Boundary conditions on continuum theories of granular flow

Continuum theories of highly agitated granular flows have recently been developed based on ideas from the kinetic theory of gases, with the fluctuation velocity of the grains corresponding to the temperature of the gas. Most often the boundary conditions for a granular system at a wall have been taken to be the same as the boundary conditions for a gas (i.e. the "no-slip" boundary conditions on the average flow velocity and the temperature). However, it is clear from experimental observations that a significant slip can exist in the average flow velocity and temperature at a wall. In this paper, a model of boundary conditions on granular flows will be presented which incorporates the following points: 1. 1. The average flow velocity of the grains at the wall does not equal the wall velocity, with the shear stress at the wall being proportional to the difference in these velocities (the "slip velocity"). 2. 2. Small-amplitude vibrations of the wall can be regarded as one factor in an effective wall "temperature". The other factor is the effect of the roughness of the wall coupled with the slip velocity. The flux of "thermal" energy between the granular system and the wall is determined by the relative values of this effective wall "temperature" and the granular system "temperature". 3. 3. Due to differences between grain-grain and grain-wall collisions, the density of the granular system may exhibit a "jump" at the wall. 4. 4. For walls of insufficient roughness, measured angles of effective internal friction may reflect more the effect of shearing at the wall than in the bulk. These boundary conditions are illustrated by solving a problem in Couette flow. © 1991.

Duke Scholars

Author Peter K. Haff Earth and Climate Sciences