Free settling velocity

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 ... 

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... 

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

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] ... 

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... 

The final application or requirements (e.g., determination of free-settling velocity y. minimum fluidization velocity Vm minimum transport velocity Vfmm, and/or pipeline air pressure drop Apt)... 

Richardson and Zaki(11) found that m, corresponded closely to u0, the free settling velocity of a particle in an infinite medium, for work on sedimentation as discussed in Chapter 5, although u, was somewhat less than n0 in fluidisation. The following equation for fluidisation was presented ... 

Crystal size Smallest in fluidised bed = 0.3 mm, (free settling velocity = 40 mm/s) Smallest in system = 0.1 mm... 

Notation U, is a fluid velocity, Up is particle velocity, U, is particle free settling velocity, ms is mass rate of flow of solid, D = pipe diameter, Dp is particle diameter, g = 9.806 m/sec2 at sea level. 

Although it is accepted that within a given crystallizer the linear growth rate is independent of size per se, the growth rates may differ due to effects such as the dependence of the free settling velocity on size. If all crystals, regardless of their size, were treated in exactly the same manner, the equations presented in this section could be used to predict product size for any seed size distribution. 

In real slurry reactors, where particles move at velocities much greater than the free-settling velocity and where the particles are often large, the actual Ks is much larger than K - Harriott37,38 showed that the ratio Ks/K usually falls between 1 and 4. As a first estimate, Ks may be twice Kt, which is estimated, under conditions of free flowing velocity of a particle, from Eq. (9-51). 

The magnitude of the free-settling velocity has proven useful in characterizing solid suspension problems into easy, moderate, or difficult categories, as reported in Table iJ ... 

The following equation enables one to calculate the free settling velocity of a particle ... 

Gravity separations depend essentially on rite density differences of rite gas, solid, or liquids present in the mix. The particle size of the dispersed phase and the properties of die continuous phase are also factors with rite separation motivated by die acceleration of gravity. The simplest representation of this involves rite assumption of a rigid spherical panicle dispersed in a fluid with rite terminal or free-settling velocity represented by... 

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