A non-Brownian, inertialess, dense suspension of rigid hollow glass spheres is studied with time sweep oscillatory experiments. The measured apparent complex viscosity is shown to depend on the amplitude of the applied strain, in agreement with the literature, and, unexpectedly, also on the angular frequency. Two different regimes are individuated depending on the applied strain. For values smaller than 1, when the structure evolution is driven by the shear-induced diffusion, the complex viscosity depends on the frequency, for values larger than 1, it is rate independent. In the first regime, the dependence on the applied strain amplitude and the angular frequency can be lumped into a single parameter: The maximum shear rate, the applied strain amplitude times the angular frequency. The results obtained are quite surprising since in a non-Brownian, inertialess, dense suspension, the particle interactions do not have a characteristic time scale and, consequently, the governing equations of motion result rate independent. Only the presence of a nonhydrodynamic force can introduce a characteristic time. We observe that this nonhydrodynamic force must be so small to be neglected in simple shear, since the behavior of the investigated suspension in the steady shear flow is found to be rate independent, and it must show its effects only in oscillatory experiments with strain amplitude smaller than 1. The frequency dependence is also observed with two less concentrated suspensions and all the data collapse on a single master curve, proving that the physics underneath the rate dependence is independent of the concentration.

Newtonian non-Brownian concentrated suspensions show a mismatch between the steady state and the complex viscosity, whatever the strain amplitude imposed in the oscillatory flow. This result is counterintuitive in the two extreme cases of vanishing strain amplitude and very large one. In the first case, the oscillatory flow should not be able to alter the steady microstructure, as well as in the other opposite limit for which the strain amplitude is so high that the oscillatory flow resembles a steady flow reversal. If the microstructure is not altered with respect to the steady one, similarly the complex viscosity should be equal to the steady one. We here investigate experimentally and numerically the origin of the viscosities mismatch at any imposed strain amplitude. We focus on the first two or three cycles of oscillations and different particle concentrations. Experimental and numerical results agree and allow to prove that for intermediate amplitudes, the oscillatory shear induces the breakage of particle clusters and the microstructure modifies so to minimise particle collisions. For very small strain amplitudes, the oscillatory shear only induces the rotation of few couples of touching particles and the complex viscosity results slightly smaller than the steady one, while for very large strains, the oscillatory flow reshuffles the particles inducing a microstructure as clustered as the steady state one but with a different angular distribution function. We show that the vast majority of the microstructure rearrangement takes place in the first half cycle of oscillation.

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