Instability of Dilute Bidisperse Suspensions Resulting from Particle Interactions
Abstract
Experimental evidence shows that initially homogeneous bidisperse suspensions become unstable due to initial perturbations in particle concentrations. As a result of this instability, the particles segregate and form vertical streams (socalled fingering phenomena) during their sedimentation process. In this thesis we deal with modelling the macroscopic behaviour and studying the stability of the suspension. A continuum model is developed and used in order to model the formation of vertical streams and study the instability of dilute bidisperse suspensions. The macroscopic behaviour of the suspension is closely related to and depends on the microstructure and the relative motion of particles in the suspension. Thus the calculation of the trajectories of the particles is an essential step in the mathematical modelling of the behaviour of the suspension. Classical low Reynolds number hydrodynamics predicts that sedimenting solid spherical particles approach one another typically to within 10^{3} of a radius, indicating that the surface roughness of the particles can become significant and takes part in the interaction process. The trajectories of two solid spheres sedimenting in either a quiescent fluid or a shear flow are calculated. It is shown that as a result of physical contact between the particles, a horizontal flux of each species of particles is generated. These results are used to calculate the detailed macroscopic equations for the concentrations. Finally the macroscopic equations are solved for two specific suspensions using a linear stability analysis and also numerically using a ControlVolumeFiniteDifference technique. The obtained results predict the instability of these specific suspensions and the formation of vertical streams which have been observed experimentally.
 Publication:

Ph.D. Thesis
 Pub Date:
 January 1990
 Bibcode:
 1990PhDT.......125T
 Keywords:

 BIDISPERSE SUSPENSIONS;
 VERTICAL STREAMS;
 Engineering: Civil; Physics: Fluid and Plasma