On transport of suspended particulates in tube flow

Abstract

Blood cells suspended in shear flows exhibit much larger dispersive motions than those predicted by the Stokes-Einstein formula for Brownian diffusion. The lateral migration and the erratic motions of the 8IJ.m red blood cells (RBC) is thought to be analogous to a diffusive process. It is shown that the often cited convective-diffusion theory may not be an adequate model for describing the transverse migration of suspended cells in blood flow.

A comprehensive review of both the classical theory and of contemporary work in particle transport is presented, with particular emphasis on low Reynolds number tube flows. The mechanisms of Taylor dispersion, the effects of Brownian perturbations on translational and rotational motions of the suspended particles in shear fields, and the influence of integratable and chaotic advections, are individually examined.

The classical experiment by Segre and Silberberg (1962) lead us to believe that particle hydrodynamics may play an important role in transverse migrations. In this light, we have further examined the hydrodynamic aspects of the so-called “tubular pinch” effect, the lateral migration of rigid spheres. We have also discussed the transverse motions of liquid drops, and the reversibility of the organization of suspensions in transport.

The convective accelerations in the entrance region of a tube can produce relative velocities between fluid medium and various type of particulates if there is a difference in density. The deformable RBC, an “active-type” particle, can provide feedback to the flow from both mass and momentum considerations; the more rigid platelet, a “passive-type” particle, will experience a much smaller relative velocity as compared to the RBC.

We may expect that particles of different densities are transported to different equilibrium annular positions before entering the fully developed flow region. The erratic, lateral movement of suspended particulates in steady laminar tube flow can be described by the usual Lagrangian coordinates.