FLUID SKIMMING AND PARTICLE ENTRAINMENT INTO A SMALL CIRCULAR SIDE PORE

It is a well-known observation in fluidization technology, axial filters and the blood microcirculation that the discharge concentration of a particulate suspension through a small circular side pore which is fed by a large main tube can be significantly lower than the feed concentration. Two underlying mechanisms are believed to be responsible for this exit concentration defect: the fluid skimming from the particle-free layer at the main tube wall and the particle screening due to the hydrodynamic interaction with the pore entrance. In this paper we shall focus our attention only on the first mechanism and shall present a theory which relates the discharge concentration to the dimensionless volume discharge rate 2-pi-Q through the side pore (scaled to the wall shear rate in the main tube and the pore radius) and the ratio of the particle to pore entrance diameters, under creeping flow conditions and for small particle concentrations. First, the shape of the capture tube cross-section upstream of the pore is computed on the basis of a simplified three-dimensional velocity field which neglects the disturbance produced by the orifice on the incoming shear flow. Surprisingly simple closed-form expressions for this shape are derived as Q --> infinity or as Q --> 0. Also, using a recently developed exact solution for the simple shear flow past an orifice (Davis 1991), we are able to rigorously demonstrate that, even for small Q, the disturbance produced by the orifice on the shear flow has only a minor effect on the capture tube cross-section far upstream. This simplified flow field is then used to construct a three-dimensional theory for the discharge concentration defect due to pure fluid skimming for a dilute suspension of spheres. The qualitative features of the theoretical predictions show the same trends as the experimental observations in the microcirculation, although the limits of this theory are well below the observed hematocrit concentrations and the particles are taken as rigid spheres.