Settling velocity particle size

Theory for cyclone separators. It is assumed that particles on entering a cyclone quickly reach their terminal settling velocities. Particle sizes are usually so small that Stokes law is considered valid. For centrifugal motion, the terminal radial velocity v,n is given by Eq. (14.4-8), with v,] being used for v,. 

Figure 19. Velocity gradient effects of flocculation and settling on particle size distribution function ((A) G = 50 sec (B) G = 0 sec )...

Nobbs, D., Tang, P. and Raper, J. A. (2002). The design, construction and commissioning of a low-cost optical particle size analyser specifically for measurement of settling velocities and size of floes. Meas. Sci. Technol., 13, 297-302. 

The terminal velocity in the case of fine particles is approached so quickly that in practical engineering calculations the settling is taken as a constant velocity motion and the acceleration period is neglected. Equation 7 can also be appHed to nonspherical particles if the particle size x is the equivalent Stokes diameter as deterrnined by sedimentation or elutriation methods of particle-size measurement. 

Here again an equation is estabUshed (2) to describe the trajectory of a particle under the combined effect of the Hquid transport velocity acting in the x-direction and the centrifugal settling velocity in thejy-direction. Equation 13 determines the minimum particle size which originates from a position on the outer radius, and the midpoint of the space, between two adjacent disks, and just reaches the upper disk at the inner radius, r. Particles of this size initially located above the midpoint of space a are all collected on the underside of the upper disk those particles initially located below the midpoint escape capture. This condition defines the throughput, for which a 50% recovery of the entering particles is achieved. That is,... 

Equipment. Centrifugation equipment that separates by density difference is available in a variety of sizes and types and can be categorized by capacity range and the theoretical settling velocities of the particles normally handled. Centrifuges that separate by filtration produce drained soflds and can be categorized by final moisture, drainage time, G, and physical characteristics of the system, such as particle size and Hquid viscosity. 

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 ... 

Hindered Settling When particle concentration increases, particle settling velocities decrease oecause of hydrodynamic interaction between particles and the upward motion of displaced liquid. The suspension viscosity increases. Hindered setthng is normally encountered in sedimentation and transport of concentrated slurries. Below 0.1 percent volumetric particle concentration, there is less than a 1 percent reduction in settling velocity. Several expressions have been given to estimate the effect of particle volume fraction on settling velocity. Maude and Whitmore Br. J. Appl. Fhys., 9, 477—482 [1958]) give, for uniformly sized spheres,... 

As shown by Fig. 14-90, entrainment droplet sizes span a broad range. The reason for the much larger drop sizes of the upper curve is the short disengaging space. For this cui ve, over 99 percent of the entrainment has a terminal velocity greater than the vapor velocity. For contrast, in the lower cui ve the terminal velocity of the largest particle reported is the same as the vapor velocity. For the settling velocity to limit the maximum drop size entrained, at least 0.8 m (30 in) disengaging space is usually required. Note that even for the lower cui ve, less than 10 percent of the entrainment is in drops of less than... 

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)]. 

Gravitational Sedimentation Methods In gravitational sedimentation methods, particle size is determined from settling velocity... 

What is the settling velocity in cm/sec in air at 25°C and 1 atmosphere for a 100 mesh size spherical particle, i.e., one which just passes through the opening in the sieve (specitlc gravity = 2.0) ... 

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. 

Since the size range of the particles to be removed is less than the critical diameter, we are confident that the particles will follow Stokes law. Hence, the settling velocity for a 50 ft size particle is ... 

Calculate the settling velocity of coal particles in water at 20 C. The average size of the particles is 225 /tm. 

Note - In designing a system based on the settling velocity of nonspherical particles, the linear size in the Reynolds number definition is taken to be the equivalent diameter of a sphere, d, which is equal to a sphere diameter having the same volume as the particle. 

Parameter P is equal to the ratio of the liquid volume entrained and the sum of the volumes of this liquid and particles. Values of P are determined experimentally from measured settling velocities. In general, the smaller the effective particle size, the more liquid is entrained by the same mass of solids phase. For example, particles of carborundum with d = 12.2 //.m have P = 0.268 d = 9.6 ftm, p — 0.288 and d = 4.6 fim, p = 0.35. 

Determine the maximum size of quartz particles settling in water (t = 20° C) that can be described by Stokes law. What is this particle s settling velocity The specific weight of quartz is 2650 kg/m ... 

Calculate the sizes of elongated coal particles (pp, = 1,400 kg/m ) and plate-like particles of shale (ppj = 2,200 kg/m ) that have the same settling velocities of 0.1 m/sec through water at 20° C. 

Settling velocity The velocity that has to be attained to ensure that particles of a particular size settle at a given distance from the generation source due to the influence of gravity. 

V = settling velocity of parliclesevalualedal the average particle size in i ... 

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