Flow reversal triggers discontinuous shear thickening response across an erodible granular bed in a Couette-Poiseuille-like flow

Granular rheology is experimentally investigated in a vertical Couette-Poiseuille-like channel flow of photoelastic disks, where an erodible bed is sheared intermittently by an upward-moving shear band and a gravity-induced reverse flow. The shear band conforms to the existing nonlocal Eyring-like rheology but the bed exhibits discontinuous shear thickening from the Bagnold inertial regime near the band-bed interface to the Herschel-Bulkley plastic regime near the static wall. This newly discovered bed rheology is rate dependent and is associated with the fragility of the contact networks indicated by the statistics of local stress states inferred from the material photoelastic responses.

Figure 1

(a) Experimental set-up marking the region of interest. (b) Typical evolution of instantaneous vertical velocity profiles $v(x,t)$ during a flow reversal process at $V_0^{*}=5.53\times {10}^{-2}$. Top and bottom insets: Instantaneous photoelastic image before and after the contact network rearranged during the reversal. (c) Spatiotemporal diagrams for $v(x,t)$. (d) Scaled flow reversal frequency profiles under different $V_0^{*}$. Inset: Scaled mean FF ($V_{+}$) and RF ($V_{-}$) velocity profiles.

Figure 2

(a) Time-averaged scaled velocity profiles, where the downward flow segments are enlarged in (b); [(c) and (d)] scaled shear rate profiles within the shear band and the bed, respectively; (e) scaled shear band widths versus $V_0^{*}$; (f) solid fraction profiles; and (g) scaled shear stress profiles. The symbols correspond to different $V_0^{*}$ given in Fig. 1.

Figure 3

Rheological relations for shear stress $\tau$ versus shear rate $\dot{\gamma }$ in (a) the shear band ($0<x<{\delta }_i$) and (b) the bed (${\delta }_i<x<W$). Solid lines in (a): the Eyring model in Eq. (1) with the fitting parameters given in the insets. (c) The fitting parameters for the Bagnold and the HB model shown in (b).

Figure 4

Flow-regime map. The open circles threaded by the solid line presents the shear-band width data in Fig. 2.

Figure 5

Probability distribution functions of the normalized stress state $P\left(f\right)$ across the flow for (a) $V_0^{*}=5.53\times {10}^{-2}$ and (b) $V_0^{*}=6.6\times {10}^{-1}$. $P\left(f\right)$ on the walls and the flow regime boundaries are marked by thick colored lines while the thin lines denote $P\left(f\right)$ within the flow regimes. The insets show $P\left(f\right)$ in the strong-stress state ($f>1$).