Rheology of a suspension of long plates in a Poiseuille flowH. 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
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.
47.57.E- - Suspensions.
47.57.Qk - Rheological aspects.
47.50.-d - Non-Newtonian fluid flows.
© Europhysics Letters Association 2007