Settling velocity particle shape

Effect of Particle Shape and Orientation to Flow. As indicated by Figure 10-2, the shape of the particle, and particularly its orientation to flow, affects the settling velocity. Particle shape is often quantifled by the sphericity, l , which is the ratio of the surface area of a spherical particle of the same volume to that of the nonspherical particle. Chapman et al. (1983) reported that for particles with sphericity between 0.7 and 1, it is sufficient to use eqs (10-3) and (10-4) and replace the particle diameter, dp, with the diameter of a sphere of equal volume. For particles with sphericity less than 0.7, the estimation of the settling velocity is complicated by the fact that the orientation to flow is a function of the Reynolds number. The effect of shape on the settling of such particles must be evaluated experimentally. Correlations presented by Pettyjohn (1948) and Becker (1959) are recommended only for preliminary estimates. 

Solids settling and deposition to bottom sediments is a complex process by which particulate materials, including both individual and aggregate solids, settle from the water column and adhere to the sediment bed. According to Stokes law, particle settling is dictated by particle diameter and density, but important factors causing nonideal settling include particle shape and concentration, flow velocity and turbulence, and flocculation. Deposition onto and attachment to the sediment bed are usually described as probabilistic processes, affected by turbulence at the sediment-water interface and by the cohesiveness of the solid material. 

Pettyjohn and Christiansen Chem. Eng. Prog., 44, 157-172 [1948]) present correlations for the effect of particle shape on free-settling velocities of isometric particles. For Re < 0.05, the terminal or free-setthng velocity is given oy... 

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)]. 

The settling velocity of a nonspherical particle is less than that of a spherical one. A good approximation can be made by multiplying the settling velocity, u, of spherical particles by a correction factor, iji, called the sphericity factor. The sphericity, or shape factor is defined as the area of a sphere divided by the area of the nonspherical particle having the same volume ... 

When a particle falls under the influence of gravity it will accelerate until the frictional drag in the fluid balances the gravitational forces. At this point it will continue to fall at constant velocity. This is the terminal velocity or free-settling velocity. The general formulae for any shape particle are [13] ... 

Airborne particulate matter may comprise liquid (aerosols, mists or fogs) or solids (dust, fumes). Refer to Figure 5.2. Some causes of dust and aerosol formation are listed in Table 4.3. In either case dispersion, by spraying or fragmentation, will result in a considerable increase in the surface area of the chemical. This increases the reactivity, e.g. to render some chemicals pyrophoric, explosive or prone to spontaneous combustion it also increases the ease of entry into the body. The behaviour of an airborne particle depends upon its size (e.g. equivalent diameter), shape and density. The effect of particle diameter on terminal settling velocity is shown in Table 4.4. As a result ... 

Peden, J.M. and Luo, Y. "Settling Velocity of Variously Shaped Particles in Drilling and Fracturing Fluids," SPE Drilling Engineering. December 1987, 337 343. 

Pettyjohn and Christiansen (1948) gave equations for the terminal settling velocities of particles which deviate from a spherical shape. 

HEISS, J. F. and Coull, J. Chem. Eng. Prog. 48 (1952) 133. The effect of orientation and shape on the settling velocity of non-isometric particles in a viscous medium. 

No fully satisfactory method is available for correlating the drag on irregular particles. Settling behavior has been correlated with most of the more widely used shape factors. Settling velocity may be entirely uncorrelated with the visual sphericity obtained from the particle outline alone (B8). General correlations for nonspherical particles are discussed in Chapter 6. 

Aerodynamic diameter The diameter of a unit density sphere having the same settling velocity as the particle in question of whatever shape and density. 

For quartz spheres, the maximum particle radius compatible with Eq. 23-10 is only 24 pm. In contrast, biogenic particles have a much smaller excess density, ps - pw, and complicated shapes (a small). Typical settling velocities for these particles are 0.1 md 1 for 1-pm particles and lOOmd-1 for 100-pm particles (Lerman, 1979). The 100-pm particles just meet the laminar flow limit (Re = 0.1). 

Sometimes a diameter is defined in terms of particle settling velocity. All particles having similar settling velocities are considered to be the same size, regardless of their actual size, composition, or shape. Two such definitions which are most common are... 

Aerodynamic diameter Diameter of a unit density sphere (density = 1 g/cms) having the same aerodynamic properties as the particle in question. This means that particles of any shape or density will have the same aerodynamic diameter if their settling velocity is the same. 

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. 

Experimental data were embodied in tables presenting C Re in terms of Re/Cf) and vice versa. Since the former expression is independent of velocity and the latter is independent of particle diameter, the velocity may be determined for a particle of known diameter and the diameter determined for a known settling velocity. Heywood also presented data for non-spherical particles in the form of correction tables for four values of volume-shape coefficient from microscopic measurement of particle-projected areas. 

Definitions of particle diameters derived by different methods have been described in detail [4]. The aerodynamic diameter is defined as the diameter of a unit-density sphere having the same settling velocity, generally in air, as the particle. This encompasses particle shape, density, and physical size, all of which influence the aerodynamic behavior of the particle. As a dynamic parameter, it can generally be linked with aerosol deposition and specifically with that in the lung [5]. 

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