Pipe flow of suspensions

Abstract

This study shows that fully developed pipe flow of a particulate suspension is defined by four dimensionless parameters of particle-fluid interactions in addition to the Reynolds number. Effects accounted for include the Magnus effect due to fluid shear, electrostatic repulsion due to electric charges on the particles, and Brownian or turbulent diffusion. In the case of a laminar liquid-solid suspension, electrostatic effect is negligible but shear effect is prominent. Solution of the basic equations gives the density distribution of particles with a peak at the center (Einstein, Jeffery) or at other radii between the center and the pipe wall (Segré et al) depending on the magnitudes of the various flow parameters. In the case of a turbulent gas-solid suspension, the Magnus effect is significant only within the thickness of the laminar sublayer. However, charges induced on the particles by the impact of particles at the wall produce a higher density at the wall than at the center of the pipe. The velocity distribution of particles is characterized by a slip velocity at the wall and a lag in velocity in the core from the fluid phase. These results are verified by earlier measurements.