Abstract
The flow of granular materials through a vertical channel is examined using the discrete element method (DEM) and the recent continuum models of Henann & Kamrin (Proc. Natl Acad. Sci. USA, vol. 110, 2013, pp. 6730–6735), Barker et al. (Proc. R. Soc. Lond. A, vol. 473, 2017, p. 20160846), Schaeffer et al. (J. Fluid Mech., vol. 874, 2019, pp. 926–951) and Dsouza & Nott (J. Fluid Mech., vol. 888, 2020, p. R3). The channel is bounded by walls separated by a distance $2 \, W$ in the $x$ -direction. For the DEM, periodic boundary conditions are used in the $z$ - and $y$ - (vertical) directions with no exit at the bottom of the channel. The governing equations reduce to ordinary differential equations in the $x$ -direction. There is a plug layer near the centre and a shear layer near the wall, as observed in experiments. There is a decrease in the solids fraction $\phi$ in the shear layer, except for the models of Barker et al. and Henann & Kamrin. A modification of the latter gives more realistic $\phi$ profiles. The thickness of the shear layer depends on $2\,W$ and the bulk solids fraction $\bar {\phi }$ . For all the models, solutions could not be obtained for some parameter values. An example is the negative fluidity in the model of Henann & Kamrin. The model of Dsouza & Nott predicts much higher normal stresses, possibly because of large contributions from the non-local terms. None of the models specify a complete set of boundary conditions (b.c.). The DEM results suggest that the slip velocity and the wall friction b.c. lead to a slip length and an angle of wall friction that are independent of $2\,W$ . The models are based on extensions of the equations for slow, rate-independent flow. A model that includes collisional effects, such as kinetic theory, should be combined with the present models. A preliminary analysis of the kinetic theory model of Berzi et al. (J. Fluid Mech., vol. 885, 2020, p. A27), shows that it may have undesirable feature.
Highlights
The flow of granular materials occurs in a variety of natural and industrial settings such as landslides, desert dunes, silos and rotary kilns
A modified version of the Coulomb model, known as critical state soil mechanics, incorporates compressibility by modifying the yield condition (Schofield & Wroth 1968; Jackson 1983; Rao & Nott 2008) and specifying a flow rule that relates the stress to the rate of deformation tensor
Granular flow through a vertical channel: discrete element method (DEM) and models the rate of deformation tensor
Summary
The flow of granular materials occurs in a variety of natural and industrial settings such as landslides, desert dunes, silos and rotary kilns. A modified version of the Coulomb model, known as critical state soil mechanics, incorporates compressibility by modifying the yield condition (Schofield & Wroth 1968; Jackson 1983; Rao & Nott 2008) and specifying a flow rule that relates the stress to the rate of deformation tensor. Granular flow through a vertical channel: DEM and models the rate of deformation tensor. The simulation box is a rectangular parallelepiped, with a bottom and four flat frictional walls, of dimensions 2 W, H and B in the x-, y- and z-directions, respectively (figure 1a). As the flow is expected to be fully developed far above the exit slot, the motion of a reasonable number of particles, say 5 × 104–2 × 105, is simulated by applying periodic boundary conditions in the y- and z-directions.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
