A kinetic description of collisional frictions between particles and solid boundary in simple sheared granular flows

• An expression for collisional friction coefficient with shear effect is obtained.
• The collisional friction coefficient increases with increasing shear rate.
• The collisional friction coefficient decreases with increasing concentration.
• The theory well predicts the collisional friction coefficient.

In this study, the collisional friction between particles and solid boundaries, which plays an important role in bounded granular flows, was investigated based on the kinetic theory for granular flows. Two limiting states of relative motion between particles and solid walls, i.e., large friction/no sliding and small friction/all sliding, as well as the transition between these limiting states were considered. In order to determine the momentum transfer between solid walls and particles experiencing apparent shears, we used a second-order approximation solution to the Boltzmann equation to determine the velocity distribution function of particles, instead of assuming a simple delta or a Gaussian distribution of particle velocity as has been done in previous studies. The second-order velocity distribution function provides a detailed vision about the energy dissipation due to inelastic particle–wall collisions as well as particle–particle collisions, as it makes it possible for us to discuss how a shear rate affects the collisional friction in bounded granular flows. Comparisons with experimental observations were made for the large friction/no sliding limit, which shows that the predicted and observed collisional friction coefficients are in well agreement. Furthermore, the calculated collisional friction coefficient coincides with computer simulations in the transition regime. Analyses show that the collisional friction is significantly affected by the shear of bounded granular flows.

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