An order parameter equation for the dynamic yield stress in dense colloidal suspensions

Abstract

Abstract. We study the dynamic yield stress in dense colloidal suspensions by analyzing the time evolution of the pair distribution function for colloidal particles interacting through a Lennard-Jones potential. We find that the equilibrium pair distribution function is unstable with respect to a certain anisotropic perturbation in the regime of low temperature and high density. By applying a bifurcation analysis to a system near the critical state at which the stability changes, we derive an amplitude equation for the critical mode. This equation is analogous to order parameter equations used to describe phase transitions. It is found that this amplitude equation describes the appearance of the dynamic yield stress, and it gives a value of 2/3 for the shear thinning exponent. This value is related to δ in the Ising model.

Growing length and time scales in a suspension of athermal particles

“…consistent with a theory in which shear stress is an order parameter that undergoes marginal stability at the jamming transition point [23,24]. The slow relaxation is also apparent in view of the particle dynamics.…”

Vortex jamming in superconductors and granular rheology

“…The flow curves in rheology, the shear-stress vs the shear-rate, correspond to the current-voltage curves in superconductors [4]. Exploring this analogy further we here demonstrate by computer simulations that there exist the zero-temperature jamming transitions and glassy non-linear rheology, originally found in granular and other materials [5,6,7,8,9,10,11,12,13,14,15,16], in a class of highly frustrated anisotropic Josephson junctions arrays (JJA) on a square lattice. Our key observation is that anisotropy of Josephson coupling plays the role of normal load or density in granular system such that a jamming transition takes place in the limit of isotropic Josephson coupling at zero temperature.…”

“…The scaling function (master flow curve) is expected to behave asymptotically asJ(x) ∝ x for small enough x in the Here we used the notations reflecting the analogy with the equilibrium critical behaviour of ferro-magnets under magnetic field as noticed by Wolf, Gubser and Imry [36]: the shear plays the role of symmetry breaking field like the magnetic field and the critical current emerges as an order parameter like the magnetization (see [11] for a similar argument in the context of rheology). As shown in Fig.…”

Emergence of Rigidity at the Structural Glass Transition: A First-Principles Computation

“…Our result of a plateau shear modulus emerging continuously below T c disagrees with the conventional MCT [6], which predicts that the shearmodulus jumps discontinuously to a finite value at T c from the liquid side. Our result means that the density field is frozen at T c as the MCT predicted, but the system is just marginally stable there [12], a picture which is consistent with the energy landscape picture of the RFOT [18][19][20][21][22]. For the visco-elastic measurements, this continuous transition suggests a power law behaviour G ′ (ω), G"(ω) ∝ ω λ .…”