Mixing can be defined as an operation which reduces the degree of nonuniformity of all properties of a system, single or multiphase with one or many components. It is carried out in equipment (Mixers) which rearrange the components of the system into a state where they are, ideally, uniformly distributed in the system and completely dispersed to their ultimate, smallest pieces. The relative importance of distribution and dispersion to overall mixing is illustrated in Figure 1. The size of these ultimate pieces maybe that of a molecule, a drop, a bubble or a particle depending on the nature of the components and phases of the system. As well as homogenizing a system and its properties, Figure 1 shows that mixing also creates large interfacial areas between the components of a mixture and thus promotes and enhances mass and heat transfer and chemical reaction. It is therefore an important unit operation in all processing industries, as described by Harnby et al. (1992) and Sterbacek and Tausk (1965), and one which controls the quality and consistency of the final products whether they issue from a simple blending operation or a complex chemical reaction. In roost applications perfect mixing is not feasible nor necessary and it is sufficient that the degree of mixing achieved meets the requirements of a process or a product. A method of evaluating the degree of mixing achieved is, however, critical for assessing and controlling the performance of a process and the ensuing quality of the product.
The true measure of the standard of mixing in a batch or in a run is the degree of uniformity of the product. This requires consideration of gross uniformity, texture and local structure of a sample withdrawn from the product. Sampling in itself can be difficult, particularly when solids are involved. In practice, the scale of examination of the sample should be just enough to indicate whether the mixing has been sufficient and thus will vary for different processes. Gross uniformity is a crude measure of how overall a minor component or phase is distributed in a mixture. Texture describes non-uniformity of composition in a mixture. It is a measure of the scale and intensity of segregation of the minor component or phase in the mixture and may be apparent through the presence of regions of unmixed or poorly mixed material. Local structure is the way in which the ultimate pieces are arranged, either clumped together as agglomerates, large bubbles and drops or dispersed individually. Local structure is therefore a measure of the degree of dispersion in a mixture and require a scale of scrutiny sufficiently fine to allow resolution of these ultimate entities. The physical meaning of these three quantitative measures of mixing derives directly from the concepts of distribution and dispersion illustrated in Figure 1.
The mathematical definition of these indices can easily be derived [see Tadmor and Gogos (1979)] using the size and number distribution of the dotted pieces illustrated in Fig. 1. The evaluation of the degree of mixing is not always assessed from measurements carried out on the product but also from on-line monitoring, at one or more points in the mixer, of concentration, conductivity, light or noise adsorption and other properties as described comprehensively by Shah (1992). Whichever technique is used, the aim of the measurements is usually to obtain a mixing time (i.e., the time necessary to achieve the desired degree of mixing) from which the mixing rate (i.e., the rate at which uniformity is approached) can be obtained and to correlate the data against the variables of the mixer system, particularly the power input and thus obtain a mixer effectiveness.
Since the number of design and operation variables in a mixer are large, Dimensional Analysis is used to correlate the data, and the principles of similarity are used to scale up equipment. In most cases it is difficult to satisfy all the scale-up criteria (beside the essential geometric similarity) and a consideration of the physical factors of the mixer is necessary. In the mixing of fluids in agitated vessels for example, the Reynolds Number plays an important part since it is a measure of the relative importance of the inertial and viscous forces, i.e., it indicates the onset and level of turbulence in the flow. In the mixing of gas-liquid or immiscible liquid-liquid systems, in addition to the Reynolds number, the Weber Number must also be considered since it represents the ratio of applied to surface tension forces, which control the mixing and mass transfer characteristics of bubbles and drops. These and other aspects of mixing have been reviewed by Sweeney (1978) and recently more comprehensively by Shah (1992).
Three basic mechanisms, either singly or in combination, can be present in a mixing operation; molecular diffusion, eddy diffusion and bulk or convective flow. Molecular diffusion is spontaneous, driven by the gradients of concentration and temperature and can be found in the mixing of miscible liquids of low viscosities and all gases. In most practical operations it is a slow process and eddy diffusion must be superimposed on it to speed up mixing. Eddy diffusion results from Turbulence in the flow of fluids and requires greater energy input. In the mixing of fluids thus, Viscosity is the dominant property of the system resisting mixing and the lower it is the easier the turbulent, conditions can be achieved and the quicker the mixing operation. Examples of mixing systems which use flow turbulence are the pumping of liquids in pipes, their mechanical agitation in vessels, the jetting of a liquid into another liquid and the airlifting of liquids as reviewed in details by Harnby et al. (1992) and Sterbacek and Tausk (1965).
