Liquid free settling

For suspension of free-settling particles, circulation of pseudoplastic slurries, and heat transfer or mixing of miscible liquids to obtain uniformity, a speed of 350 or 420 r/min should be stipulated. For dispersion of dry particles in liquids or for rapid initial mixing of liquid reactants in a vessel, an 1150- or 1750- r/min propeller should be used at a distance Df/4 above the vessel bottom. A second propeller can be added to the shaft at a depth Da below the liquid surface if the submergence of floating liquids or particulate solids is otherwise inadequate. Such propeller mixers are readily available up to 2.2 kW (3 hp) for off-center sloped-shaft mounting. 

Sedimenting and Filtering Centrifuges Under centrifugal force, the solid phase assumed to be denser than the liquid phase settles out to the bowl wall—sedimentation. Concurrently, the lighter, more buoyant liquid phase is displaced toward the smaller diameter—flotation. This is illustrated in Fig. 18-149a. Some centrifuges run with an air core, i.e., with free surface, whereas others run with slurry filled to the center hub or even to the axis in which pressure can be sustained. 

Usnally, there are fonr zones in a thickener the clarification zone, the feed zone, the transition zone, and the compression zone. Not all of these zones will be present for all types of slurries. Liquid flows out of the feed zone, up through the clarification zone, and toward the overflow. Below the feed is the transition zone, where the particles start a downward motion. The concentration just below the supernatant-suspension (or sediment) interface assumes a value dictated by the dominance of either free settling or the presence of a compacting sediment. The region containing the particles offers resistance to liqnid flow and accepts only a portion of the liquid. The remainder reverses direction and exits as overflow. Under steady-state conditions, both solids and liquid fluxes are constant and independent of depth in the snspension and/or sediment zone. No liquid is squeezed out and upward in the sediment unless channels exist. 

Gravity separations depend essentially on rite density differences of rite gas, solid, or liquids present in the mix. The particle size of the dispersed phase and the properties of die continuous phase are also factors with rite separation motivated by die acceleration of gravity. The simplest representation of this involves rite assumption of a rigid spherical panicle dispersed in a fluid with rite terminal or free-settling velocity represented by... 

Free-settling (terminal) velocity of the liquid entrainment under the action of gravity in feet per second. 

The liquid, free from the first fraction, is filtered. To obtain the second fraction, add volume of the salt solution the precipitate is washed with a salt solution, f saturated, is redissolved several times in water, and each time is reprecipitated with the I saturated solution The third fraction is obtained when the filtrate from the second fraction is saturated with powdered ammonium sulphate. The fourth fraction precipitates when to the filtrate from the third fraction is added iV of a volume of dilute sulphuric acid, saturated with ammoiiium sulphate. To obtain a complete precipitate, allow this acidulated liquid to settle for two days wash the precipitate with a saturated and acidified solution of sulphate, and, finally, purify imder conditions similar to those used for the purification of the preceding fractions. The fifth fraction remains in solution in the liquid resulting from the four preceding fractions. The first fraction is given the name primary albumose fractions 2, 3, 4, the names detUero-albumoses A, B, C the fifth is peptone. 

In Fig. VIII. 5 we show the change in adhesion of spherical glass particles with a diameter of 50 5 /zm, on painted surfaces (ordinary and hydrophobic), due to differences in conditions of particle deposition. In these tests, the particles were either apphed in a drop of Hquid (water, acetone, or alcohol) with subsequent evaporation of the drop, or were applied by free settling in air. When the particles were applied in the liquid (curves 1-3 and 1 -3 ), the adhesion was greater than when the particles were deposited from air (curves 4 and 4 ). 

In the thickener the entering slurry spreads radially through the cross section of the thickener and the liquid flows upward and out the overflow. The solids settle in the upper zone by free settling. Below this dilute settling zone is the transition zone, in which the concentration of solids increases rapidly, and then the compression zone. A clear overflow can be obtained if the upward velocity of the fluid in the dilute zone is less than the minimal terminal settling velocity of the solids in this zone. 

Sedimentation or free settling refers to the sinking of solid particles in a volume of liquid which is large with respect to the total volume of particles, hence particle crowding is a neg-Hgible phenomena. Usually, free setthng predominates when the mass fraction of solids is less than 15 wt.%. 

That is, the larger and/or heavier particles are assumed to move through a pseudofluid having the properties, and flowing with the superficial velocity (or volumetric flux), of the combined pure liquid and smaller and/or lighter particles. The free settling terminal velocity, C/qi, is thus based on a pseudofluid density of... 

The actual process of sedimentation in a tube is based on the settling (or terminal) speed that was discussed at great length in Chapter 3. It is also depicted in Figure 7-43. Initially, the slurry is uniformly mixed. Gradually, the solids sink, forming three layers of liquid free of solids, a dilute mixture, and a relatively dense layer. Eventually, all the solids in the dilute layer sediment out, leaving only two layers, one of water and one of a dense mixture with solids at minimmn void ratio. The use of certain chemicals can accelerate the sedimentation of solids. 

The magnitude of the free settling velocity has proven useful in characterizing solid suspension problems into easy, moderate, or difficult categories (see Table 10-2). It is also used in solid-liquid mixing correlations, as described below. 

Example 10-1 Calculation of Settling Velocity. Calculate the free settling velocity for AICI3 crystals in methylene chloride using Figure 10-3 and also eqs (10-3) and (10-4). The solid and liquid properties are ... 

The important hydrodynamic variables are the relative velocity. Vs, between the solids and the liquid (also know as slip velocity) and the rate of renewal of the liquid layer near the solid surface. The relative velocity, Vg, obviously varies from point to point within the vessel, and the average value is difficult to estimate. So, in practice, the relative velocity. Vs, is assumed equal to the free settling velocity, Vt. The renewal of the boundary layer depends on the intensity of turbulence around the solid particle as well as the convective velocity distribution in the vessel. 

Impeller diameter (ft, m) diffusivity (ft /h, mVs) mass-mean diameter (ft, m) mean particle diameter of the ith size (ft, m) particle size or diameter (ft, or m) gravitational constant (32.17 ft/sec or 9.81 m/sec ) diffusional mass transfer coefficient rate of diffusional mass transfer impeller speed (rps) number of particles in the ith size class impeller speed for just suspended state of particles (rps) impeller power (hp, W) vessel diameter (ft, m) particle-free settling velocity (ft/s, or m/s) particle-hindered settling velocity (ft/s, or m/s) mass ratio of suspended solids to liquid time 100 (kg solid/kg liquid) X100 liquid depth in vessel (ft, m)... 

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