| The diffusive behavior of spherical particles suspended in a viscous fluid was investigated under conditions of negligible inertial and Brownian-motion effects. The diffusive behavior in these systems, termed hydrodynamic dispersion, is due only to viscous interactions between the suspended particles and results from sensitivity to initial conditions. The investigation consisted of two main parts: measurement of dispersion coefficients in sedimenting suspensions and examination of the effects of hydrodynamic dispersion on the stability of fluidized beds. Dispersion coefficients were determined in the sedimentation experiments from fluctuations in the settling speed on an individual sphere in the midst of suspensions of like spheres. The experimental coefficients, non-dimensionalized with the mean settling speed and the particle radius, were O(1) for solids volume fractions of 0.025-0.10. This demonstrated that hydrodynamic dispersion is significant and provided impetus to study its effect on the stability of liquid fluidized beds. Stable, uniform fluidization was observed in beds of glass beads fluidized with water, especially with small beads. These observations may be compared to predictions of linear stability theory, based on two different theoretical descriptions of fluidized beds. Both theoretical descriptions, one an extension of a continuum model proposed by Anderson & Jackson and the other an ensemble average approach by Batchelor, predict stability of uniform fluidization, near minimum fluidization, for beds of sufficiently small particles. The general validity of these predictions was verified, but the anticipated scaling were found to be inadequate. Further work is therefore necessary before the observed stability can be definitely attributed to hydrodynamic dispersion. |
