Rate of settling

The terminal or maximum settling velocity of a small droplet or particle in a gas is governed by one of Newton s equations. 

In laminar flow the friction factor becomes a simple function of the Reynolds number, 

When this substitution is made, the falling velocity becomes 

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Fig. 5. Effect of polymer dosage on different observed properties of flocculated slurry (40). Comparison of five parameters in a flocculation system (8%fluorite suspension + polyacrylamide Cyanamer P250). A, Rate of settling of floe boundary, in cm/s B, height of settled bed, cm C, height of consoHdated filter-cake, cm D, refiltration rate, arbitrary units and E, clarification, % optical transmission of 1 cm of supernatant Hquid after 3 min settling...

Both particle size and the liquid viscosity affect the rate of particle settling. The rate of settling due to gravitational force decreases with decreasing particle size and increasing viscosity. The process mechanisms are sensitive to the relative rates of filtration and gravity sedimentation. 

Hence, the application of these formulas only applies to very dilute systems. At high particle concentrations, mutual interference in the motion of particles exists, and the rate of settling is considerably less than that computed by the given expressions. In the latter case, the particle is settling through a suspension of particles in a fluid, rather than through a simple fluid medium. 

Mass Ratio Fluid to Solids Fluid Rising per Lbs Solids (Lbs/Lbs) Calculated Fluid Rising (ftVbr) Measured Rate of Settling (ft/hr)... 

AM. OF PAH TICKS N MICRONS U.S, ST 0 MESH SCALE OF ATMOSPHERIC IMPURITIES RATE OF SETTLING IN F PJII. FOR SPHERES SfEC.GRAVI AT Jfff... 

The rate of settling of solid particles in a fluid depends on the particle-size of the solid and the nature of the fluid. The terminal velocity (v) is given by ... 

The rate of settling of suspended particles in a gas stream may be greatly increased if centrifugal rather than gravitational forces are employed. In the cyclone separator shown... 

Equation 5.113 gives the rate of fall of the interface between zones (b) and (c) that is the apparent rate of settling of the zone of mixed particles. The velocity of fall // of the interface between zones (a) and (b) is the sedimentation rate of the suspension composed only of fine particles, and will therefore depend on the free-falling velocity u<)S and the concentration Cf of this zone. ... 

Another problem encountered with jet fuels is due to contaminants and the consequent plugging of filter systems in the jet aircraft. Handling and distribution systems for jet fuels are usually underground. Fuel is pumped out of the tank by water displacement. Understandably, when fuel is moved, there is some agitation. If an additive is present, emulsification is possible. Also, there may be many contaminants such as rust, dirt, and water. The rate of settling, naturally is a function of viscosity and density. 

The weight w represents the cutoff size corresponding to time f, and dW/dt represents the rate of settling of particles smaller than the above cutoff size. 

It is not always easy to determine what procedure to follow in making a particle-size distribution. Obviously, if the particles are soluble in water or any other fluid, sedimentation procedures must be applied with caution. It is likewise clear that any sedimentation technique is markedly affected by the shape of the particles used, and that results are subject to interpretation. In other words, determinations depending upon sedimentation (and elutriation) are merely equivalent measures of spheres having the same rate of settling. Greatest reliance naturally applies to that size range whose motion is known to be specified by Stokes law. 

Effect of Container Diameter—The rate of settling, as well as ultimate compacting of the particles, is affected by the diameter of the container in which settling takes place. No data are available on particle-size, but in general, for laboratory experimentation the diameter of the settling tube should not be less than 40 mm for substances such as calcium carbonate, barium sulfate, and silica (Kammermeyer, loc tit). 

Rate of Settling—At the present time two methods are widely used for computing settling rates of liquid suspensions. Rollason, cited by Egolf and McCabe (1937), proposed the use of Stokes equation in the form... 

Egolf and McCabe propose the following equation to determine the rate of settling ... 

From the standpoint of applying Stokes law this procedure is sufficiently accurate since the rate of settling is actually small enough to... 

Digestion and Settling Rates of the Precipitate. To design the proper short leg-suction-jet, it was necessary to know the volume of slurry to be expected in the tank, rate of settling, and the minimum distance above the slurry that the jet must be to prevent movement of the slurry. 

Equation 9.13 shows that nonphysically and nonchemically interacting particles of a given density and relatively large diameter settle faster than particles with similar composition but relatively smaller size. Additionally, particles with a given diameter and a relatively large density settle faster than particles with the same diameter but a relatively smaller density. The rate of settling (Sr) in meters per hour (m s 1) can be described by... 

The theory of the centrifuge is given below. The rate of settling rs (cm s-1) of spherical particles of density dp and of radius a (cm) in a medium of dynamic viscosity r/ (poise) and of density dm is given by Stokes law ... 

The relative rates of settling in a centrifuge tube and in a stationary test-tube may be derived as follows. The centrifugal force Fc upon a particle of effective mass m (grams) moving in a circle of diameter r (cm) at n revolutions per second is given by ... 

Figure 6. Comparison of surface interactions of coacervate drops of various co-acervate systems, as measured by rates of settling of coacervate aggregates...

Flow-Through Velocity and Overflow Rate OF Settling Basins... 

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