Settling hindered

When the particles are close together, hindered settling occurs. Hindered settling has been studied by many authors [6]. In all cases. 

FIGURE 11.4 Hindered settling of spheres, h. 4 ), where is the volume fraction. 

Svarovsky (1984) reviewed some important correlations accounting for the hindered settling effect and demonstrated that their differences are minimal. 

According to this, the simple Richardson and Zaki equation is an obvious choice in practice. Such relation can be expressed as 

The relationship above applies only to free, particulafe separafion unaffected by coagulation or flocculation, and where all particles are of uniform density. 

As mentioned earlier, the terminal falling velocity of a sphere is also influenced by the presence of neighboming particles. 

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  

In visco-elastic fluids, some internal clusters of particles form during hindered settling and the interface tends to be diSiise [Allen and Uhlherr, 1989, Bobbroff and Phillips, 1998]. For 100-200 gm glass spheres in viscoelastic polyacrylamide solutions, significant deviations from equation (5.22) have been observed. 

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. 

The velocity of a single glass bead is calculated first. In view of the small size and rather high consistency coefficient of the solution, the particle Reynolds number will be low, equation (5.11) can be used. From Table 5.1, X( ) = 1.24 corresponding to n = 0.8. 

Set up a table wth coliunns for the various stages of the calculation. Use Tables 3.1 and 3.2 to obtain logic (u/Q) from logic Px- 

Calculate from Equation (3.13) the maximum particle size at which Stoked law will apply  

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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). 

P. H. T. I Jhlherr, Hindered Settling in Non-Neirtonian Fluids—an Appraisal, CHER 75-1, Dept, of Chemical Engineering, Monash University, Melbourne, Austraha, Jan. 1975. 

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,... 

Basically a tube with hydraulic water fed near bottom to produce hindered settling. Underflow withdrawn through valve at base. Column maybe filled with network to even out flow. 

Feed to be sized is put into hindered-settling condition by hydraulic water in quantity only sufficient to teeter the smallest particle wanted in the coarse product. The finer fractions report to the overflow or pass into the upper column for removal in a three-product unit. 

Coarse solids are discharged by siphons extending to the bottom of the hindered-settling zone. Siphon control is obtained by a novel hydrostatically actuated valve which makes or breaks the siphon to flow only when the teeter zone is in correct condition. Discharge by an intermediate fraction from the upper column is by means of additional siphons. Hydraulic-water consumption is considerably lower than required for multipocket sizers. 

FIG. 19-26 Movement of particles in a jig. a) Displacement of the bed as a function of time, (h) Starting position of particles, (c) After dilation. (d) After differential initial acceleration, (e) After hindered settling, (f ) After consolidation trickling. 

Ut = Terminal settling velocity, ft/sec Fs = CoiTection factor for hindered settling p, po = Density of water or oil, Ib/ff ... 

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. 

At high solids eontents, settling oeeurs in a multi-partiele system at a slower rate than single partiele ease. This is known as hindered settling . There are several potential eauses... 

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. 

Examination of equation 2.43 shows that the mass flux initially increases as concentration increases but then passes through a maximum and finally declines as velocity decreases due to hindered settling (Figure 2.8). 

Davis, R.H. and Gecol, H., 1994. Hindered settling function with no empirical parameters for disperse suspensions. American Institution of Chemical Engineers Journal, 40, 570-575. 

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

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