The gravity flow of a granular material between two vertical walls separated by a width $2W$ is simulated using the discrete element method (DEM). Periodic boundary conditions are applied in the flow (vertical) and the other horizontal directions. The mass flow rate is controlled by specifying the average solids fraction $\bar {\phi }$, the ratio of the volume of the particles to the volume of the channel. A steady fully developed state can be achieved for a narrow range of $\bar {\phi }$, $\bar {\phi }_{max} \geq \bar {\phi } \geq \bar {\phi }_{cr}$, and the material is in free fall for $\bar {\phi } < \bar {\phi }_{min}$. For an intermediate range of $\bar {\phi }$ ($\bar {\phi }_{cr} > \bar {\phi } \geq \bar {\phi }_{min}$), there are oscillations in the horizontal coordinate of the centre of mass, velocity components and stress. As $\bar {\phi }$ decreases in the range $\bar {\phi }_{cr} > \bar {\phi } \geq \bar {\phi }_{min}$, the amplitude of the oscillations increases proportional to $\sqrt {\bar {\phi }_{cr} - \bar {\phi }}$ and the frequency appears to tend to a non-zero value as $\bar {\phi } \rightarrow \bar {\phi }_{cr}$, indicating a supercritical Hopf bifurcation. The relation between the dominant frequency and the higher harmonics of the position, velocity and stress fluctuations are explained using the momentum balance. It is found that dissipation in the inter-particle and particle–wall contacts is critical for the presence of an oscillatory state.

The steady dense granular flow in a vertical channel bounded by flat frictional walls in one horizontal direction and with periodic boundary conditions in the other horizontal and vertical directions is studied using the discrete element method. The shape of the scaled velocity profile is characterized quantitatively by a universal exponential function, and the ratio of the maximum and slip velocities is independent of the average volume fraction $\bar {\phi }$ and the channel width $W$. For sufficiently wide channels, the maximum and slip velocities increase proportional to $\sqrt {W}$, and the thickness of the shearing zones increases proportional to $W$. There are four zones in the flow, each with distinct dynamical properties. There is no shear in the plug zone at the centre, but there is particle agitation, and the volume fraction $\phi$ is lower than the random close packing volume fraction $\phi _{rcp}$. In the adjoining dense shearing zone, $\phi$ is greater than the volume fraction for arrested dynamics $\phi _{ad} = 0.587$, and the granular temperature and shear rate depend on the particle stiffness. Adjacent to the dense shearing zone is the loose shearing zone where $\phi < \phi _{ad}$. Here, the properties do not depend on the particle stiffness, and the constitutive relations are well described by hard-particle models. The rheology in the loose shearing zone is similar to the dense flow down an inclined plane. There is high shear and a sharp decrease in $\phi$ in the wall shearing zone of thickness about two particle diameters, where the particle angular velocity is different from the material rotation rate due to the presence of the wall.

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.

CoCrMo alloy was deposited on a metallic substrate using laser engineered net shaping (LENS™) – a laser-based additive manufacturing technique. Several samples with five layers of deposit were fabricated at different combinations of laser power, powder feed rate, and scan velocity to study their influence using L4 Orthogonal array. The deposits were evaluated for their microstructure, hardness, wear resistance, and electrochemical performance. Grey relational grade analysis and analysis of variance were applied to identify optimum process parameters. The x-ray diffraction and microstructural analysis of the deposits showed uniform and fine microstructural features. Our experimental results revealed that the coatings fabricated using high laser power (350 W), low powder feed rate (5 g/min), and high scan velocity (20 mm/s) provide the highest hardness (446 ± 2.87 Hv) and wear resistance (1.80 ± 0.0007 mm3/Nm). However, the corrosion resistance was observed to be high for the deposits fabricated using low laser power (200 W), low powder feed rate (5 g/min), and low scan velocity (10 mm/s).