Dynamics of vibrated granular suspensions probed by mechanical spectroscopy and diffusing wave spectroscopy measurements
Résumé
In this paper, we investigate the dynamics of vibrated granular suspensions by mechanical spectroscopy and multi-speckle diffusing wave spectroscopy (MSDWS), with the aim of relating microscopic dynamical mechanisms, at a grain scale, to the resulting macroscopic rheological behavior of the samples. Rheological experiments reveal that the samples exhibit a Maxwellian behavior at low frequencies leading to eta(0) G tau(R), where eta(0) is the low shear viscosity of the suspension (Newtonian plateau), G is the shear modulus (modulus of rigidity) and tau(R) is the longest relaxation time. The two macroscopic parameters, G and tau(R), of the Maxwell model can be related to structural parameters in order to link microscopic and macroscopic levels. To do so, in a first step, we show that the macroscopic parameter G is related to the structural parameters sigma(f) and gamma(c) through the relation G = sigma(f)/gamma(c) where sf is the frictional stress and gc the critical strain corresponding to the onset of contact breaking. In a second step we show that the relaxation time tau(R), determined by mechanical spectroscopy, matches precisely with the decorrelation time tau(D), derived independently from local optical measurements. We show that, similarly to the plateau viscosity eta(0) both are controlled by the dimensionless Peclet number Pelub in that tau(R) alpha 1/Pe(lub) and tau(D) alpha 1/Pelub where Pelub sigma(lub)/sigma(f) has been defined in a previous article as the ratio of the lubrication stress, induced by vibrations, and the frictional stress