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International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.9

ISSN Imprimir: 2152-5102
ISSN On-line: 2152-5110

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v22.i1.40
pages 41-65

Modeling of Vertical Fine Suspension Flow
I. Model Foundations and Particle Velocity Fluctuations

Yu. A. Buyevich
CRSS, University of California, Santa Barbara, USA

RESUMO

This paper presents a heuristic model for the random fluctuating motion found in macroscopically uniform vertical flows of a quiescent suspension. Suspended particles are presumed to be large enough so that their thermal fluctuations are insignificant. At the same time, the particles are presumed to be sufficiently fine so that interparticle exchange by fluctuation energy and momentum is facilitated by hydrodynamic interactions using random fields of ambient fluid velocity and pressure. Particle fluctuations are viewed as the random motion of groups (clusters) composed of fully correlated particles; however, the groups themselves are assumed to be statistically independent. Forces that originate fluctuating motion are caused by the interaction between random fluctuations in suspension concentration and relative fluid flow. These forces are opposed by special friction forces that are caused by an excessive viscous dissipation of energy that accompanies the fluid and particle velocity fluctuations and that supposedly occur mainly within the boundary layers that separate particle groups as these groups move relative to each other. The theory developed in this paper yields expressions for spectral density tensors representing particle and fluid velocity fluctuations; these tensors afford an opportunity to calculate various correlation functions. Vertical and horizontal particle velocity variances and particle self-diffusion coefficients are found to be functions both of physical parameters and mean suspension concentration. They are also shown to agree with available experimental data.


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