Multiphase Science and Technology A Quarterly

ISSN for PRINT: 0276-1459

For Online Access

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1994, Volume8

Issue 1-4

786 pages

Issue price - $560.00

J. C. R. Hunt
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, CB3 9EW, UK

R. J . Perkins
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, CB3 9EW, UK

J. C. H. Fung
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, CB3 9EW, UK

This review of recent literature and new concepts begins with a consideration of the force of a small rigid particle, and the relevant dimensionless parameters which are defined in terms of properties of the flow field, the particle and the fluid. Force expressions are developed for the limiting cases of inviscid flow and viscous flow, and we discuss how these should be combined for low Reynolds number and high Reynolds number flows (since different interactions occur in the two extremes). The final expressions agree with experimental data and recent numerical calculations.
We then consider the motion of a particle or bubble, beginning with rising bubbles in still fluid, followed by particles in simple non-uniform flows. The importance of difference forms of lift force is discussed.
We review previous studies of the motion of small particles in turbulence. Recent computer simulations are presented to show how the lift and acceleration forces affect bubbles in non-uniform turbulent pipe flows inclined at different angles to the origin. A simple 1-D model of turbulence is developed to explain why most previous models gave incorrect results for the diffusivity of particles as a result of neglecting the spatial structure of turbulence. This model provides the basis for order-of-magnitude calculations of the diffusivity of particles in turbulence and the spectra of their velocities. These hypotheses are tested by computing the trajectories of particles in velocity fields that simulate turbulence (Kinematic Simulation).
In the last section we review how low concentrations of particles interact between each other and affect the average flow field. The latter effect is larger than the former, so that, to a good approximation, direct interactions between particles can be neglected. By a fundamental examination of how a mean flow can be generated by the drag of many small particles, it is shown that a steady flow can only be generated by a steady stream of particles if the particles interact.

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