Rheology of a suspension of long plates in a Poiseuille flow

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: 6 July 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 (, 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 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.