Critical scaling of Bagnold rheology at the jamming transition of frictionless two-dimensional disks.
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 lim_{γ[over ̇]→0}p/γ[over ̇]^{2},σ/γ[over ̇]^{2}∼(ϕ_{J}-ϕ)^{-β} as the jamming transition ϕ_{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 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.
Process & Energy Laboratory, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands.
Daniel
D
Vågberg
Department of Physics, Umeå University, 901 87 Umeå, Sweden.
Peter
P
Olsson
Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA.
S
S
Teitel