Stirrer critical speed

The optimum stirrer, from the point of view of energy efficiency, is the one that requires the least power at the critical speed of rotation. In terms of a dimensionless relation, this can be expressed as the condition where Ne Fr3/jj is minimum. For a propeller stirrer with Ne = 0.50 and a turbine stirrer with Ne = 10.0, and with the values of b already given for the two stirrers, the propeller stirrer requires only 20% of the power needed by the turbine stirrer. Mixing Equipment Co, CA, has recently introduced a new impeller design that consists of a pitched blade turbine (three blades). At the tips of the... 

If satisfactory suspension is obtained in a small tank, whether judged by visual observations, particle velocities, or mass transfer rates, the safe scaleup rule is to keep geometrical similarity and constant power per unit volume. The ratios DJDf — 5 and / >, = 5 are often recommended, though some prefer DJD, = 0.4 for solids suspension. The critical speed can be reduced by decreasing the clearance, but it may be hard to start the stirrer if it is in a layer of solids very near the bottom. 

The shear forces are mainly in the range of 1 to lONm. This exposure causes cell death between 20 and 80% depending on the exposure duration which is between a few seconds and several hours. Studies performed in a bioreactor have an exposure duration of several days. The results are partly contradictory. Tramper et al. [30] found a critical stress level of 1.5 Nm" for insect cells, whereas Oh et al. [31] could not show an influence on hybridoma cells even at high stirrer speed. This shows that each cell line reacts different and that there is a necessity for defined stress systems if the results is to be comparable. 

The critical feed time t it depends on the location and number of feed pipes, stirrer type, and mixing intensity, and increases with increasing reactor volume. When a constant power-to-volume ratio is preserved, ta-u is proportional to and where D., is the stirrer diameter and Vr the reactor volume (Bourne and Hilber, 1990 Bourne and Thoma, 1991). The productivity of the reactor expressed as the amount of product formed per unit time becomes almost independent of reactor volume. The reason is that the reaction goes to completion in the zone nearby the stirrer tip. The size of this zone increases independently of the tank size it only depends on the velocity of the liquid being injected, the location of the nozzle, and the stirrer geometry and speed of rotation. Accordingly, for rapid reactions, the feed time will also be the reaction time. 

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). 

On occasion, solid particles - such as catalyst particles, immobilized enzymes, or even solid reactant particles - must be suspended in liquid in stirred-tank reactors. In such cases, it becomes necessary to estimate the dimension and speed of the stirrer required for suspending solid particles. The following empirical equation [15] gives the minimum critical stirrer speed (s ) to suspend the particles. 

The critical stirrer speed for solid suspension increases slightly with increasing aeration rate, sohd loading, and non-Newtonian flow behavior [14]. 

A further exceedingly important mixing operation consists of whirling up solid particles ( suspension of solids ) to obtain their surfaces completely accessible to the surrounding liquid (dissolution of salts, solid catalyzed reactions in a S/L/G system, and so on). To work out the criteria important for this task, research concentrated on measuring the critical stirrer speed necessary for the flow state in which no particle lingered longer than 1 second on the bottom of the vessel. 

Circulation models indicate N6 to be also dependent upon the heights of the impeller from the bottom of the vessel and the heights of the unagitated liquid level (see Eqs. (2.11)—(2.14). For an aerated vessel, the use of Eq. (2.15) for NO is recommended. Generally, both gas and liquid are considered to be completely backmixed for a stirrer speed greater than N0. While more information on gas-phase backmixing is needed, if the reaction depends on the partial pressure of gas, an optimum impeller speed to achieve the maximum space-time yield lies in the vicinity of critical impeller speed. 

From the above correlation, it is clear that the critical stirrer speed Nc mainly depends on the geometry of the stirrer d, and the vessel (H/dx), the type of stirrer, the density (pL) and viscosity (vL) of the liquid, the solids mass ratio ps = mj(ms + mL), and the particle diameter (dp) and density (pp). On the basis of a dimensional analysis, one gets the dimensionless relation... 

