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Abstract

Recent experiments [1] as well as molecular dynamics simulations [2,3] confirm the heterogeneous nature of the flow in amorphous solids. Due to limitations in the available time and length scales, however, no conclusion could be made regarding the long time behavior of the flow and the related fluctuations. In this study, we address this and related questions via lattice Boltzmann computer simulations of non-Newtonian fluids. The non-Newtonian character of the fluid enters the LB iteration scheme via a shear rate and density dependent relaxation time, thus encoding the shear rate and density dependence of viscosity. Furthermore, the dependence of the hydrostatic pressure on local density and shear rate is accounted for via a corresponding force term. All the input parameters of the relevant constitutive laws are taken from the preceding molecular dynamics simulations [3]. The present approach thus provides the link between microscopic (MD) simulations and macroscopic hydrodynamic response of the system. The reliability of the lattice Boltzmann simulations is tested by analytic studies of the linear stability phase diagram. As a detailed comparison shows, both the linear stability phase diagram and the dispersion relation for the decay rate of fluctuations in the stable regime are nicely born out by lattice Boltzmann simulations. Studies of the unstable regime, on the other hand, unreveal quite a rich spatio-temporal behavior.
References:
[1] R. Besseling, L. Isa, P. Ballesta, G. Petekidis, M.E. Cates, W.C.K. Poon, Phys. Rev. Lett. 105, 268301 (2010).
[2] F. Varnik, L. Bocquet, J.-L. Barrat, L. Berthier, Phys. Rev. Lett. 90, 095702  (2003).
[3] S. Mandal, M. Gross, D. Raabe, F. Varnik, Phys. Rev. Lett. 108, 098301 (2012).