Granular temperature model for oscillated slurries: A cell model

Abstract

Diffusive flux models, generally used to describe migration in slurry flow applications are shown to be inadequate for vibrated slurry applications, as in these models the diffusion is linked to a mean shearing flow. As a result they cannot describe a vibrated slurry in the steady state (the zero-motion problem). The granular temperature model by McTigue and Jenkins is able to describe this problem and is therefore suitable for oscillated slurries. The parameters that are required to operate the model are derived from a cell model. Previously they had been set to unity, in the absence of any other clue as to what they might be. In the cell model, developed in this paper, which employs the mean field approximation, the parameters are also found to be of the order of magnitude of unity, but especially the parameter that is associated with dissipation is rather larger than unity. It is shown that this larger parameter leads to a more localized effect in oscillated slurry applications than with the previous estimates. The cell model is verified against viscosity measurements and found to be in good agreement when the number of nearest neighbours is set to six.