# Deriving a constitutive model for soft dense suspensions : from microstructure to macrorheology

When |
Nov 23, 2021
from 11:00 to 12:00 |
---|---|

Where | Salle des thèses |

Attendees |
Nicolas Cuny |

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Soft dense suspensions, such as microgels or emulsions, cover a large spectrum of materials made of soft particles immersed in a liquid phase. Although the nature of those particles can be very different, soft dense suspensions share some common rheological properties under simple shear. Above jamming, they exhibit a yield stress and their rheology follows a Herschel-Bulkley law. For those materials startup flows can exhibit an overshoot in shear stress. On flow cessation, one observes a residual stress whose value is smaller than the yield stress, and all the more so with increasing shear rate applied during the preshear.

Establishing an evolution equation for the stress tensor as a response to a given time-dependent deformation is of great importance in order to describe the flow of such systems. Most attempts to obtain a constitutive model are phenomenological. They are typically based on symmetries, such as frame indifference, and while usually motivated by a microscopic physical picture, they do not directly relate the parameters they rely on to microscopic (i.e., particle-level) quantities.

In this talk, I will present a way to obtain a 2D constitutive model for the rheology of athermal soft particles suspensions above jamming starting from the microscopic dynamics. It takes the form of a Ginzburg-Landau-like tensorial evolution equation on the deviatoric part of the stress tensor, which predicts a Bingham fluid with the emergence of a yield stress above a critical jamming fraction. The model shows interesting transient dynamics, predicting stress overshoots upon step increase of the applied shear rate as well as the counter-intuitive dependence on the applied shear rate of the residual stresses after flow cessation, and perhaps more importantly provides a microscopic picture for these phenomena.