Equal-settling particles

Particles of materials 1 and 2 whose diameters conform to the above equation are called equal-settling particles ... 

For settling in the Newton s-law range the diameters of equal-settling particles, from Eq. (7.43), are related by the equation... 

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 ... 

This result follows from the Richardson-Zaki equation. In their original work, Richardson and Zaki (1954) studied batch sedimentation, in particular the settling of coarse solid particles through a liquid in a vertical cylinder with a closed bottom. Richardson and Zaki found that the settling speed uc of the equal-sized particles in the concentrated suspension was related to the terminal settling speed u, of a single particle in a large expanse of liquid by the equation... 

We note that in steric FFF the centers of equal-sized particles, unaffected by Brownian motion, will settle into the same plane, thus effectively forming... 

Many chemicals in surface waters are sorbed onto suspended particles, which ultimately settle to the bottom of the water body. The settling of particles to the bottom of a water body is a mechanism for chemical removal from the water column. The magnitude of the settling flux of a chemical is equal to the product of the rate of sediment deposition and the chemical concentration associated with the settling particles. 

Thus for pseudoplastic fluids (n < 1), the terminal velocity is more sensitive to both sphere diameter and density difference than in a Newtonian fluid and it should, in principle, be easier to separate closely sized particles. For equal settling velocities. 

For particles of equal settling velocities, d, = v,g and we obtain, by equating Eq. (14.3-20) to (14.3-21), canceling terms, and squaring both sides. 

For particles settling in the turbulent range, Eq. (14.3-24) holds for equal settling velocities. For particles where and settling is in the turbulent Newton s law... 

Clearly, v decreases with increasing < > and reaches 0 at a critical volume fraction (the so-called maximum packing fraction) rj reaches infinity as approaches p. The maximum packing fraction is 0.6 for random packing of equal sized particles. It is >0.6 for polydisperse suspensions. Most practical suspensions are prepared well below the maximum packing and hence settling is the rule rather than the exception. 

Under these circumstances, the settling motion of the particles and the axial motion of the Hquid phase are combined to determine the settling trajectory of these particles. The trajectory of particles just reaching the bowl wall near the point of Hquid discharge defines a minimum particle size that starts from an initial radial location and is separated in the centrifuge. A radius ris chosen to divide the Hquid annulus in the bowl into two equal volumes initially containing the same number of particles. Half the particles of size i present in the suspension are separated the other half escape. This is referred to as a 50% cutoff. 

Particle diameter is a primary variable important to many chemical engineering calculations, including settling, slurry flow, fluidized beds, packed reactors, and packed distillation towers. Unfortunately, this dimension is usually difficult or impossible to measure, because the particles are small or irregular. Consequently, chemical engineers have become familiar with the notion of equivalent diameter of a partiele, which is the diameter of a sphere that has a volume equal to that of the particle. 

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