Just suspensed speed, solids

Critical speed of agitation for complete suspension of solids (rev/s) Critical speed of agitation for just suspension of solids in solid-liquid... 

Critical speed for just suspension of solid in three-phase (gas-liquid-solid) system (rev/s)... 

Difference in the critical speed for just suspension of solid in three-phase (gas-liquid-solid) and two-phase (solid-liquid) system (rev/s) Difference in the minimum speed for just suspension of the solid in three-phase system in the presence and absence of helical coil (rev/s) Power input (W, kW)... 

Solid-Liquid The most-used technique to study sohd suspension, as documented in hundreds of papers in the hterature, is called the speed for Just suspension, N. The original work was done in 1958 by Zwietering and this is stiU the most extensive range of variables, although other investigators have added to it considerably. 

Solids suspension speed to just suspend solids14 ND0SS D2A5 One of many correlations for particle suspension... 

The just-suspended state is defined as the condition where no particle remains on the bottom of the vessel (or upper surface of the liquid) for longer than 1 to 2 s. At just-suspended conditions, all solids are in motion, but their concentration in the vessel is not uniform. There is no solid buildup in comers or behind baffles. This condition is ideal for many mass- and heat-transfer operations, including chemical reactions and dissolution of solids. At jnst-snspended conditions, the slip velocity is high, and this leads to good mass/heat-transfer rates. The precise definition of the just-suspended condition coupled with the ability to observe movement using glass or transparent tank bottoms has enabled consistent data to be collected. These data have helped with the development of reliable, semi-empirical models for predicting the just-suspended speed. Complete suspension refers to nearly complete nniformity. Power requirement for the just-suspended condition is mnch lower than for complete snspension. 

The solid phase (catalyst/reactant) shows different behavior in different mnlti-phase reactors. In sparged reactors, there is an exponential decay of the solid concentration along the vertical axis. For stirred multiphase reactors operated at the critical speed for just suspension of the solid, N, there is a substantial variation in axial solid concentration. The speed required for achieving uniform solid concentration and the corresponding power input are relatively very high (Nienow 1969, 2000 Shaw 1992). Hence, most stirred multiphase reactors operate at rather than For venturi loop reactors, Bhutada and Pangarkar (1989) have shown that above a certain power input at which the three-phase jet reaches the reactor bottom, the solid concentration is uniform both axially and radially. In this respect, venturi loop reactor is a definitely better option (Chapter 8). 

Critical speed for just suspension solid (2 phase), Ns 0.338 0.193... 

Both these correlations require a knowledge of the minimum speed for just suspension of the solids. Details of estimation of the critical speed for solid suspension are discussed earlier in Section 7B.11 as well as Chapter 7A. 

There are a large number of techniques available that can provide both qualitative and quantitative information on the suspension and distribution of solids in a liquid-filled stirred tank. Other techniques can be used to determine the just suspended speed (or just drawn-down speed with floating solids). 

Techniques for measuring the speed required for the condition for just suspension are discussed in Chapter 4 of this book and by Choudhury (1997). Also discussed are key aspects of the criteria, techniques, and precautions that one must take to obtain reliable data for solids suspension correlations. The Zwietering criterion of no particle remaining at the base of the vessel for more than 1 to 2 s is the basis for most of the published studies. 

Example 10-2 Calculation of the Impeller Speed for Just Suspension. Calculate the just suspension impeller speed for suspending AICI3 crystals in methylene chloride. The solid and liquid properties are given in Example 10-1. Other data are as follows Ratio of solid to liquid, X 0.4. Kinematic viscosity of the liquid, v (0.001 kg/m s)/1326 kg/m or 7.541 x 10 m /s. 

Njs just suspended speed for solids suspension (rps) p power draw (W)... 

Mixing requirements for achieving and maintaining off-bottom suspension of solids (the just suspended speed, Njs)... 

Reeently, Corpstein et al. [43] found that high-effieieney impellers provide the same levels of solids suspension at redueed eapital and operating eosts. They introdueed the term just-suspended for the most eommonly eneountered level of liquid solid agitation. This oeeurs when none of the solid partieles remains stationary on the bottom of the vessel for longer than 1-2 see. They developed a eorrelation of the speed required to aehieve just-suspended eonditions as ... 

Apart from the critical impeller speed for solid suspension and efficient gas dispersion, flooding is also a very important phenomenon in three-phase systems. Flooding may take place at low impeller speed or high gassing rate. Under these conditions, the gas is dispersed just around the central shaft of the tank, whereas the solids are settled at the bottom. Flooding characteristics are not affected by particles. Furthermore, high-viscosity liquids are able to handle more gas before flooding than low-viscosity liquids. 

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 ... 

Sodium metal may be dispersed by melting on various supporting solids (sodium carbonate, kieselguhr, etc.) or by high-speed stirring of a suspension of the metal in various hydrocarbon solvents held just above the melting point of the metal. Dispersions of the latter type may be poured in air, and they react with water only with effervescence. They are often used synthetically where sodium shot or lumps would react too slowly. Sodium and potassium, when dispersed on supports such as carbon, alumina, or silica are often more reactive than the metals. 

Just as the critical gas velocity is required to suspend the particles in a three-phase fluidization in an agitated reactor, some minimum agitation intensity is required to keep the particles in suspension. Calderbank11 has described the methods of estimating this minimum agitation intensity. For an agitated liquid-solid slurry vessel, the correlation of Zweitering150 for the calculation of the minimum impeller speed which completely suspends the particles, namely... 

Calculation of the Just-Suspended Impeller Speed, A/js, in Solid-Liquid Suspensions... 

Solid-liquid mixing involves the suspension, distribution, and the drawing down of solids by agitation. In addition to vessel geometiy, impeller variables include type, diameter, number, speed, and location. Process results include the desired level (quality) of suspension, such as just off-the-bottom, complete uniformity, or any intermediate condition. The slurry properties, density difference (solid/liquid), viscosity, and solids concentration all determine how difficult the task may be. As alternatives to stirred vessels, jets (see Section 9.10) can be used for light-duty suspension. Literature references deal mainly with settling solids as opposed to floating solids. We will try to address both conditions. 

More power is needed to create suspensions of floating than for settling solids. A 45° PBT placed at a depth of T/4 from the surface in combination with a second impeller placed lower down in the vessel usually works well and should avoid gas entrainment. The placement of baffles is critical. If a central vortex is to be used to incorporate solids, the vessel should be baffle-free in the upper half of the tank. Short, wide baffles suspended from the top of the tank extending to a depth of T/3 are an alternative for initiation of engulfment [39]. A large DIT = 0.6, four-blade 45° PBT placed near the bottom of the tank was used in Joosten s work. The minimum speed /V p for just-suspending conditions is given by Equation (9.32) ... 

Complete suspension or complete oiF-bottom suspension. All the particles are suspended off the tank bottom or do not stay on the bottom more than 1 or 2 s. When this condition is just reached, there will generally be concentration gradients in the suspension and there may be a region of clear liquid near the top of the tank. The gradient in solid concentration will have little effect on the performance of the unit as a dissolver or a chemical reactor, and the mass-transfer coefficient will not increase very much with further increases in stirrer speed. 

Sodium metal may be dispersed by melting on various supporting solids such as sodium carbonate, kieselguhr, etc., or by high-speed stirring of a suspension of the metal in various hydrocarbon solvents held just above the... 

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