Spreading of the interface at the top of a slightly polydisperse sedimenting suspension

Abstract

The interface at the top of a dilute sedimenting suspension of small particles which are not identical does not remain sharp but instead becomes increasingly diffuse as the sedimentation proceeds. For more concentrated suspensions, the self-sharpening effect of hindered settling leads to a considerable reduction in the observed spreading of the sedimenting interface. In order to quantify this spreading, a light extinction technique was used to measure the concentration profile in the interface of a suspension of particles with a small spread of sizes as it fell past a thin sheet of light. A particle volume-fraction range of 0.002 ≤ Φ0 ≤ 0.15 was examined, and each fluid-particle system had a particle Reynolds number less than 10−3 and a Péclet number greater than 107 so that inertia and colloidal effects were negligible. Calculations of the spreading arising from the small degree of polydispersity in particle sizes and the self-sharpening effect are presented. Surprisingly, the measured vertical thickness of the interface was found to be several times that predicted from this theory.It is proposed that the observed spreading may be attributed to hydrodynamic interactions between particles that lead to fluctuations in particle settling velocities about the mean. An analysis of the data shows that the measured interface thickness, after subtracting off that predicted from polydispersity and self-sharpening, increases approximately with the square root of the settling distance and may therefore be described as a diffusion process, termed ‘self-induced hydrodynamic diffusion’. By sealing the hydrodynamic diffusivity as $D = au_{\frac{1}{2}}\hat{D}(\Phi_0)$, where u½ is the median hindered settling velocity, a is the median particle radius, and Φ0 is the volume fraction of particles well below the interface, an approximate analysis of the data was used to infer that the dimensionless scaled diffusion coefficient, $\hat{D}$, is between 1 and 2 for the smaller particle volume fractions examined, increases very rapidly with increasing concentration to a value between 10 and 15 for particle concentrations of a few percent by volume, and then levels off or declines slightly as the particle concentration is increased further.