Hindered settling ratios

In Eqs. (18-106) and (18-107), under hindered settling and 1 g, the solids flux ()sV, is assumed to be a linear function of ( ), decreasing at a rate of Vgo. Also, the solids flux is taken to be zero at the maximum solids concentration As G/g 1, this solids flux behavior based on 1 g is assumed to be ratioed by G/g. 

Particle-Particle Interaction and Hindered Settling. At solids concentrations of <0.5% by volume, the individual particles are on average so far apart they do not affect each other (i.e., no particle-particle interaction) as they move through the fluid (i.e., laminar flow). For practical purposes, there is no particle-particle interaction in suspensions where the ratio of particle diameter to interparticle distance is <0.1. 

When a particle is at a sufficient distance from the walls of the container and from other particles so that its fall is not affected by them, the process is called free settling. Interference is less than 1% if the ratio of the particle diameter to the container diameter is less than T.200 or if the particle concentration is less than 0.2 vol % in the solution. When the particles are crowded, they settle at a lower rate and the process is called hindered settling. The separation of a dilute slurry or suspension by gravity settling into a clear fluid and a slurry of higher solids content is called sedimentation. 

Design variables are not the only ones to affect the cyclone number. While the effects of pressure, flow rate, viscosity and the densities of the fluid and particles are included, the strong influence of the feed concentration and of underflow orifice control are not. Most of the theories only apply to low solids concentrations, some (Holland-Batt, Schubert and Neesse) offer a correction for hindered settling and others consider to some extent the effect of the underflow-to-throughput ratio (Bradley) or the limited capacity of the underflow orifice (Schubert and Neesse). Once again, the effect of solids concentration for the purpose of scale-up is best described by dimensionless correlations derived from pilot tests and this is shown in some detail later. 

Impeller diameter (ft, m) diffusivity (ft /h, mVs) mass-mean diameter (ft, m) mean particle diameter of the ith size (ft, m) particle size or diameter (ft, or m) gravitational constant (32.17 ft/sec or 9.81 m/sec ) diffusional mass transfer coefficient rate of diffusional mass transfer impeller speed (rps) number of particles in the ith size class impeller speed for just suspended state of particles (rps) impeller power (hp, W) vessel diameter (ft, m) particle-free settling velocity (ft/s, or m/s) particle-hindered settling velocity (ft/s, or m/s) mass ratio of suspended solids to liquid time 100 (kg solid/kg liquid) X100 liquid depth in vessel (ft, m)... 

These trajectory methods have been used by numerous researchers to further investigate the influence of hydrodynamic forces, in combination with other colloidal forces, on collision rates and efficiencies. Han and Lawler [3] continued the work of Adler [4] by considering the role of hydrodynamics in hindering collisions between unequal-size spheres in Brownian motion and differential settling (with van der Waals attraction but without electrostatic repulsion). The results indicate the potential significance of these interactions on collision efficiencies that can be expected in experimental systems. For example, collision efficiency for Brownian motion will vary between 0.4 and 1.0, depending on particle absolute size and the size ratio of the two interacting particles. For differential... 

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