Boundary conditions for granular flows at randomly fluctuating bumpy boundaries
Abstract
In this paper we focus attention on the interactions between rapid flows of identical, smooth spheres that interact with bumpy boundaries through inelastic collisions. The boundaries translate with specified mean velocities, and deviate about the mean with specified fluctuation velocities. Based upon Maxwellian velocity distribution functions that describe the velocities of both the flow particles and boundaries, we calculate the rates at which linear momentum and kinetic energy are exchanged between the two. Using these exchange rates, we write down conditions that ensure that both momentum and energy are balanced at bumpy boundaries. Finally, we employ a constitutive theory that is consistent with these conditions to calculate the granular temperature and solid fraction profiles within a granular material confined between two parallel, bumpy surfaces that randomly fluctuate about zero mean velocity.
 Publication:

Presented at the 2nd USJapan Seminar on Micromechanics of Granular Materials
 Pub Date:
 1991
 Bibcode:
 1991mgm..conf....4R
 Keywords:

 Boundary Conditions;
 Distribution Functions;
 Granular Materials;
 Inelastic Collisions;
 Kinetic Equations;
 Spheres;
 Velocity Distribution;
 Kinetic Energy;
 Kinetic Theory;
 Mathematical Models;
 MaxwellBoltzmann Density Function;
 Momentum Transfer;
 Fluid Mechanics and Heat Transfer