Dynamics of vibrated granular suspensions probed by mechanical spectroscopy and diffusing wave spectroscopy measurements

Abstract

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 η0 = GτR, where η0 is the low shear viscosity of the suspension (Newtonian plateau), G is the shear modulus (modulus of rigidity) and τR is the longest relaxation time. The two macroscopic parameters, G and τR, 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 σf and γc through the relation G = σf/γc where σf is the frictional stress and γc the critical strain corresponding to the onset of contact breaking. In a second step we show that the relaxation time τR, determined by mechanical spectroscopy, matches precisely with the decorrelation time τD, derived independently from local optical measurements. We show that, similarly to the plateau viscosity η0, both are controlled by the dimensionless Peclet number Pelub in that τR ∝ 1/Pelub and τD ∝ 1/Pelub where Pelub = σlub/σf has been defined in a previous article as the ratio of the lubrication stress, induced by vibrations, and the frictional stress [Hanotin et al., Phys. Rev. Lett., 2012, 108, 198301].