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. 

The critical stirrer speed can also be predicted on the basis of the liquid flow generated by the impeller. For a six-bladed disk turbine, the average liquid circulation velocity in the bulk can be expressed as... 

In waste-water treatment, the energy-efficient transfer of oxygen in the aqueous phase is very critical. Since reactions are slow, a long contact time is required. Both of these can be achieved by a conventional surface aerator or novel UNOX surface aeration system. The minimum impeller speed needed for surface aeration in the absence of gas sparging can be obtained from Eq. (6.30). Similar calculations in the presence of gas sparging can be carried out using either Eq. (6.31) for a turbine stirrer or Eq. (6.36) for other stirrers. The gas entrainment and the power consumption in the presence of gas entrainment can be obtained using Eqs. (6.37) and (6.38), respectively. 

The components of an ELM system are the diluent, surfactant, internal aqueous phase, continuous phase, and carrier in the case of type 2 facilitation. Emulsification is usually achieved by high speed or ultrasonic stirrers for batch operations and high-pressure static dispersion or colloid mills for continuous mode [46]. The presence of a surfactant is necessary to ensure adequate stability of the emulsion during the extraction process. However, an ultra stable emulsion is not desirable as it will lead to difficulties in the demulsification stage. Eor the effective working of an ELM all components must be carefully chosen and each composition is critical. Some of the desirable properties of the various components are listed in the following sections. 

Interdependency analysis is performed for each critical process variable to select the actuator. For example, the dependency of the DO concentration (response variable) on the air flow rate stirrer speed (sensitivity parameters) is shown in fig 5. The air flow rate is more sensitive compared to the irta-dq deryamiysis... 

Repeating the procedure for all critical control variables yields actuators as follows coolant flow rate for temperature, ammonia flow rate for pH, air flow rate for DO and dissolved CO2, stirrer speed for homogeneity control in the fermentor, steam flow rate for heat sterilization temperature control and stirring duration for homogeneity in the mixing tank. 

In dealing with the problem of mechanical stress one has to distinguish between the aspects which concern device construction and those which are of concern to the device users. Information over the mechanical forces, which operate on the stirrer, the shaft, the shaft bearings and the shaft seal, together with the critical stirrer speed etc., can be obtained from the brochures of the stirrer manufacturers [0.14, 526] and from research papers such as [123, 393, 420]. In this section only those aspects which are of interest to the comparatively large group of users of mixing equipment will be considered. 

The above expressions enable the determination of any vortex depths h. To determine the critical stirrer speed at which the vortex depth reaches the stirrer, h is set equal to H. In the case of slow stirrer speeds air is generally not entrained even for h = H. ... 

For solids to be dissolved rapidly in liquids, their total surface must be accessible to the liquid, i.e. the solid particles must be completely suspended in the liquid. In this case that critical stirrer speed is of primary interest, at which this state is just attained, and the other stirring conditions (stirrer type and instalation), which ensure the maintenance of these flow conditions with the lowest stirrer power. 

When different criteria for describing the suspension state are in use, these must also be taken into consideration in the formulation of the suspension characteristics. Depending on which criterion is used in the determination of the critical stirrer speed Wx , which can be represented by x for the 1-s criterion, for the particle layer height criterion h = 0.9 or by a required distribution quality the process numbers are correspondingly designated e.g. Re or Fr. ... 

The stirrer which operates most favorably energetically is that which expends the lowest stirrer power at the critical stirrer speed. In the turbulent flow range, for which Fr = const applies, see (5.4), this condition is described by the relationship NeFr = min. With Ne = 0.35 and 5.0 for the propeller and turbine stirrers respectively (see Table in Fig. 2.2) and the above-mentioned constants for equation (5.4) it can be calculated that the propeller stirrer only requires 28% of the power of the turbine stirrer. From an energetic standpoint stirrer types which convey the liquid axially downwards are clearly superior to axially operating ones. 

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