I'he measurements of the integral physical quantities such as circulation, mixing and blending times for helical screw impellers with the draught tube are presented in this paper. The influence of shear-thiuning and elastic properties of the liquids on these quantities are analysed both experimentally and theoretically.'I'he overall circulation was found to be independent of the shear-thinning character of the liqnid. The influence of elasticity is considered in the light of the existing knowledge on ~oiiie simple flow situations. A relation which incorporates the geometry of the mixer and the rheological properties of the liqiiid is proposed.'I'he mixing and blending time results are analysed and rclated to the hydrodynamics using the laminar mixing approach of hlohr and his co-workers. Although the analysis is approximate, it provides a useful tool in explaining the effects of rheology. It also soggcsts a way to estimate the blending times.he influence of rheology on the performance of T the mixer has not been the subject of many previous studies. I t is needless to say that the rheology of the liquids will play an important role in governing the hydrodynamics in the vessel. Obviously the investigations of the detailed velocity profiles will provide the most useful information f o r analysing the performance of the mixer. However, such experiments a r e tedious and time-consuming and sometimes very difficult. The hydrodynamic equations also become complex and mathematically intractable. Therefore, the previous investigations in this area a r e mainly based upon the analysis of the integral physical qualities such as power consumption"', circulation capacity'*' and mixing times'".The variables like power consumption and circulation capacity not only serve a useful basis for selection of a mixer for a specific purpose but also help in correlating and scaling-up some other physical quantities such as heat and mass transfer coefficients. Mixing time, which may be defined as the time necessary to achieve the required uniformity in all the parts of the vessel, is mainly useful for comparing different agitation systems. However, i t can provide useful guide-lines especially in the design of blending operations or polymer reactors with relatively fast reactions. It cas also give a rough estimate of average residence time required in a continuous system.The effects of the rheology of the liquids on the above mentioned variables will be discussed in this paper. The geometrical arrangement chosen for this exercise is a helical screw impeller with a draught tube (Figure 1 ) . The choice is made mainly on the basis of its usefulness f o r the high consistency media'"'. f l I wscn t address : Unilever Refiearch, Vlanrdingen. The Netherlands. 0 1 prhente, dans le present travail, les niesures des qumltitks physiques et intkgrales, telles que la circulation, les temps de malaxage et de mblange, dam le cas de rotors ? ivis hklicofdale avec tube de tirage; on y aiialyse experinientaleinent et thkoriquement l'influence sur ces qu...

Generalized power correlations have been presented for a variety of dose-clearance helical impellers, i.e., helical screw impellers with a draught tube, helical ribbon impellers, and combined ribbon-screw impellers.

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With simple hydrodynamic concepts, a physical model is developed to describe the flow at the wall close to the impeller blade. The parameters of this model were evaluated from the large amount of data on power consumption and checked with some independent data on velocity profiles. Together with the physical insight provided by the model, it helped to obtain general relationships for power and heat transfer coefficients. Equations for the latter were developed using Lev6que's approximation. Agreement between the predicted results and the literature data of several independent studies was rather good. A method to analyze mixing or blending results is also suggested. SCOPEFor many industrial operations, such as mixing or blending of liquids, dispersing pigments into liquids and heat transfer, and for polymerization, impellers like ribbons, screws or combined ribbon-screws were often used. These are proved to be particularly efficient with the highly viscous liquids and thus are often operated at low Reynolds numbers (Re < 50).Research into the hydrodynamics in such vessels has began as early as 1956 and general flow patterns have been known since that time. Quantitative studies to a greater extent were undertaken in early 70's in a number of laboratories. Most available information is, however, on the power consumption.Some data on circulation capacities, mixing times and heat transfer have also been collected. Data have often been empirically correlated; although a couple of semitheoretical attempts were made, they neither provided the complete physical picture nor did they obtain general relationships. A model capable of putting the most of experimental data in a proper perspective, general enough to describe more than one phenomena like power consumption, mixing and heat transfer, and simple enough to be readily usable was therefore highly desired. Development and application of such a physical model is the subject of this paper. CONCLUSIONS AND SIGNIFICANCEMost of the literature data on velocity profiles, circulation capacities, power consumption, mixing times and heat transfer in vessels agitated by ribbons, screws in draft tube and combined ribbon have been thoroughly analyzed in this paper. The proposed hydrodynamic model has been successful in providing a basis to analyze transport phenomena in these agitated vessels.Further, general relationships have been developed for predicting power consumption and heat transfer and are also useful for scale-up and extrapolation. The model also helps to quantitatively analyze the effect of geometrical variables such as the impeller pitch and the gap between the impeller and the vessel on the physical quantities. Several conclusions of such effects are elaborated. In summary, the proposed model and analysis provides a better understanding of the phenomena in these vessels which should help design better mixers and scale-up complex situations such as polymerization or fermentation reactors.

Coyle et al. (1970) published a report on the influence of geometry and pseudoplasticity upon the performance of helical ribbon impellers. In this note, we indicate how their results can be extended for liquids showing a viscoelastic behavior. This extension will be found particularly useful for the design of batch-operated or continuous stirred reactors for polymerization in bulk or in solvent. Coyle et al. (1970) measured the time a fluid element takes for one circulation in the vertical plane using viscous Newtonian and some inelastic liquids and employing the particle-follower technique. They obtained identical circulation times for both the Newtonian and pseudoplastic liquids if the geometry and rotational speed remained constant. These workers have also measured the mixing-time employing dye-dispersion technique and found that the mixing time also does not depend upon the fluid properties and that its value is three times higher than that of the corresponding circulation time.In an investigation comparing different impellers, Nagata et al. (1972) also report some data on these impellers with conclusions similar to those of Coyle et al. Here the influence of elasticity on the performance of this mixer was investigated. The kinematics were studied by following a small polystyrene particle (density about lg/cm3, characteristic dimension lmm) . The liquids used were translucent (density about lg/cm3) aqueous solutions of Carbopol, CMC, PAA, and a mixture of Glycerine and PAA solutions. The rheological properties of these liquids were measured by Weissenberg Rheogoniometer. In this viscometer, where the liquid sample is placed between a flat plate and a small angle cone, both the torque T and the total axial thrust F between the cone and the plate are measured by sensitive transducers during the shearing of the liquid. The torque T is related to the variable viscosity 9 of the liquid by 7 = 3T/%R3j (1) where + = d a is the shear rate in the conical gap (a being the gap angle and o the angular velocity of rotation) and R is the radius of the cone-and-plate setup.The axial thrust F can be related to the primary normal stress coefficient of the liquid u1 which is the measure of the liquid's elasticity 'TI = 2F/aR2 4 (2) Both 7 and u1 were found to depend strongly upon the shear rate y in the range 0.2s-1 < y < 50s-', and the data were therefore interpreted by the following interpolation formulae:The values of k, h, n, and m are given in Table 1 for all the liquids used.The transparent vessel made of perspex was used for experiments. The impeller diameter (d1, in Figure 1 Several measurements were made to obtain the time the particle takes to complete one circulation in the vertical plane (axial circulation time e, ) and in the horizontal plane (angular circulation time 0,' ). Although the individual observations are subject to random variations, the average values of e, and e, ' are in a way related to the overall axial flow and the overall angular flow, respectively. These averages are plotted against the ro...