Extensions and refinements of a Markov model for sedimentation

Abstract The Markov model developed in previous papers is applied to the study of the slurry-supernate interface in batch sedimentation. The variability of particle velocities explains the induction period and the fuzziness of interfaces. Using the velocity-concentration curve indicated by experimental measurements of individual particles in the interior of dispersions, the Markov model predicts that slurries with initial concentrations in a critical range will suffer a depletion of particles near the top of the slurry. This results in an attenuated interface. The remnant concentration is the same for all attenuated interfaces. All attenuated interfaces have the same ultimate velocity. Outside this critical range, the ultimate velocity of the interface is equal to the mean of the steady-state pdf of particle velocities. Earlier papers introduced the concept of a parametric concentration as a weighted average of local solids concentrations. The introduction of suitable metrics for this parameter and particle personality (size and shape) extends theorems for monodisperse systems to slurries containing a countable number of species and shows that a family of nearly identical particles can be uniformly approximated by a single species. These results hold across realizations from continuous distributions of personality and initial position. Finally, sufficient conditions are established for classification in dilute slurries of multifarious particles.

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