Spheres settling, falling

A suspension of a mixture of large particles of terminal falling velocity uol and of small particles of terminal falling velocity uqs may be considered, in which the fractional volumetric concentrations are Cl and Cy, respectively. If the value of n in equation 5.76 is the same for each particle. For each of the spheres settling on its own ... 

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 ... 

Free-falling diameter Also known as sedimentation or Stokes diameter, the diameter of a sphere with the same terminal settling velocity and density as a nonspherical or irregular particle. 

To determine the settling characteristics of a sediment, you drop a sample of the material into a column of water. You measure the time it takes for the solids to fall a distance of 2 ft and find that it ranges from 1 to 20 s. If the solid SG = 2.5, what is the range of particle sizes in the sediment, in terms of the diameters of equivalent spheres ... 

Two spheres of equal terminal falling velocity settle in water starting from rest at the same horizontal level. How far apart vertically will the particles be when they have both reached 99 per cent of their terminal falling velocities It may be assumed that Stokes law is valid and this assumption should be checked. 

It would take a 3 micron diameter particle of wajer in air two days to fall the same distance that a sphere of water the size of a baseball can fall in one second after it reaches its maximum velocity of fall (settling velocity). 

Example 6.4 A 30- xm-diameter unit-density sphere (t = 2.75 x 10-3 s) falling at a terminal settling velocity of 2.7 cm/s is captured by a horizontal airflow of 100 ft/min which is flowing into a hood. Find its velocity 1 ms later, relative to the point at which it was captured. 

The term in the square brackets in this integral is the terminal settling velocity for a dilute suspension of spheres. The size, di, is the size which would just fall the full distance h in time t and is given by... 

If the particle-size distribution of a powder composed of hard, smooth s eres is measured by any of the techniques, the measured values should be identical. However, there are many different size distributions that can be defined for any powder made up of nonspheri-cal particles. For example, if a rod-shaped particle is placed on a sieve, its diameter, not its length, determines the size of aperture through which it will pass. If, however, the particle is allowed to settle in a viscous fluid, the calculated diameter of a sphere of the same substance that would have the same falling speed in the same fluid (i.e., the Stokes diameter) is taken as the appropriate size parameter of the particle. 

In concentrated suspensions, the settling velocity of a sphere is less than the terminal falling velocity of a single particle. For coarse (non-colloidal) particles in mildly shear-thinning liquids (1 > n > 0.8) [Chhabra et al., 1992], the expression proposed by Richardson and Zaki [1954] for Newtonian fluids applies at values of Re(= up to about 2 ... 

Liquid-solid fluidised systems are generally characterised by the regular expansion of the bed which takes place as the liquid velocity increases from the minimum fluidisation velocity to a value approaching the terminal falling velocity of the particles. The general form of relation between velocity and bed voidage is found to be similar for both Newtonian and inelastic power-law liquids. For fluidisation of uniform spheres by Newtonian liquids, equation (5.21), introduced earlier to represent hindered settling data, is equally applicable ... 

---