Soft glassy dynamics and rheology: A damped soft-sphere model

The mechanical response of a diverse family of seemingly disparate materials, like foams, cells, and emulsions, exhibiting a similar response to applied deformation, has largely defied explanation. One example being their rheology, where the complex modulus shows a weak power-law dependence on frequency, that we recently postulated could be a direct manifestation of the fractal energy landscape of these materials. In this work, we extend our previous study by performing bubble dynamics simulations with damped, non-inertial bubbles evolving similar to ripening observed in foams. We study the coarsening system in the dynamic scaling state, and the resulting physical and dynamic properties over a range of damping effects. As shown before, the under-damped system gives rise to spatially correlated dynamics with avalanches while traversing fractal paths in 3N-dimensional configuration space through super-diffusive motion. Further, we investigate the statistical nature of avalanches in time and their disappearance in the over-damped limit, and the corresponding changes in the rheology of the system. Lastly, we study the aging of the system after strong perturbations and look for signatures of self-organization in the dynamical steady state.