Mathematical Problems in Engineering
Volume 6 (2001), Issue 6, Pages 505-526

Vertical flow of a multiphase mixture in a channel

Mehrdad Massoudi1 and C. Lakshmana Rao2

1National Energy Technology Laboratory, U.S. Department of Energy, P.O. Box 10940, Pittsburgh 15236, PA, USA
2Department of Applied Mechanics, Indian Institute of Technology-Madras, Chennai 600038, India

Received 4 January 2000; Revised 17 April 2000

Copyright © 2001 Mehrdad Massoudi and C. Lakshmana Rao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.