Issue
EPL
Volume 79, Number 5, September 2007
Article Number 54002
Number of page(s) 5
Section Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics
DOI http://dx.doi.org/10.1209/0295-5075/79/54002
Published online 01 August 2007
EPL, 79 (2007) 54002
DOI: 10.1209/0295-5075/79/54002

Rheology of a suspension of long plates in a Poiseuille flow

H. Ez-Zahraouy1, H. Mansouri1, A. Benyoussef1, P. Peyla2 and C. Misbah2

1  Laboratoire de Magnétisme et de la Physique des Hautes Energies, Université Mohammed V, Faculté des Sciences - Avenue Ibn Battouta, Rabat B.P. 1014, Morocco
2  Laboratoire de Spectrométrie Physique, Université Joseph Fourier, Grenoble1 BP87, F-38402 Saint Martin d'Hères, France


received 28 March 2007; accepted in final form 6 July 2007; published September 2007
published online 1 August 2007

Abstract
An analytical study of a suspension of long solid plates in a plane Poiseuille geometry is presented. The flow rate, the dissipation, and the apparent viscosity $\eta $ ( $\equiv \eta _{0}Q_{0}/Q$, $\eta _{0}$ is the fluid viscosity, and Q0 and Q the flow rates with and without particle, for a given pressure drop) are determined as a function of the underlying structure. For a single particle, it is found that both dissipation and flow rate are maximal, for a given pressure drop, when the particle is at the center, while $\eta $ is minimal. We provide analytical results for these quantities for a set of N particles distributed in an arbitrary fashion in the channel. This is exploited for a periodic distribution of N particles. The dissipation is found to be quasi-linear as a function of the wavelength of the structure and is a nontrivial nonlinear function of the volume fraction.

PACS
47.57.E- - Suspensions.
47.57.Qk - Rheological aspects.
47.50.-d - Non-Newtonian fluid flows.

© Europhysics Letters Association 2007