Complete suspension

Complete suspension is achieved, when no particle or no particle cluster stays longer than 1 second on the bottom. This 1-s criterion establishes the so-called 

A time criterion is an easy to determine, but inaccurate measured quantity, which possesses a low sensitivity. Who can decide purely visually, whether it is 0.7 or 1.3 s. In addition, this quantity is unfortunately chosen from the dimensionally analytical and scale-up standpoint, because it is not dimensionless [112]. However, this situation is not disadvantageous, simply because this quantity is so insensitive. 

Were a dimensionless time number to be chosen rather than the time t [s], e.g. 

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Kato (K3) measured so-called critical gas velocities corresponding to the complete suspension of solids, and presents a graphical correlation of the results for glass spheres (diameters from 0.074 to 0.295 mm), magnetite particles (particle size from 0.038 to 0.175 mm), and sand particles (particle size 0.147 to 0.295 mm). 

Slurry reactors. For three-phase systems the definition of conditions at which (catalyst) particles are in motion is important. Two limiting states with respect to particle behaviour can be distinguished (1) complete suspension, i.e. all particles just move, and (2) uniform suspension, i.e. the particles are evenly distributed over the whole reaction zone. The power required to reach the second state is much higher, while uniform suspension is not often necessary. Circulation of the liquid with the dissolved gas is usually sufficiently fast to provide reactants to the surface of catalyst particles if they are suspended at all. 

The presence of a gas in the suspension results in an increase of the stirrer speed required to establish the state of complete suspension. The propeller usually requires a higher speed than the turbine. Furthermore, a critical volume gas flow exists above which drastic sedimentation of particles occurs. Hence, homogenisation of the suspension requires an increase of the rotational speed and/or a decrease of the gas flow rate. The hydrodynamics of suspensions with a solid fraction exceeding 0.25-0.3 becomes very complex because such suspensions behave like non-Newtonian liquids. This produces problems in the scale-up of operations. Hydrodynamics, gas hold-up, mass-transfer coefficients, etc. have been widely studied and many correlations can be found in literature (see e.g. Shah, 1991). 

The coefficients in unbaffled tanks increased with only the 0.3 power of the stirrer speed. At the speed needed for complete suspension in a baffled tank, the coefficients are about the same with or without baffles. At higher speeds, the more uniform dispersion of the particles and the greater velocity fluctuations make the coefficients larger with baffles present. 

The gas velocities that are required for homogeneous suspension are far greater than those required for complete suspension. The gas velocity required to achieve complete suspension can be obtained from the correlation of Roy et al. (Ramachandran and Chaudhari, 1984) ... 

Agitated vessels (liquid-solid systems) Below the off-bottom particle suspension state, the total solid-liquid interfacial area is not completely or efficiently utilized. Thus, the mass transfer coefficient strongly depends on the rotational speed below the critical rotational speed needed for complete suspension, and weakly depends on rotational speed above the critical value. With respect to solid-liquid reactions, the rate of the reaction increases only slowly for rotational speed above the critical value for two-phase systems where the sohd-liquid mass transfer controls the whole rate. When the reaction is the ratecontrolling step, the overall rate does not increase at all beyond this critical speed, i.e. when all the surface area is available to reaction. The same holds for gas-liquid-solid systems and the corresponding critical rotational speed. 

By means of the Zwietering equation (3.114), with S = 6.5 for propellers (see Table 3.6), we find that the minimum rotational speed for complete suspension is 40.58 ips, much higher than the operating value of 3.33 ips (200 rpm). This means that the solid particles are not fully suspended in the liquid phase. 

Suspension of Catalyst Particles. There were concerns about complete catalyst suspension due to the density of the panicles. Calculations indicated that total suspension of the dense A12C>3 panicles should occur by 600 RPM (ref. 14). Such calculations are normally valid for agitated reactors with 1 1 height to diameter ratios, and a turbine impeller at 1/4 height. Lower clearance in the reactor (the present case) will decrease the impeller speed required for complete suspension of the panicles. Visual inspection of the open reactor confirmed complete suspension of the catalyst at 450-600 RPM. 

As homogeneous suspension in nonaerated stirred vessels can hardly be achieved, even with very high stirrer speeds, mainly Nc, needed for complete suspension, is of interest for the design purposes. This value, by definition, is characterized by the just-suspended criterion, i.e., the state where only a small fraction of the solids remains at the bottom of the reactor for one second at maximum (Einenkel, 1979). Zwietering (1958) proposed the following correlation to predict Nc, the minimum rotational speed of agitation required for the complete suspension ... 

Joosten et al. (1977) and Kolar (1967) also studied suspension of solids in stirred vessels. The correlations of Baldi et al. (1978) and Zwietering (1958) are based on data over a wide range of conditions and are also in good agreement with each other. Baldi et al. (1978) also proposed a new model to explain the mechanism of complete suspension of solid particles in cylindrical flat-bottomed stirred vessels. According to this model the suspension of particles at rest on certain zones of the tank bottom is mainly due to turbulent eddies of a scale of the order of the particle size. The model leads to an expression... 

For spherical particles of the same size, smax = 0.74 and therefore, ps = p[l + 0.926 s/(0.74 — il/J]2. The increasing particle concentrations have a similar effect on the state of complete suspension in aerated and nonaer-ated systems, i.e. 

