Vertical Flow of a Multiphase Mixture in a Channel

The flow of a multiphase mixture consisting of a viscous fluid and solid particles between two vertical plates is studied. The theory of interacting continua or mixture theory is used. Constitutive relations for the stress tensor of the granular materials and the interaction force are presented and discussed. The flow of interest is an ideal one where we assume the flow to be steady and fully developed; the mixture is flowing between two long vertical plates. The non-linear boundary value problem is solved numerically, and the results are presented for the dimensionless velocity profiles and the volume fraction as functions of various dimensionless numbers.