Free settling

Measurement of single particle settling velocity in a turbulent field is not easy. However, it is known to be a function of free settling velocity which for spherical particles can be estimated from the following ... 

Sohds in either phase are sedimented to the underside of the disks and shde outward along the surfaces because of their density. The aggregated sohds must move by free settling from the outer edges of the disks to the bowl wall some may be reentrained into new feed material, and carried into the disk stack, which accounts in part for actual performance falling short of theoretical prediction. 

A particle falling under the action of gravity will accelerate until the drag force balances gravitational force, after which it falls at a constant terminal or free-settling velocity given by... 

Pettyjohn and Christiansen Chem. Eng. Prog., 44, 157-172 [1948]) present correlations for the effect of particle shape on free-settling velocities of isometric particles. For Re < 0.05, the terminal or free-setthng velocity is given oy... 

For suspension of free-settling particles, circulation of pseudoplastic slurries, and heat transfer or mixing of miscible liqiiids to obtain uniformity, a speed of 3.50 or 420 r/min should be stipulated. For dispersion of dry particles in hquids or for rapid initial mixing of hquid reactants in a vessel, an 11.50- or 1750- r/min propeller should be used at a distance Df/4 above the vessel bottom. A second propeller can be added to the shaft at a depth below the hquid surface if the submergence of floating hquids or particiilate solids is other wise inadequate. Such propeller mixers are readily available up to 2.2 kW (3 hp) for off-center sloped-shaft mounting. 

The above analysis applies only to the free settling velocities of single particles and does not account for particle-particle interactions. 

For example, at n = 1200 rpm = 20 liter/sec and r = 0.5 m, the settling velocity in the centrifuge is almost 28 times greater than that in free settling. Note that the above expressions are applicable only for Re > 500. For small particles. Re < 2, migration toward the wall is laminar. The proper settling velocity expression for the gravitational field is... 

When a particle falls under the influence of gravity it will accelerate until the frictional drag in the fluid balances the gravitational forces. At this point it will continue to fall at constant velocity. This is the terminal velocity or free-settling velocity. The general formulae for any shape particle are [13] ... 

When two free settling particles of different dimensions, D p] and D po and different densities, pp and pp2, fall through a fluid of density, pf, they will attain equal velocities when ... 

Acceleration due to gravity ut Stokes Law free-settling velo-... 

Free settling means that the particle is at a sufficient distance from the boundaries of the container and from other particles, and that the density of the medium is that of a pure fluid, as for example, water. If two different mineral particles of densities pj and p2 and diameters d1 and d2 respectively fall in a fluid of density p3 with the same settling rate, then their terminal velocities must be the same. From Stokes law this gives for the laminar range... 

The above expression is known as the free settling ratio of the two particles (minerals) under laminar conditions. In a similar way the ratio under turbulent conditions can be obtained from Newton s law as... 

From the above two expressions for the ratio dj/d2, a general expression for the free settling ratio can be written down as... 

There are essentially three different approaches to describing hindered settling. One approach is to define a correction factor to the Stokes free settling velocity in an infinite Newtonian fluid (which we will designate F0), as a function of the solids loading. A second approach is to consider the suspending fluid properties (e.g. viscosity and density) to be modified by the... 

The foregoing expressions give the suspension velocity (Fs) relative to the single particle free settling velocity, V0, i.e., the Stokes velocity. However, it is not necessary that the particle settling conditions correspond to the Stokes regime to use these equations. As shown in Chapter 11, the Dallavalle equation can be used to calculate the single particle terminal velocity V0... 

---