Much knowledge has been gained on turbulent mixing of low viscosity fluids and suspensions using experimental techniques such as Laser Doppler Anemometry to map flow circulation patterns and velocities and levels of flow turbulence in various mixing systems and mixer designs. With the advent of fast and powerful computers, theoretical computational fluid dynamics analyses, as described in the proceedings of the 8th European Conference on Mixing (1994), are increasingly reproducing experimentally observed flow distributions, though much work is still needed to overcome the intrinsic complexities of mixer design, fluids rheological behavior and multiphase features.
All research points to the need of providing the correct balance between the levels of turbulence and flow circulation rates to ensure effective mixing of particular systems. A top to bottom axial-flow circulating propeller, for example, is very well suited for homogenizing miscible liquids and keeping solid sediments suspended in large tanks. Gas-in-liquid dispersions, on the other hand, are better achieved using radial-flow turbine type impellers which produce high shear zones near the impeller blade tips to break the incoming gas into fine bubbles. Very fine bubbles indicate very good mixing but usually require greater coalescing times, hence, yield poor mass transfer. Turbulence levels induced by the impeller must be tuned to produce optimal size bubbles. Even higher shear can be obtained with fast moving sawtooth-disc stirrers which are particularly suited for emulsification and dispersion of liquids over a wide range of viscosities.
When turbulence is not experienced, bulk or convective flow is required for mixing, and can be achieved by rearranging the materials without deforming them or by deforming the materials in the laminar shear or elongational flows associated with systems of very high viscosities. The no-deformation rearrangement mode clearly cannot yield any dispersive mixing; it is distributive in nature and can be either ordered, as for example in the in-line static mixer for blending polymer melts, food pastes and other similar high viscosity materials or random, as in a V-blender for mixing free-flowing solid-solid systems which segregate when sheared, vibrated or fluidized and can only be effectively mixed by bulk convective flow. The laminar flow rearrangement mode of mixing is governed by the extent of strain undergone by the pockets of the minor component or phase when distributive mixing is the only concern. When dispersive mixing is required in laminar flow, the stresses within the field of flow become important to break down solid agglomerates, for example, and clearly the application of power and the forces brought to bear become of greater significance. Mixers for such duties are bulky and hold much less material. Examples of equipment are vessels agitated with anchors and helical ribbons for the processing of high viscosity materials, single or twin extruders, blade and Banbury mixers and mixing rolls for kneading, shearing and tearing pastes, polymer melts and cohesive solid systems.
Two fundamental observations on mixing in laminar flow should be made. The first is with regard to the ability of elongation of creating larger interfacial area than shearing for the same strain. Clearly, when designing mixers extensional flow features should be incorporated. However, while it is easy to generate high flows by shear, in practice extensional flows are difficult to obtain. The second observation concerns the importance of orientation of the sheared or elongated layers during mixing. For a given strain, the largest interfacial area is usually achieved when the layers are perpendicular to the plane of shear or elongation. Application of such simple observations yields large improvement in mixing in extruders, such as when pins, barrier flights and cavities are implanted in the flow field to disrupt shear, reorient and elongate layers to improve distribution and dispersion.
Harnby, N., Edwards, M. R, and Nienow, A. W. (1992) Mixing in the Process Industries, Butterworth Heinemann Ltd., Oxford.
Eigth European Conference on Mixing (1994). I Chem E Symposium Series No 136, Cambridge, 21-23 Sept 1994.
Shah, Y. T., (1992) Design Parameters for Mechanically Agitated Reactors, Advances in Chemical Engineering, Vol. 17, Academic Press Inc.
Sterbacek, Z. and Tausk, P. (1965) Mixing in the Chemical Industry, Pergamon Press, Oxford.
Sweeney, E. T. (1978) An Introduction and Literature Guide to Mixing, BHRA Fluid Engineering Series, Vol. 5, Cranfield.
Tadmor, Z and Gogos, C. G. (1979) Principles of Polymer Processing, John Wiley & Sons, Inc., New York.