Velocity distribution, settling

Figure 3. A typical variation of settling velocity distribution of a natural suspension underlying aggregating phenomena in a flowing system. Data are observed with a photosedimentometer in an aggregating kaolinite suspension, where the suspending medium was a water sample from a river, upstream (A) and downstream (O) from a waste discharge.

The properties of solids that need to be known include the solids concentration, the particle size distribution, settling velocity (free settling or hindered settling), and the slurry rheology. 

The liquor to be clarified flows between closely spaced conical discs from the outside to the axis. A parabolic velocity distribution exists between the discs and the.particles settle to the underside of the discs by virtue of the radial centniugal force, settling from the high-velocity zone to 4lere the velocity is zero. Thus the settled solids slide down the underside of the discs and into the chamber outside the disc. If a is the distance between the stacks and n is the number of stacks ... 

We see that the velocity autocorrelation function of a free Brownian particle falls exponentially with time. The time required for an arbitrary initial velocity distribution of the particle to settle down to the Maxwell-Boltzmann form corresponding to the temperature of the bath (thermaliza-tion of velocities) is on the order of... 

The important hydrodynamic variables are the relative velocity. Vs, between the solids and the liquid (also know as slip velocity) and the rate of renewal of the liquid layer near the solid surface. The relative velocity, Vg, obviously varies from point to point within the vessel, and the average value is difficult to estimate. So, in practice, the relative velocity. Vs, is assumed equal to the free settling velocity, Vt. The renewal of the boundary layer depends on the intensity of turbulence around the solid particle as well as the convective velocity distribution in the vessel. 

The particle size deterrnined by sedimentation techniques is an equivalent spherical diameter, also known as the equivalent settling diameter, defined as the diameter of a sphere of the same density as the irregularly shaped particle that exhibits an identical free-fall velocity. Thus it is an appropriate diameter upon which to base particle behavior in other fluid-flow situations. Variations in the particle size distribution can occur for nonspherical particles (43,44). The upper size limit for sedimentation methods is estabHshed by the value of the particle Reynolds number, given by equation 11 ... 

For solid-liquid systems, settling velocities of the 10, 50. and 90 percent by w eight fractions of particle size distribution must be available from calculations or measurements. 

Small solid particles, present in dust and grit emissions, have very low settling velocities (Table 4.4) The collection efficiencies of simple cyclones are tlierefore, as shown in Figure 17.3, relatively low. Fabric filters, electrostatic precipitators or wet scrubbers may be required to remove particles <5 pm in size with an acceptable efficiency. Therefore the cost of pollution control inevitably increases when dealing with particle size distributions skewed towards the lower end. 

In this diagram the key features are A - Diffusion baffle this serves four roles. First to dissipate the velocity head, thereby improving the overall hydraulic characteristics of the separator. Next, to direct incoming flow downward and outward maximizing the use of the separator volume. Third, to reduce flow turbulence and to distribute the flow evenly over the separator s cross-sectional area. Finally, to isolate inlet turbulence from the rest of the separator. B- Internal chambers In the sediment chamber, heavy solids settle out, and concentrated slugs of oil rise to the surface. As the oily water passes through the parallel corrugated... 

With particles, the contaminant concentration in the duct is determined by isokinetic sampling with subsequent laboratory analysis use of a calibrated direct reading instrument. If the concentration distribution in the duct is uneven, a complete survey of the concentration distribution with the corresponding duct velocities and cross-sectional area is required. National and ISO standards provide information on isokinetic sampling and velocity measurements. In the case of particles, the airborne emission differs from the total emission, for example in the case of granular particulate. The contaminant settling on surfaces depends on particle distribution, airflow rates, direction in the space, electrical properties of the surfaces and the material, and the amount of moisture or grease in the environment. 

Increasing the surface area of a combustible solid enhances the ease of ignition. Hence dust burns more rapidly than the corresponding bulk solid combustion of dust layers can result in rapid flame spread by train firing . Solid particles less than about 10 pm in diameter settle slowly in air and comprise float dust (see p. 51 for settling velocities). Such particles behave, in some ways, similarly to gas and, if the solid is combustible, a flammable dust-air mixture can form within certain limits. Larger particles also take part, since there is a distribution of particle sizes, and ignition can result in a dust explosion. 

Activity Median Aerodynamic Diameter (AMAD)—The diameter of a unit-density sphere with the same terminal settling velocity in air as that of the aerosol particle whose activity is the median for the entire size distribution of the aerosol. 

The settler. In this unit, gravitational settling frequently occurs and, in addition, coalescence of droplets must take place. Baffles are fitted at the inlet in order to aid distribution. The rates of sedimentation and coalescence increase with drop size, and therefore excessive agitation resulting in the formation of very small drops should be avoided. The height of the dispersion band ZB is influenced by the throughput since a minimum residence time is required for coalescence to occur. This height Zb is related to the dispersed and continuous phase superficial velocities, //,/ and uc by ... 

Stokes law is another concept around which several instruments are designed to give particle size or size distributions. Stokes law is used to determine the settling velocity of particles in a fluid medium as a function of their size. Equation (1.10) below is a useful form of Stokes law... 

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