Effect of confining conduit on effective viscosity of dilute colloidal suspension

In this article, we discuss the effect of the bounding cylinder on the rheology of a dilute suspension. We consider a colloidal solution of spherical particles flowing through a cylinder under creeping motion assumption. For transport of such particulate fluid, the increase in the viscous loss due to the existence of suspended particles can be described in terms of enhanced effective viscosity eta(eff) for the medium. Einstein's formula quantifies this increase in viscosity when the flow-domain is unbounded. For bounded domain, however, the increase in viscosity is not only dictated by the properties of the solutes but also affected by the geometry of the confinement. We illustrate this effect of geometry on the effective viscosity by accurately resolving the viscous interaction between a freely suspended sphere and a confining cylinder. First, we take into account a solution of equal spheres, and present the effective viscosity for different cylinder to sphere size ratio as well as for different excluded volume near the cylinder periphery for electrostatic interactions. Then, we also consider a variation in size distribution and determine the rheological properties for different means and variances of the distribution.