A nonlocal constitutive law for slow granular flows · revision history
Revision 1
Accepted · first revision · record
- Title
- A nonlocal constitutive law for slow granular flows
- Plain
- A simple local friction law describes fast flows of grains well but fails when the flow is slow: grains creep below the expected stopping point and thin layers stop earlier than thick ones. The correct replacement law, and its basis in grain-scale physics, is not established.
- Precise
- The local $\mu(I)$ rheology gives the stress ratio $\mu = \tau / P$ as a function of the inertial number $I = \gamma_{\mathrm{dot}} d / \sqrt{P / \rho_s}$ (shear rate $\gamma_{\mathrm{dot}}$, grain diameter $d$, pressure $P$, grain density $\rho_s$). It fails as $I \to 0$: creep below the yield ratio $\mu_s$, thickness-dependent stopping height $h_{\mathrm{stop}}$ of flowing layers, and flow induced by distant shear. Find a constitutive law (for example a fluidity model with cooperativity length $\xi \sim \mid \mu - \mu_s \mid^{-1/2}$) that predicts all three effects quantitatively for frictional spheres, with parameters derived from grain-scale physics.
- Settled by
- A law with grain-scale-derived parameters that predicts creep profiles, $h_{\mathrm{stop}}(\theta)$ and remote-shear fluidization in several geometries within experimental error.
- Kind
- phenomenon
- Answer type
- mechanism
- References
- (empty)
- Literature status
- partially-resolved
- Status note
- Nonlocal fluidity models introduced from 2012 fit several geometries, but their microscopic basis and the cooperativity exponent remain debated (2026).
- Posed since
- (empty)