Turbulent Gas-Particle Flow in Vertical Risers

Publication Reference: 
09-15
Author Last Name: 
Jackson
Authors: 
R Jackson S Sundaresan S Dasgupta
Report Type: 
ARR
Research Area: 
Powder Flow
Publication Year: 
1995
Publication Month: 
03
Country: 
United States

Abstract

The singular nature of the hard sphere potential combined with lubrication stresses near contact poses interesting issues with respect to the high frequency viscoelastic behavior. Dilute theories demonstrate clearly that soft potentials and/or lubrication stresses that reduce the relative mobility to zero at contact lead to a well defined plateau in G’ as w + 00, whereas a hard sphere potential without hydrodynamic interaction produces G’ FZ: c l/2 in this limit. The former follows from a small deformation of the equilibrium structure due solely to the oscillatory convection and the latter from a diffusional boundary layer near contact required to satisfy the no- flux boundary condition. Two sets of data that delineate the high frequency response for colloidal hard spheres at high volume fraction appear to differ in this regime, suggesting different physics for the interactions at small separations.

Here we apply our nonequilibrium theory to extend the existing treatments to high volume fractions to predict both limits quantitatively and provide a possible interpretation for the experimental results. The two experimental systems only differ in the surface modification of the particles and the high frequency modulus is the only rheological property sensitive to this difference. The predictions of our theory with varying extent of hydrodynamic interaction illustrate the link between the behavior of the high frequency modulus and the hydrodynamic properties very near the particle surface.