News and Comments

on “Scaling Properties of Granular Rheology near the Jamming Transition”
J. Phys. Soc. Jpn. 77 (2008) 123002


New Scaling Laws for the Jamming Transitions

by Hisao Hayakawa (Yukawa Institute for Theoretical Physics, Kyoto University)
Published December 10, 2008


The term "jamming" is widely used to describe the obstruction of the flow of dense elements cannot flow under a driving force. A common example of such a condition is a traffic jam which occurs when the density of vehicles exceeds a critical value. A similar condition can occur in emulsions, foams, or granular particles under external forces, in which shear modulus and bulk moduli become greater than the critical density. This type of the rigidity transition is called as a jamming transition. Recently, the jamming transition has been regarded as an important phenomena that occurs in dense glassy systems, and many researchers have been investigating the critical behaviors observed near the jamming transition point, (also called as the J point) [1,2].

Among the numerous studies on the jamming transition, a noteworthy one is that conducted by Olsson and Teitel[3]; they proposed a scaling law for the shear stress of a system near the jamming point which might be characterized by a continuous rheological transition. However, the kinetics of their model cannot describe granular systems suitably. Hatano[4] performed an extensive simulation of frictionless granular particles under a constant shear rate, and demonstrated the existence of scaling laws for the shear stress, the pressure and the kinetic temperature defined by the velocity variance (see Fig.1). He also demonstrated that the scaling exponents strongly depend on the power law for the contact force between the particles. The results of his study indicate that the jamming transition of frictionless granular particles resembles a conventional second-order phase transitions. His study is of great interest to many researchers who are interested in glassy behaviors, and it highlights one approach to the study of jamming transitions.

Fig. 1: A scaling plot of the shear stress, where S, γ, and Φ denote the shear stress, the shear rate, and the excess volume fraction at the J point. The inset shows the volume fractions used in the simulation. The solid line represents Bagnold’s scaling law (S is proportional to γ2 in the liquid region). (Fig. 2(a) of ref. 4)

After his paper [4] was submitted, he, along with many other researchers, conducted further related studies and clarified the following issues: (i) the critical exponents of the rheological properties discussed in his paper appeared to be independent of the spatial dimensions, (ii) similar behaviors can be observed even in systems of Josephson junction arrays, and colloidal models, (iii) the exponent of the correlation length might depend on the spatial dimension unlike the case of the rheological exponents as discussed in (i), and (iv) the properties of frictional granular particles seem to be completely different from those of frictionless systems. Since (i) and (iii) are contradictory, we should clarify the relationship between the scaling laws observed in this paper and the increase in the correlation length near the jamming transition. In addition, we must determine the effect of the dynamical heterogeneity observed in many experiments (see Fig.2) on the scaling laws reported in this paper. In this sense, the paper by Hatano[4] has been of great importance in this field. With the increasing interest in the study of jamming transitions, we are attempting to develop a simulation that models this phenomenon accurately.

Fig. 2: Dynamical heterogeneity of sheared granular particles in a 2D simulation. The different colors indicate the speeds of the particles, and the arrows indicate the direction of the shear stress. (Courtesy of Dr. T. Hatano)

References


Note The above article should be referred as “H. Hayakawa: JPSJ Online—News and Comments [December 10, 2008]” when citing.

Copyright © 2008 The Physical Society of Japan.