The relation between particle settling velocity and shape: A critical review

This research has tried to find a relation between particle settling velocity and shape. This was done by taking the settling velocity log-contrast of a non-spherical particle and an equivalent spherical particle. This log-contrast should be the logarithmic function of a certain shape factor. Settling data of several shapes were taken from previous authors and with those data several existing and new shape factors were tested to form a single relation. Recently a simple equation was developed which can explicitly predict the settling velocity of spherical particles for any Reynolds number. This equation was tested to be fairly accurate for spherical data. However, the spherical data showed a systematic error which needs to be resolved for the equation to be perfectly accurate. The equation also showed to be fairly accurate for non-spherical sieve diameter data. However sieve diameter data cannot be used to define the shape of a particle as there is no direct relation between sieve diameter and actual particle size and shape. In order to find a relation between particle settling velocity and shape, a correct shape factor must be found. For that matter several shape factors from previous authors were tested on data directly available from previous authors. The existing shape factors were proved to not be able to combine all investigated shapes into a single relation for settling velocity and a new shape factor was found with which a single relation might be formed. This new equation is a generalization of the Corey Shape Factor, the Boekhout Shape Factor: BSF=D_s/(?D_l?^n D_i^(1-n) ). However due to the small amount of data, important data gaps exist so that nothing can be concluded with certainty. Therefore more settling experiments should be done over a large range of Reynolds numbers to be able to conclude whether the Boekhout Shape Factor is the correct link between particle settling velocity and shape.

Subject

settling velocity
particle shape

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Student theses

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bachelor thesis

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