Particle migration in pressure-driven flow of a Brownian suspension

Shear induced particle migration of 2 μm diameter spherical colloidal particles flowing through rectangular capillary tubes (50 μm × 500 μm cross section) is studied by confocal microscopy. The confocal microscope allows imaging of the flowing particles far from the walls of the tube, at particle velocities up to 8000 μm s−1. The particle volume fraction is varied from φ = 0.05–0.34, and the flow rate is also varied, which results in a bulk Péclet number (Pe) which varies by two orders of magnitude. Concentration profiles are measured across the narrow dimension of the tube; particles at the larger volume fractions migrate toward the centreline, with the migration progressively stronger as Pe increases. The flow has been analyzed using an existing mixture flow model under the assumption of fully-developed flow and a proposed constitutive law which describes the suspension normal stresses as a function of both φ and Pe, the latter of which is defined as a variable quantity through the local shear rate. Shear thinning and shear thickening are not included. Comparisons made with the experimental data indicate that the dependence of the extent of migration upon Pe is well captured but discrepancies arise, at least in part because the assumption of full development is not valid for these experiments. To whom correspondence should be addressed: Present address: Halliburton Energy Services, 2600 S. 2nd Street; Duncan, OK 73536.