Nagata (1975) showed that in aerated suspensions, a significantly higher stirrer speed and thus power consumption per unit volume is required to establish the state of complete suspension. Furthermore, the propeller normally requires a higher stirrer speed for complete suspension than the turbine. Arbiter et al. (1969) reported that drastic sedimentation of suspended particles occurs when the aeration number JVA = QJN d (here Qg is the volumetric gas flow rate) exceeds a critical value. This critical gas flow coincided with the point where the power drawn by the agitator decreased suddenly with a small increase in the gas sparger rate. Thus, an increase in gas... 

In order to achieve simultaneous suspension of solid particles and dispersion of gas, it is necessary to define the state when the gas phase is well dispersed. Nienow (1975) defined this to be coincident with the minimum in Power number, Ne, against the aeration number, 1VA, relationship (see Fig. 12 [Sicardi et al., 1981]). While Chapman et al. (1981) accept this definition, their study also showed that there is some critical particle density (relative to the liquid density) above which particle suspension governs the power necessary to achieve a well-mixed system and below which gas dispersion governs the power requirements. Thus, aeration at the critical stirrer speed for complete suspension of solid particles in nonaerated systems causes partial sedimentation of relatively heavy particles and aids suspension of relatively light particles. Furthermore, there may be a similar (but weaker) effect with particle size. Wiedmann et al. (1980), on the other hand, define the complete state of suspension to be the one where the maximum in the Ne-Ren diagram occurs for a constant gas Reynolds number. 

Here APslat is the static pressure drop, fa the volume fraction of solid, uf0 the fluid velocity, and toc the critical impeller velocity for the complete suspension. All the parameters in this relation (except (oc) can be obtained from the graphical representation of the drag of fluidized particles as a function of the concentration. Molerus and Latzel (1987) verified their results in two geometrically similar vessels equipped with a marine propeller (dr = 0.19 and 1.5 m, djdj = 0.315, H/dT = 1) and for solids concentration 0.5% fa< 30%. They also suggested that coc oc dT0 64, with the proportionality constant increasing with the solids concentration. 

The power in aerated slurry reactors in regime c can be calculated using Equation (3.3). In general, relations summarized by Baldi (1986) can be used for the calculation of power consumption. The most widely used correlation for the minimum rotational speed of agitation required for complete suspension of solids is that of Zweitering (Equation (3.6)). The most versatile... 

Hirsekorn and Miller (H2) made visual qualitative observations of the suspension of solids by paddle agitation in very viscous liquids (to about 50,000 cp.). For low impeller Reynolds numbers (about 10) in geometrically similar systems (6-, 12-, 18-in. vessels) the major factor in effecting particle suspension appeared to be power input per unit volume. In any given case the power required for complete suspension of all the particles was affected by system geometry and the settling velocity of the solids. No detailed correlation of the observations was presented. 

The above model assumes complete suspension of the particles. Fluid velocities in pipes of 1 m/s are ample for suspension of typical solid alkali reagents. Typical agitation intensities of around. 2 W/kg are adequate for suspension of typical calcium hydroxide preparations in tanks. 

Continuous leaching can also be carried out on a laboratory scale, with one or more tanks (in series or in parallel) and with recycling of solids, if necessary. The difficulties that arise in long-term operation of these systems are usually due to wear on the equipment due to the action of the mineral particles, problems in maintaining complete suspension and homogeneity of the mineral, and accurate transfer of relatively small volumes of mineral suspensions from the feed tank to the... 

Off-Bottom or Complete Suspension (Just-Suspended) Regime This state is characterized by the complete off-bottom motion of all particles with no particle remaining on the base of the vessel for more than 1-2 sec (Zwietering criterion).Under this condition, the total surface area of the particles is exposed to the fluid for chemical reaction, mass or heat transfer. The just-suspended regime refers to the minimum agitation conditions at which all particles attain complete suspension. 

Fig. 8 Degrees of suspension. (A) Partial suspension some solids rest on the bottom of the tank for short periods, a useful condition only for dissolution of very soluble solids. (B) Complete suspension all solids are off the bottom of the vessel, minimum desired condition for most solid-liquid systems. (C) Nearly uniform suspension solids suspended uniformly throughout the vessel, required condition for crystallization, solid-catalyzed reaction. (From Ref.t l.)...

Fig. 9 Relative mass transfer as a function of impeller power. The mass transfer increases sharply up to the point of complete suspension, and at a much lower rate to nearly complete uniformity. (From Ref.. )...

Armenante, P.M. Uehara Nagamine, E. Effect of low off-bottom impeller clearance on the minimum agitation speed for complete suspension of solids in stirred tanks. Chem. Eng. Sci. 1998, 53, 1757-1775. 

Kneule [286, 0.11] has pointed out, that under operating conditions for complete suspension (1-s criterion) different flow conditions can exist. Thus the solid can e.g. form strands or local agglomerations, which have to be whirled up, or, however, be uniformly distributed over the entire bottom and must be brought into and maintained in suspension. It is thus to be expected that there will be two boundary laws to describe the suspension state at 1-s point. 

According to Fig. 5.21 the mixing time increases with the fraction of suspended particles and attains a maximum upon complete suspension (l-s criterion). Above this, a further increase in stirrer speed shortens the mixing time to such an extent, that upon achieving the layer thickness criterion h = 0.9 there is only a small difference compared with the homogenization process in a pure liquid. 

It was Hixon and Baum [210], who as early as 1941 pointed out, that the process characteristic of the pi-space (5.51) depended essentially upon the particular suspension condition concerned, see Fig. 5.23. Before the condition of complete suspension, the fraction of the suspended and wetted by liquid particles is particularly increased with increasing stirrer speed. Subsequently only the liquid boundary layer is further reduced, This is also expressed in the two process characteristics ... 

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