Scale of mixing in a stirred vessel

Abstract

Although stirred vessels are widely used in chemical technology, they have been characterized almost exclusively by empirical methods, for example power absorption per unit volume (11) The present work investigates simultaneous mixing and reaction of a basic tracer stream with a surrounding acid medium. A steady state condition is achieved by continuously introducing a tracer sodium hydroxide solution into an acid stream which flows slowly upward through the stirred vessel. Both base and acid streams contain phenolphthalein indicator; hence the distance from the impeller required for complete reaction of tracer solution is visually measurable. Any realistic and detailed description of this exceedingly complex shearing and interlarding of the reacting streams by the impeller blades would be prohibitively complicated even if the additional effects of molecular diffusion and reaction are not considered. A first-order and necessarily very crude solution is now obtained with an extremely idealized model which may even be accused of being too much of a simplification. The model assumes:1. The impeller action reduces the entering tracer stream to very thin packets. Simultaneously the shearing or other action of the blades interlards the tracer packets with the bulk circulating stream.2. The above shearing and interlarding processes OCcurs very quickly, that is before the fluid is ejected from the impeller.3. After the impeller is left, no further shearing occurs, and the acid base reaction is now controlled by molecular dihsion as outlined by Toor ( 1 2 ) .Within the impeller, effects such as flow patterns, jet mixing of the entering streams, effective eddy diffusivities, etc. are not considered separately. Their combined action is expressed in terms of packet size and subsequent reaction time. In the effluent stream only mixing on the molecular level is considered to enhance chemical reaction; larger scale eddies have little effect. If eddies in A. W. Rice is at Princeton University, Princeton, New Jersey. stirred vessels are similar to those in pipes, their dimensions are quite large, of the order of vessel diameter, impeller diameter, blade size, etc. Reaction of the basic tracer streaks in the effluent stream is now considered quantitatively. THEORYThe flat-bladed turbine impeller produces a horizontal fluid sheet that maintains its radial direction until it reaches the vessel wall. At the wall the flow divides into doughnut-shaped circulation patterns above and below the impelIer. There are two mixing processes in the vessel, the basic tracer with the acid recirculation stream at the impeller and the recirculating stream with the fresh entering acid at the bottom of the vessel.Within the confines of the impeller the tracer solution is pictured as being sheared into very thin elements (slabs, cylinders, or spheres) which are then surrounded by the recirculating stream. Reaction between these interlarded layers of acid and base then occurs when the mixture leaves the impeller and becomes part of the horizontal fluid...

Performance Evaluation of Two High‐Shear Impellers in an Unbaffled Stirred Tank

“…These results illustrate strong flow compartmentalizations which also have been reported in previous experimental and numerical studies for Newtonian laminar flow fields in a stirred tank equipped with a RT 21–23 and also for a sawtooth HSI in the turbulent flow regime 12. Rice et al 23 stated that for Re < 500 the flow induced by many flat‐blade turbines divides the tank in two regions of two ring vortices. It was found that there is a greater intensity (about 6 %) of the axial flow in the upper loop in both HSIs with respect to the lower loop, and in general this behavior is similar for the RT.…”

Tracer Dispersion in Stirred Tank Reactors: Asymptotic Properties and Mixing Characterization

“…These investigations were oriented towards the evaluation of the power curves of different impeller configurations under various operating conditions. Furthermore, methods for estimating mixing times have been set up from the experimental analysis of tracer dispersion (Metzner and Taylor, 1960;Biggs, 1963;Rice et al, 1964).…”

A note on mixing rates in stirred tanks

“…The scale expression, Equation (6), when applied to the test conditions of Rice et a1 (11) predicts length scale values which are larger by a factor of about 30 than estimated by their experiments. However, it may be noted that scale values of the same order of magnitude as those of Rice can be obtained by Equation (6) if the volume swept out by the impeller is used as the volume term in Equation (7).…”

“…This is because of the large amount of information required for such a description: n ( n -1)/2 diffusivities and associated activity data for a system of n diffusing species.' The most complete available treatments appear to be those of Spiegler (13) and Mackay and Meares (11).…”