Apparent wall-slip of colloidal hard-sphere suspensions in microchannel flow

We investigated the dependence of the apparent slip length (β) on the particle concentration for suspensions of colloidal hard spheres flowing through microchannels with smooth walls. Hydrostatic pressure was used to pump monodisperse suspensions of 1 μm silica spheres in water–glycerol mixture through a poly(dimethylsiloxane) microchannel with rectangular cross section. Confocal scanning laser microscopy allowed accurate measurement of velocity profiles via particle tracking velocimetry. Apparent slip lengths were measured by extrapolating the velocity profiles to zero. Systematic variations were made of the particle volume fraction Φ (0.03–0.42) and the Peclet number (2–50). In these regimes the apparent slip length shows a weak dependence on Pe and the slip velocity near the wall grows linearly with shear rate irrespective of Φ. However, β turns out to increase strongly with Φ, tending toward an asymptotic behavior for Φ ≫ 0.3. To explain these observations, we worked out a conceptually simple model, in which the apparent slip is caused by a local reduction in volume fraction due to excluded volume, and the local viscosity is calculated using the Krieger–Dougherty equation. The predictions by this model match the experimental results remarkably well.