Soft Dynamics simulation: 2. Elastic spheres undergoing a T1 process in a viscous fluid
arXiv:0901.0171 · doi:10.1140/epje/i2009-10528-1
Abstract
Robust empirical constitutive laws for granular materials in air or in a viscous fluid have been expressed in terms of timescales based on the dynamics of a single particle. However, some behaviours such as viscosity bifurcation or shear localization, observed also in foams, emulsions, and block copolymer cubic phases, seem to involve other micro-timescales which may be related to the dynamics of local particle reorganizations. In the present work, we consider a T1 process as an example of a rearrangement. Using the Soft dynamics simulation method introduced in the first paper of this series, we describe theoretically and numerically the motion of four elastic spheres in a viscous fluid. Hydrodynamic interactions are described at the level of lubrication (Poiseuille squeezing and Couette shear flow) and the elastic deflection of the particle surface is modeled as Hertzian. The duration of the simulated T1 process can vary substantially as a consequence of minute changes in the initial separations, consistently with predictions. For the first time, a collective behaviour is thus found to depend on another parameter than the typical volume fraction in particles.
11 pages - 5 figures
References in corpus (10)
- A constitutive law for dense granular flows
- Critical Scaling of Shear Viscosity at the Jamming Transition
- Strain-Rate Frequency Superposition (SRFS) - A rheological probe of structural relaxation in soft materials
- Yielding and flow in adhesive and non-adhesive concentrated emulsions
- The jamming transition as probed by quasistatic shear flow
- Relaxation time of the topological T1 process in a two-dimensional foam
- Relaxing in foam
- Statistics of Bubble Rearrangements in a Slowly Sheared Two-dimensional Foam
- Two dimensional foam rheology with viscous drag
- Slow viscoelastic relaxation and aging in aqueous foam