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Modeling of continuous particle classification in a liquid medium Chen, Aihua

Abstract

Previous studies of sedimentation, wherein particles fall under the influence of gravity through a fluid in which they are suspended, are first reviewed. This technique can be used to separate particles having different settling velocities. Various hydrodynamic models, including a batch, a differential and a continuous model, of the particle segregation and classification in liquid fluidized beds for binary and polydisperse systems are described. A stochastic model, the Markov Chain Model, recently written for the liquid classifier by Zhang (1998) of our group, is also introduced. The emptying phenomenon encountered in industrial classifiers can be explained in terms of a limiting voidage in the column of the classifier, below which the particles cannot move downwards and be removed from the bottom of the classifier. Continuous classification of particles by size is studied in a solid- liquid classifier of 191 mm diameter and 1540 mm height under steady and unsteady state conditions, similar in geometry to industrial units. Spherical glass beads of uniform density, and Rosin-Rammler particle size distributions, were employed in the tests. The mean particle diameter and the operating conditions were dynamically similar to those used in industry. During the particle classification operation, a dense suspension of particles in water enters the classifier through a radial feed port near the top, while water without particles is injected upwards from the bottom. A relatively dilute stream containing mostly small particles is taken off the top as an overflow stream, while an underflow stream enriched in coarser particles is removed near the base of the column. Differential hydrodynamic models are developed to describe the steady and the unsteady state motions of the particles and liquid, based on mass and momentum conservation laws and knowledge of the sedimentation behavior of individual species within the mixture. The boundary conditions require that the particle concentration in the overflow stream be equal to the concentration at the top of the classifier and the particle concentration at any vertical level in the discharge stream equal the horizontally adjacent concentration in the column of the classifier. The correlation of Di Felice (1994) is used to calculate the drag force on the particles, and the particle dispersion force is introduced according to the concept of Thelen and Ramirez (1999). Any turbulence in the flow is taken into account indirectly via an axial dispersion coefficient, assumed to be uniform throughout the classifier. This sole fitted parameter is correlated in terms of the relevant dimensionless parameters. The degree of classification becomes better with increasing feed voidage, feed flow rate and fluidizing liquid flow rate, but is worse at higher underflow discharge rates. The performance of the classifier is better for a broad than for a narrow particle size distribution of the feed stream. The classification can be improved by increasing the height of the cylindrical zone. Predictions of the model agree reasonably well with experimental results.

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