Sedimentation hindered settling

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,... 

If the feed rate exceeds the maximum of the design, particulate matter are unable to settle out of the normal clarification zone. Hence, there is an increase in the solids concentration, resulting in hindered settling. The result Is a corresponding decrease in the sedimentation rate below that observed for the feed slurry. 

The thickener is the industrial unit in which the concentration of a suspension is increased by sedimentation, with the formation of a clear liquid. In most cases, the concentration of the suspension is high and hindered settling takes place. Thickeners may operate as batch or continuous units, and consist of tanks from which the clear liquid is taken off at the top and the thickened liquor at the bottom. 

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 ... 

Calculate the equilibrium between sedimentation and diffusion for the particle given in problem 9 assuming hindered settling at = 50%. 

A-B of Fig. 7.28(b) there is hindered settling of the particle interface at a constant rate at B-C a transitional settling occurs from C to D consolidation of the sediment occurs. 

For more concentrated suspensions (q> >0.2), the sedimentation velocity becomes a complex function of At > 0.4, a hindered settling regime is usually entered whereby all of the particles sediment at the same rate (independent of size). A schematic representation for the variation of v with is shown in Figure 9.12, which also shows the variation of relative viscosity with rp. It can be seen from these data that v decreases exponentially with increase in approaches zero when cp approaches a critical value (the maximum packing fraction). The relative viscosity shows a gradual increase with increase in cp such that, when cp = the relative viscosity approaches infinity. 

A problem of some practical importance that arises in connection with clarifier-thickener systems, in which continuously sedimented material is continuously withdrawn, is to deduce the behavior of the flux / as a function of p with hindered settling. For example, with reference to Fig. 5.4.4, the concentration change that is shown there as being brought about by upward-propagating waves (characteristics) is only true if the flux-density dependence is such that u = -djldp > 0. 

Figure 5.4.4 Interface positions as a function of time in batch sedimentation with hindered settling of the suspension.

Figure 5.4.5 Flux curve for batch sedimentation with hindered settling.

Figure 5.4.6 Simple concave downward flux curve with a maximum and no inflection point for batch sedimentation with hindered settling.

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. 

This equation defines the characteristic speed, that is, the kinematic wave speed. Note that for s = constant the characteristic speed drldt= which is analogous to the wave speed in the gravity sedimentation problem except that here is not constant with distance. The analogy also holds with s — s p) if s d sp)/dp is defined as a hindered settling factor G(d>) (Eq. 5.4.18). 

The solution behavior with a concentration-dependent sedimentation coefficient that decreases with increasing p (hindered settling) has a similar form as for s = constant, but with Eq. (5.5.15b) replaced by... 

MANDERSLOOT, W.G.B., SCOTT, K.J. 8c GEYER, C.P. 1986. Sedimentation in the hindered settling regime. In Advances in Solid-Liquid Separation (ed. H.S. Muralidhara), pp. 63—77. Columbus Battelle. 

---