Critical scaling of Bagnold rheology at the jamming transition of frictionless two-dimensional disks
2016 (English)In: Physical Review E, ISSN 2470-0045, Vol. 93, no 5, 052902Article in journal (Refereed) PublishedText
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 sigma. Our analysis determines the critical exponent beta that describes the algebraic divergence of the Bagnold transport coefficients lim((gamma) over dot -> 0) p/(gamma) over dot(2), sigma/(gamma) over dot(2) similar to (phi(J) -phi)(-beta) as the jamming transition phi(J) 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 beta approximate to 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.
Place, publisher, year, edition, pages
2016. Vol. 93, no 5, 052902
IdentifiersURN: urn:nbn:se:umu:diva-122562DOI: 10.1103/PhysRevE.93.052902ISI: 000376644900013OAI: oai:DiVA.org:umu-122562DiVA: diva2:949859