Effect of viscosity on the shaking-induced fluidization in a liquid-immersed granular medium.

Abstract

A liquid-immersed granular medium is shaken vertically under a wide range of accelerations (Γ in dimensionless form) and frequencies (f) and its fluidization process is studied. The granular medium is formed by settling and consists of two size-graded layers (particle diameter d) such that the upper layer is fine grained and is less permeable. When Γ>Γ(c), a liquid-rich layer formed by the accumulated liquid at the two-layer boundary causes a gravitational instability. The upwellings of the instability are separated horizontally by a distance (wavelength) λ, and their amplitude grows exponentially with time [∝exp(pt)] at a growth rate p. We conduct experiments for two liquid viscosity cases such that the particle settling velocity (V(s)) of the same particle differs by a factor of 17. We find that for both cases, Γ(c) is at a minimum in an optimum frequency band centered at f∼100 Hz. However, the high-viscosity (HV) case has a smaller Γ(c), a shorter λ, and a faster dimensionless growth rate [p'=p/(V(s)/d)]. We also measure granular rheology under an oscillatory shear and find that (i) interparticle friction decreases when the strain amplitude becomes large and (ii) friction is smaller for the HV case. From (i), we infer that the shear strain of the shaking experiments becomes largest at around f∼100 Hz. We consider that (ii) is a consequence of liquid lubrication and is a reason for a smaller Γ(c) for the HV case. We show that the low- and high-frequency limits of the optimum frequency band can be explained by introducing critical values of dimensionless jerk (i.e., time derivative of acceleration) J and dimensionless shaking energy S. The low-frequency limit corresponds to the requirement that in order to unjam the particles, the period of shaking (1/f) must be shorter than the time needed for the particles to rearrange by settling (d/V(s)), which also explains why the HV case is fluidized at a lower f compared to the LV case. We apply the results of the linear stability analyses for Rayleigh-Taylor instability. Using the measured λ and p, we infer that (i) only a thin layer beneath the two-layer boundary is mobile and the rest of the lower layer remains jammed and (ii) the effective viscosity of the upper granular layer relative to the liquid is smaller for the HV case as a result of smaller friction.