| This thesis describes a further theoretical and experimental investigation of an unexplained phenomenon, in which, an initially uniform suspension of neutrally buoyant particles within a partially filled rotating cylinder is found to segregate into bands of particles separated by regions of low particle concentration or even particle-free liquid. First of all, we investigated in considerable detail coating flows of a viscous particle-free liquid in a partially filled rotating horizontal cylinder, often referred to as rimming flows, by means of an asymptotic analysis of the thin film lubrication equations and also examined the stability of their solutions. Secondly, a number of experiments were performed to probe further the whole process of the particle segregation phenomenon. One crucial experimental result was the observation that when the suspension contains a recirculating region (puddle), the particles first segregate radially by migrating out of the puddle into the unidirectional circumferential flow before segregating along the axis of the cylinder. Thirdly, an explanation for such a phenomenon was proposed on the basis of a model of coating flows with an axially varying viscosity plus the experimental observation referred to above (i.e. the radial particle segregation). A linear stability analysis for dilute suspensions with complete radial segregation showed that such a particle distribution is unstable to axial perturbations with the surface tension being responsible for the selection of the wavelength of the most rapidly amplified disturbance. The calculated and measured spacings between the bands were found to be in good agreement. Finally, particle segregation, as expected, was also found to occur in two new geometries (a cone and a sphere) and the location of the corresponding band(s) seen experimentally was predicted theoretically by solving numerically a general model equation for rimming flows within any axisymmetric horizontal rotating container and then taking into account the observed radial particle segregation similar to that in the case of the cylinder mentioned above. |
