Terminal particle velocity Particles, different densities

Temperature rise, centrifugal pump, 207-209 Terminal particle velocity, 228, 230 Particles, different densities, 238 Single spheres, 274 Solids in air, 237 Solids in water, 237 Test pressure, piping, 18 Thickeners and settleix/decanters, Decanter, 242... 

Fig. 4. Terminal velocities in air of spherical particles of different densities settling at 21°C under the action of gravity. Numbers on curves represent tme (not bulk or apparent) specific gravity of particles relative to water at 4°C. Stokes-Cunningham correction factor is included for settling of fine particles.

FIG. 6-61 Terminal velocities of spherical particles of different densities settling in air and water at 70°F under the action of gravity. To convert fhs to m/s, multiply by 0.3048. (From Lapple, etal.. Fluid and Particle Mechanics, University of Delaware, Newark, 1951, p. 292. )... 

From the standpoint of collector design and performance, the most important size-related property of a dust particfe is its dynamic behavior. Particles larger than 100 [Lm are readily collectible by simple inertial or gravitational methods. For particles under 100 Im, the range of principal difficulty in dust collection, the resistance to motion in a gas is viscous (see Sec. 6, Thud and Particle Mechanics ), and for such particles, the most useful size specification is commonly the Stokes settling diameter, which is the diameter of the spherical particle of the same density that has the same terminal velocity in viscous flow as the particle in question. It is yet more convenient in many circumstances to use the aerodynamic diameter, which is the diameter of the particle of unit density (1 g/cm ) that has the same terminal settling velocity. Use of the aerodynamic diameter permits direct comparisons of the dynamic behavior of particles that are actually of different sizes, shapes, and densities [Raabe, J. Air Pollut. Control As.soc., 26, 856 (1976)]. 

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... 

Consider two spherical particles 1 and 2 of the same diameter but of different densities settling freely in a fluid of density p in the streamline Reynolds number range Rep< 0.2. The ratio of the terminal settling velocities un/ut2 is given by equation 9.8 rewritten in the form... 

Most processes which depend on differences in the behaviour of particles in a stream of fluid separate materials according to their terminal falling velocities, as reported in Chapter 3, which in turn depend primarily on density and size and to a lesser extent on shape. Thus, in many cases it is possible to use the method to separate a mixture of two materials into its constituents, or to separate a mixture of particles of the same material into a number of size fractions. 

In the sedimenter or gravity settler, the particles in the feed suspension settle due to difference in densities between the particles and the fluid. The settling particle velocity reaches a constant value - the terminal velocity - shortly after the start of sedimentation. The terminal velocity is defined by the following balance of forces acting on the particle ... 

In both cases the Rejmolds number is much less than 1, so that Stokes s law is valid. The difference in settling velocity between 0.1 and 1.0 pm particles is drastic and is the reason for segregation of particles in a ceramic suspensions. By inspection of this equation, differences in the terminal settling velocity can be due to either density or size differences between the two types of spherical particles. The effects of particle shape asymmetry are considered next. 

DiFTerential settling methods. Differential settling methods utilize the difference in terminal velocities that can exist between substances of different density. The density of the medium is less than that of either substance. The disadvantage of the method is that since the mixture of materials to be separated covers a range of particle sizes, the larger, light particles settle at the same rate as the smaller, heavy ones and a mixed fraction is obtained. 

---