Settling velocity particle orientation

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. 

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. 

It is common practice to define a hydraulic equivalent sphere as the sphere with the same density and terminal settling velocity as the particle in question. For a spheroid in creeping flow, the hydraulic equivalent sphere diameter is 2a- E/A and thus depends on orientation. 

Determine the settling velocity in water of a kaolin plate particle 0.01 fira thick and 3 fim in ameter. Compare this value with that of a sphere of the same diameter. Assume that the particle rotates fast so that all orientations are possible during sedimentation. 

At low volume fraction the value of h(< >) is 1, and at high volume fraction the value of h ) is much less than 1. Equation 13.34 is only a first-order approximation to the terminal settling velocity and is good for the lower volume fractions because the particles will orient themselves, allowing higher volume fractions. 

Homogeneous symmetrical particles can take up any orientation as they settle slowly in a fluid of infinite extent. Spin-free terminal states are attainable in all orientations for ellipsoids of uniform density and bodies of revolution with fore and aft symmetry, but the terminal velocities will depend on their orientation. A set of identical particles will, therefore, have a range of settling velocities according to their orientation. This... 

Miedema and Ramsdell (2011) demonstrated that the typical disk-shape of shells will reduce the settling velocity of the grains, but increase the erosion velocity required to force settled particles into suspension again. This is caused by the relative orientation of the shells to the direction of the flow during transport and after settlement. 

Sedimentation methods have been widely used during the past and many product specifications and industrial standards have been established based on these methods. However, there are intrinsic limitations associated with sedimentation. For a non-spherical particle, its orientation is random at low Reynolds numbers so it will have a wide range of settling velocities. As the Reynolds number increases, the particle will tend to orient itself to create maximum drag and will settle at the slowest velocity. Thus, for a polydisperse sample of non-spherical particles, there will be a bias in the size distribution toward larger particles and the result obtained will be broader than the real distribution. Also, all samples analyzed using sedimentation must have a... 

There are two difficulties which soon become apparent when attempting to assess the very large amount of experimental data which are available on drag coefficients and terminal falling velocities for non-spherical particles. The first is that an infinite number of non-spherical shapes exists, and the second is that each of these shapes is associated with an infinite number of orientations which the particle is free to take up in the fluid, and the orientation may oscillate during the course of settling. 

For a particle which is spherically isotropic (see Chapter 2), the three principal resistances to translation are all equal. It may then be shown (H3) that the net drag is — judJ regardless of orientation. Hence a spherically isotropic particle settling through a fluid in creeping flow falls vertically with its velocity independent of orientation. 

A spherical particle is unique in that it presents the same projected area to the oncoming fluid irrespective of its orientation. For nonspherical particles, on the other hand, the orientation must be known before their terminal velocity or the drag force can be calculated. Conversely, nonspherical particles tend to attain a preferred or most stable orientation, irrespective of their initial state, in the free-settling process. Vast literature, although not as extensive as that for spherical particles, is also available on the hydrodynamic behavior of nonspherical—regular as well as irregular type— particles in incompressible Newtonian fluids and these studies have been summarized in the aforementioned references, whereas the corresponding aerodynamic literature has been comprehensively reviewed by Hoerner (1965). 

---