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 = Gτ_R, where η₀ is the low shear viscosity of the suspension (Newtonian plateau), G is the shear modulus (modulus of rigidity) and τ_R is the longest relaxation time. The two macroscopic parameters, G and τ_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 σ_f and γ_c through the relation G = σ_f/γ_c where σ_f is the frictional stress and γ_c the critical strain corresponding to the onset of contact breaking. In a second step we show that the relaxation time τ_R, determined by mechanical spectroscopy, matches precisely with the decorrelation time τ_D, derived independently from local optical measurements. We show that, similarly to the plateau viscosity η₀, both are controlled by the dimensionless Peclet number Pe_lub in that τ_R ∝ 1/Pe_lub and τ_D ∝ 1/Pe_lub where Pe_lub = σ_lub/σ_f 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].