Hindered Settling Velocities

Quite often the settling velocity is modified by the presence of a large number of particles. This hindered settling velocity is a function of soHds concentration and should be measured experimentally or estimated from Hterature correlations (1). 

The following semi-empirical equation relates the (hindered) settling velocity of a slurry of particles to the settling velocity of a single particle, known as the Richardson and Zaki (1954) (RZ) equation. The RZ equation is also used for liquid fluidization whereby particles are supported by an up-flow of fluid. 

For 0.1 volume fraction solids for hindered settling velocity ... 

Overall coefficients, 332 Vertical plate coil, 331 Hindered settling velocities, 231, 236 Horsepower, centrifugal pump driver, 201 Hydraulic performance, calculations, 180-188... 

Eq. (1) is valid for a particle settling without the interference of other particles, i.e., for diluted systems. The particle settling velocity decreases as particle concentration increases. This phenomenon is known as hindered settling. Several equations can be found in the literature to account for this phenomenon, but a simple method to calculate the hindered settling velocity is to use Eq. (1) replacing the liquid density and viscosity by the apparent density and viscosity of the suspension [24]. 

If the particle concentration in a suspension is high, then the particles do not sediment independently, but are influenced by the motions of surrounding particles (hindered settling). Hindered settling behaviour can be described by applying a correction factor to the Stokes Law terminal settling velocity (dx/dt from Eq. 2.20) to obtain a hindered settling velocity. Several equations have been advanced to describe the correction [69]. The Richardson-Zaki equation for this is ... 

Solution Using the preceding equation for the terminal hindered settling velocity for laminar flow. 

In the case of solid-liquid fluidized beds, the setthng velocity of the particle is less than the terminal settling velocity. The hindered settling velocity is given by the well-known Richardson-Zaki equation,... 

Where W is the particle hindered settling velocity and f is a dimensionless particle diffusion coefficient, both are calculated at solids concentration averaged over the pipe cross-sectional area, c (bottom) is the solids concentration at the bottom of the pipe that can be calculated from (78) ... 

Most early observations of sedimentation in inclined channels indicated that a quasi-steady interface shape between the clarified layer and suspension was formed rapidly in times short compared with the characteristic suspension settling time. Moreover, the clarified liquid layer thickness below the upper channel wall was observed to be much thinner than the channel width b. Most of the clarified fluid accumulated above the horizontal interface at the top of the suspension. It was this kinematic shock interface that was observed to fall with a vertical velocity larger than the hindered settling velocity U measured in vertical settlers. 

Estimate the hindered settling velocity of a 25% (by volume) suspension of 200pm glass beads in an inelastic carboxymethyl cellulose solution (n = 0.8 and m = 2.5Pa S") in a 25 mm diameter tube. The density of glass beads and of the polymer solution are 2500 kg/m and 1020kg/m respectively. 

Estimate the hindered settling velocity of a 30% (by volume) defloccu- (a) lated suspension of 50 /rm (equivalent spherical diameter) china clay particles in a polymer solution following the power-law fluid model... 

Among other things, the very existence of such a difference in mean velocities proves the hindered settling velocity for a suspension to be dependent on the... 

The steady fluidization requires that the upward flow velocity v (= Q/A where A is the tank plan area) be equal to the hindered settling velocity of the fluidized bed Vh ... 

Ureij is known as the particle settling velocity in the presence of other particles or the hindered settling velocity. 

Combining Equation (3.19) with Equation (3.18) gives the following expression for Up, the hindered settling velocity of particles relative to the vessel wall in batch settling ... 

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