Hindered continuous settling

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. 

These trajectory methods have been used by numerous researchers to further investigate the influence of hydrodynamic forces, in combination with other colloidal forces, on collision rates and efficiencies. Han and Lawler [3] continued the work of Adler [4] by considering the role of hydrodynamics in hindering collisions between unequal-size spheres in Brownian motion and differential settling (with van der Waals attraction but without electrostatic repulsion). The results indicate the potential significance of these interactions on collision efficiencies that can be expected in experimental systems. For example, collision efficiency for Brownian motion will vary between 0.4 and 1.0, depending on particle absolute size and the size ratio of the two interacting particles. For differential... 

An operating line tangent to the settling flux curve, as in Fig. 30.36, case I, touches the curve at the critical concentration which is the concentration in the hindered settling zone of the continuous thickener. At this concentration, the settling flux is just equal to G — uc, as required by Eq. (30.70) for steady operation. For concentrations between Co and c, the settling flux is greater than G — mc, so zones of intermediate concentration do not form. 

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that arises in connection with clarifier-thickener systems, in which continuously sedimented material is continuously withdrawn, is to deduce the behavior of the flux / as a function of p with hindered settling.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. 

The settling through the continuous layer is hindered, and described by Eq (10). 

Rietema s theory does not take into account the radial fluid flow, it neglects any effects of inertia, it takes no account of hindered settling at higher concentrations and it assumes any influence of turbulence to be negligible. A more recent version of the residence-time theory, the so-called bulk model due to HoUand-Batt °, does take into account the radial fluid flow. He simply used the hold-up time of the liquid in the cyclone (flow rate per cyclone volume) as the residence time, average radial fluid velocity (flow rate per wall area of the cyclone) and a general continuity equation for two-dimensional flow to derive an expression for the cut size. 

Coalescence of the settled droplets is the more rapid the higher the interfa-cial tension. Interfacial tension is ordinarily low for liquids of high mutual solubility and is lowered by the presence of emulsifying or wetting agents. In addition, high viscosity of the continuous phase hinders coalescence by reducing the rate at which the residual film between drops is removed. Dust particles, which usually accumulate at the interface between liquids, also hinder coalescence. 

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