Structure formation in bidisperse sedimentation

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Abstract
It is known that when two different species of small particles with radii in the range 10–100 μm are dispersed uniformly in fluid and are settling under gravity, there may be a tendency for the particles of each species to gather together and develop a bulk vertical streaming motion, which results in much larger magnitudes of the mean velocity of at least one of the two types of particle. After a review of the published data on such streaming motions we describe new visual and photographic observations of the evolution of the internal structures (which are sometimes more globular than columnar) in a large number of different bidisperse systems. It appears that the observed structures result from instability of the statistically homogeneous dispersion to small concentration disturbances for certain combinations of values of the ratios of the sizes and densities of the two types of particle and the volume fractions of the two species.The condition for growth of a sinusoidal disturbance of the homogeneous dispersion is derived from the two particle-conservation equations and is found to involve the dependence of the two mean particle velocities on the two particle concentrations in a homogeneous dispersion. Previously calculated values of these mean velocities for a dilute dispersion suggest that the condition for instability is indeed satisfied for not-too-small particle concentrations and certain combinations of the size and density ratios of the two particle species. The results of the instability theory are generally consistent with the observed features of the structures, regarded as finite-amplitude forms of the small disturbances with maximum growth rate.

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