold rheology at the jamming transition of frictionless two-dimensional disks

Vagberg, D.L.S. (TU Delft Engineering Thermodynamics)
Olsson, Peter (Umeå University)
Teitel, S. (University of Rochester)

2016

We carry out constant volume simulations of steady-state shear-driven rheology in a simple model of bidisperse soft-core frictionless disks in two dimensions, using a dissipation law that gives rise to Bagnoldian rheology. We discuss in detail the critical scaling ansatz for the shear-driven jamming transition and carry out a detailed scaling analysis of our resulting data for pressure p and shear stress σ. Our analysis determines the critical exponent β that describes the algebraic divergence of the Bagnold transport coefficients limγ →0p/γ 2,σ/γ 2∼(φJ-φ)-β as the jamming transition φJ is approached from below. For the low strain rates considered in this work, we show that it is still necessary to consider the leading correction-to-scaling term in order to achieve a self-consistent analysis of our data, in which the critical parameters become independent of the size of the window of data used in the analysis. We compare our resulting value β≈5.0±0.4 against previous numerical results and competing theoretical models. Our results confirm that the shear-driven jamming transition in Bagnoldian systems is well described by a critical scaling theory and we relate this scaling theory to the phenomenological constituent laws for dilatancy and friction.

http://resolver.tudelft.nl/uuid:d420e560-33bd-47c8-ba0f-2ccff56fce1e

https://doi.org/10.1103/PhysRevE.93.052902

2470-0045

Physical Review E, 93 (5)

Institutional Repository

journal article

© 2016 D.L.S. Vagberg, Peter Olsson, S. Teitel