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The kinematic-wave theory of particle settling in tube centrifuges is subject to controversy. G. Anestis and W. Schneider [1] made the common assumption that the flow in a rotating tube of large length/diameter ratio can be treated in one-dimensional approximation. Their results have been found in agreement with measurements [2], [3]. However, M. Ungarish [4] performed an analysis of the two-dimensional settling process in the limit of vanishing particle concentration and obtained results that are not in accord with the one-dimensional flow approximation, irrespective of the length/diameter ratio. It is the aim of the present investigation to gain a better understanding of the process. According to this analysis, quasi-one-dimensional kinematic waves are embedded in a two-dimensional bulk flow that is governed by the boundary conditions at the walls of the tube. The results are compared with those of the one-dimensional flow approximation.

The kinematic-wave theory of particle settling in tube centrifuges has become a subject of scientific discussion. Specifically, the common assumption was made that the flow in a rotating tube of large length/diameter ratio can be treated in one-dimensional approximation. The respective results have been found in agreement with measurements. However, an analysis of the two-dimensional settling process performed in the limit of vanishing particle concentration led to some results that are not in accordance with the one-dimensional flow approximation, irrespective of the length/diameter ratio. It is the aim of the present investigation to gain a better understanding of the process. According to the analysis presented here, quasi-one-dimensional kinematic waves are embedded in a two-dimensional bulk flow that is governed by the continuity equation for the mixture plus the boundary conditions at the walls of the tube. The results based on simplification assumptions are compared with those of the one-dimensional flow approximation. Limiting cases, based on an elaborate analysis of three distinct settling models, are investigated analytically, and the plausibility of some of the respective results is evaluated also in the context of the one-dimensional approximation. Experimental observations, reported in the time span 2001 through 2008, are compared with analytical results obtained and presented. Further experimental work beyond this time span is also analyzed.