Loughborough University
EJMFLU_2016_19_Revision 1_V0.pdf (989.82 kB)

Particle-laden viscous channel flows: Model regularization and parameter study

Download (989.82 kB)
journal contribution
posted on 2018-10-08, 15:05 authored by Lennon O. Naraigh, Ricardo Lopes-BarrosRicardo Lopes-Barros
We characterize the flow of a viscous suspension in an inclined channel where the flow is maintained in a steady state under the competing influences of gravity and an applied pressure drop. The basic model relies on a diffusive-flux formalism. Such models are common in the literature, yet many of them possess an unphysical singularity at the channel centreline where the shear rate vanishes. We therefore present a regularization of the basic diffusive-flux model that removes this singularity. This introduces an explicit (physical) dependence on the particle size into the model equations. This approach enables us to carry out a detailed parameter study showing in particular the opposing effects of the pressure drop and gravity. Conditions for counter-current flow and complete flow reversal are obtained from numerical solutions of the model equations. These are supplemented by an analytic lower bound on the ratio of the gravitational force to the applied pressure drop necessary to bring about complete flow reversal.


The authors would like to acknowledge the Norwegian Research Council for financial support in generating this paper. R.B. acknowledges the support of Science Foundation Ireland under grant 12/IA/1683 and the support of the Irish Research Council under the ‘New Foundations’ Scheme 2014.



  • Science


  • Mathematical Sciences

Published in

European Journal of Mechanics B: Fluids




90 - 98


NARAIGH, L.O. and BARROS, R., 2016. Particle-laden viscous channel flows: Model regularization and parameter study. European Journal of Mechanics - B/Fluids, 59, pp.90-98.


© Elsevier


  • AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date


Publication date



This paper was published in the journal European Journal of Mechanics - B/Fluids and the definitive published version is available at https://doi.org/10.1016/j.euromechflu.2016.05.005.




  • en