#### Alladi Ramakrishnan Hall

#### Shear banding phenomenon in dense amorphous materials

#### Vishwas Vasisht

##### LIPhy, Grenoble

*Dense disordered solids, such as emulsions, foams and dense colloidal suspensions, when subjected to shear deformations at a chosen rate, yield and eventually begin to flow. Upon reaching steady state stress values, the system is expected to fluidise and flow homogeneously, but one often observes strong flow instabilities, with parts of the material completely jammed, while other parts of the material flowing at shear rates higher than the imposed rate [1]. This phenomenon is often termed as gradient shear banding, observed both in experiments [2] as well as simulations [3]. *

In this work we derive a theoretical framework for the appearance of a permanent shear banding instability due to inertial effects. Using a linear stability analysis we estimate the minimum system size necessary to observe a flow instability in the stationary flow of dense particle systems. To verify the theoretical arguments and its predictions, we subject a polydisperse soft sphere system with pure repulsive interactions to a uniform shear deformation using molecular dynamics simulations. We find that the minimum system size required to accommodate a shear band increases with a decrease in shear rate. For large enough systems, we observe in MD simulations the formation of several shear bands which coarsen into one single shear band in the long time limit.

[1] Daniel Bonn, Morton M. Denn, Ludovic Berthier, Thibaut Divoux, and Sébastien Manneville, Rev. Mod. Phys. 89, 035005 (2017).

[2] Thibaut Divoux, Marc A. Fardin, Sebastien Manneville, and Sandra Lerouge, Annual Review of Fluid Mechanics Vol. 48:81-103 (2016).

[3] GP Shrivastav, P Chaudhuri, J Horbach, Journal of Rheology 60, 835 (2016); V V Vasisht, G Roberts, E Del Gado arXiv:1709.08717 (2017).

Done