Agitation is the key to many heat and mass transfer operations that rely on mixing. Process requirements vary widely, some applications requiring homogenization at near molecular level while other objectives can be met as long as large scale convective flows sweep through the whole vessel volume. Performance is crucially affected both by the nature of the fluids concerned and on how quickly the mixing or dispersion operation must be completed. For these reasons a wide variety of agitation devices have been developed.
Conventional, mechanically agitated, stirred tank reactors may be used for either batch or continuous processes, though the design and operating constraints are different in the two cases.
Low viscosity fluids can usually be mixed effectively in baffled tanks with relatively small high speed impellers generating turbulent flows, while high viscosity (typically above about 10 Pa s) and non-Newtonian materials require larger, slow moving agitators that work in the laminar or transitional flow regimes. It is convenient to classify impellers as radial or axial pumping depending on the flow they generate in baffled tanks, Figure 1.
Figure 2 shows: a) a radial flow, "Rushton", turbine which produces considerable turbulence near the impeller, b) a "pitched blade" impeller with flat, angled blades that generates a diverging but generally axial flow, c) a hydrofoil impeller with carefully profiled blades that develop a strong, more truly, axial flow of low turbulence. Impellers suitable for viscous fluids are: d) a helical ribbon with a blade that travels close to the wall of the tank to force good overall circulation and e) an anchor that produces strong swirl with poor vertical exchange, even when baffled with stationary breaker bars or "beaver tail" baffles.
The power input P to an impeller of diameter D driven at a rotational speed N in a fluid of density ρ and viscosity η can be expressed in terms of a dimensionless Power number, P/(N3D5ρ). This is a form of drag coefficient and is a function of the mixing Reynolds number /(ND2ρ/η). For a given pattern of impeller the Po vs. Re function is always of the same form.
Figure 3 shows typical graphs of the relationship for four impellers [(see, e.g., Harnby et al. (1992)]. Each shows the transition from laminar flow, where the drag coefficient is dominated by viscosity to turbulent conditions. At high Reynolds Numbers, > ~ 105 the Power Numbers become relatively constant at values that reflect the local turbulence generation. Although these curves are typical, that for a particular design of impeller is affected by the fine detail of construction.
Figure 3. Log-log plot of power number as a function of Reynolds number for Rushton, pitched blade and hydrofoil turbines.
Paddle impellers with six flat blades are ancient [Agricola (1553)]. The popular, simple, robust and effective design with six blades mounted on a disc was adopted by Rushton as a standard for comparative tests. Providing the tank is fitted with wall baffles to eliminate gross swirl – there are usually four baffles, each with a width of about one tenth of the tank diameter – the overall flow fields sketched in Figure 1 develop.
The detail of the flow behind the blades is interesting, Figure 4a. Flow around the blade of a Rushton turbine separates with a pair of trailing vortices from the tips of each blade. These vortices, which are rather less developed in a turbine without a disc, are the locations of the greatest shear rates and most intense turbulence in the vessel (van't Riet and Smith). In the fully developed turbulence region (Re > ~ 105) the power number of a radial flow turbine is about 5. Much of the energy is small scale turbulence associated with the vortices; this decays rapidly in the outflowing stream so that about 80% of the energy transmitted from the shaft is dissipated in about 20% of the vessel volume.
Pitched Blade Turbines have lower turbulent power numbers than Rushton turbines, about 1 in the fully turbulent regime, in part at least because of the lower intensity of the single vortex from each blade end, Figure 4b. Providing the tank is baffled (without this the bulk of the liquid will swirl around with little axial motion) the axial flow will develop. However, the blades are not streamlined and there is some separation of the boundary layer giving a discharge that diverges as it leaves the impeller plane. This divergence becomes more marked the higher the fluid viscosity.
In recent years improved, more streamlined, axial flow impellers, usually with three or four blades, have been developed. These generate good axial flow with very little turbulence and are widely used when effective bulk motion of the liquid is required. The tip vortices are weaker than those of a pitched blade impeller and the energy is dissipated very uniformly throughout the vessel volume, Figure 4c. Narrow blade hydrofoils have been used for heat transfer, solid suspension and dissolution while wider blade versions are more successful in gas-liquid systems.
The near impossibility of generating turbulence in viscous and non-Newtonian materials means that effective mixing depends on ensuring that all the fluid is moving. This can only be achieved with impellers that are large and which sweep out the whole vessel volume. Several patterns have been developed, amongst them helical ribbons and anchors (Figures 2d and e). Driving these large diameter, slow moving impellers requires gearboxes that deliver a large torque; mixing equipment for these fluids is therefore usually heavy and expensive.
One measure of mixing performance is the batch mixing time. This has to convey some assessment of the asymptotic approach to homogenization, usually achieved in terms of the addition of a tracer and the subsequent approach to homogenization. The 95% mixing time is often used for this criterion.
The moment of tracer addition, is taken as zero, td is the dead time before the addition is first detected, tc the circulation time and tm the 95% mixing time, defined by the last measurement that lies outside the 5% band of the total concentration change.
Suitable tracers are pH changes, dyes and salts; even hot liquid can be used. The major difficulties include avoiding spurious affects due to density differences and establishing a reproducible protocol that can be related reliably to the desired process application.
Agricola, De Re Metallica, (1553) (rep. Dover, 1950).
Harnby, N., Nienow A. W., and Edwards, M. F. (1992) Mixing in the Process Industries, Butterworth-Heinemann.