Rheology of dense vibrated granular flows: non-monotonic response controlled by granular temperature

TL;DR

The paper investigates how vertical vibration modulates the rheology of dense granular flows using DEM simulations of a stress-imposed vane rheometer. It shows that the effective viscosity η increases with confining pressure and decreases with vibration amplitude, while η exhibits a non-monotonic response to frequency due to energy injection and dissipation balance. A central result is that the rheology is controlled by the granular temperature K relative to an confinement-energy scale K_p = p π r^3, i.e., the dimensionless ratio $\bar{K}=K/K_p$, with η in the fluidized regime collapsing as $η ∝ \bar{K}^{α}$ where $α ≈ -2$. The authors also develop a minimal two-block model reproducing the observed $A^2/p$ scaling and connect their findings to prior work on friction weakening, providing a unified framework for vibrated granular rheology with potential implications for flow control.

Abstract

We study the rheology of dense granular materials subjected to vertical vibration using numerical simulations of a stress-imposed vane rheometer. The effective viscosity increases with confining pressure, decreases with vibration amplitude, and exhibits a non-monotonic dependence on frequency: weakening is observed at intermediate frequencies but is lost at high frequencies. We show that the rheological response is governed by the balance between grain-scale agitation energy and the stabilizing effect of confinement. This framework reconciles previously observed trends in viscosity and friction weakening and emphasizes the central role of energy injection and dissipation in determining granular flow properties under vibration.

Figures (7)

• Figure 1: Granular temperature as a function of the oscillation amplitude $A$ and frequency $f$. The granular temperature increases monotonically as a function of $A$ at any fixed frequency. Meanwhile, for any fixed value of $A$, it exhibits a non-monotonic behavior, reaching a maximum at an intermediate frequency. This plot is obtained by extending the numerical results of Ref. Plati2021Getting to a broader range of $A$ and $f$ values.
• Figure 2: a) Effective viscosity as a function of the rescaled acceleration (varied through $f$) for three shaking amplitudes. Experimental data from gnoli2018controlled. b) Analogous results by numerical simulations. Each point is obtained by averaging over 3 statistically independent runs. c) Kinetic energy of the granular medium as a function of $\Gamma$ (varied through $f$) for three shaking amplitudes (simulations performed without the rotating vane). d) Effective viscosity as a function of the granular temperature in numerical simulations. The decreasing trend is well approximated by the scaling $\eta \propto K^\alpha$ with $\alpha=-2$.
• Figure 3: a) Effective viscosity as a function of $\Gamma$ (varied through $f$) for two couples of amplitudes and pressures. b) Minimum effective viscosity as a function of $A^2/p$ for four pressures. c) Effective viscosity in the fluidized state ($\Gamma > \Gamma_{\text{m}}$) as a function of $A^2/p$ for four pressures and amplitudes. d) Effective viscosity in the fluidized state ($\Gamma > \Gamma_{\text{m}}$) as a function of $\bar{K}\propto K/p$ for four pressures and amplitudes. Diamond, square, upper- and lower-triangle markers correspond to $A=6,14,26,58$$\mu$m respectively. Red, blue, green, yellow markers correspond to $p=31,92,308,924$ Pa respectively.
• Figure 4: Ratio of the dissipative power to the granular temperature (main panel) and dissipative power (inset) as a function of $\Gamma$ varied through $f$. Simulations are in the same geometry as the ones discussed in the main text but removing both the vane and the top lid. The driving amplitude is fixed to $A=26$$\mu$m.
• Figure 5: Average friction $\langle \mu \rangle$ as a function of $\Gamma = A f^2/F_P$ in the Hertzian case. Different curves correspond to different values of $A$ and $F_P$. The equations of motion are solved with $k_1=k_2=1$, and $\gamma=5$.