82 Liquid mixing

A considerable body of information is now available on batch liquid mixing and this forms the basis for the design and selection of mixing equipment. It also affords some physical insight into the nature of the mixing process itself. In mixing, there are two types of problems to be considered - how to design and select mixing equipment for a given duty, and how to assess whether an available mixer is suitable for a particular application. In both cases, the following aspects of the mixing process must be understood:

(i) Mechanisms of mixing

(ii) Scale-up or similarity criteria

(iii) Power consumption

(iv) Rate of mixing and mixing time

Each of these factors is now considered in detail. 8.2.1 Mixing mechanisms

If mixing is to be carried out in order to produce a uniform product, it is necessary to understand how mixtures of liquids move and approach uniformity of composition. For liquid mixing devices, it is necessary that two requirements are fulfilled: Firstly, there must be bulk or convective flow so that there are no dead or stagnant zones. Secondly, there must be a zone of intensive or high-shear mixing in which the inhomogeneities are broken down. Both these processes are energy-consuming and ultimately the mechanical energy is dissipated as heat; the proportion of energy attributable to each varies from one application to another. Depending upon the fluid properties, primarily viscosity, the flow in mixing vessels may be laminar or turbulent, with a substantial transition zone in between and frequently both types of flow occur simultaneously in different parts of the vessel. Laminar and turbulent flows arise from different mechanisms, and it is convenient to consider them separately.

(i) Laminar mixing

Large-scale laminar flow is usually associated with high viscosity liquids (>~10Pa s) which may exhibit either Newtonian or non-Newtonian characteristics. Inertial forces therefore tend to die out quickly, and the impeller must sweep through a significant proportion of the cross-section of the vessel to impart sufficient bulk motion. Because the velocity gradients close to a moving impeller are high, the fluid elements in that region deform and stretch. They repeatedly elongate and become thinner each time they pass through the high shear rate zone. Figure 8.1 shows such a shearing sequence.

Velocity gradient, -y = Shear rate, g decreasing thickness, t1>t2>t3>t4

increasing area

Velocity gradient, -y = Shear rate, g

decreasing thickness, t1>t2>t3>t4

Figure 8.1 Schematic representation of the thinning of fluid elements due to laminar shear flow

Figure 8.1 Schematic representation of the thinning of fluid elements due to laminar shear flow

In addition, extensional or elongational flow usually occurs simultaneously. As shown in Figure 8.2, this can be result of convergence of the streamlines and consequential increase of velocity in the direction of flow. Since for incompressible fluids the volume remains constant, there must be a thinning or flattening of the fluid elements, as shown in Figure 8.2. Both of these mechanisms (shear and elongation) give rise to stresses in the liquid which then effect a reduction in droplet size and an increase in interfacial area, by which means the desired degree of homogeneity is obtained.

In addition, molecular diffusion always acts in such a way as to reduce inhomogeneities, but its effect is not significant until the fluid elements have been sufficiently reduced in size for their specific areas to become large. It must be recognised, however, that the ultimate homogenisation of miscible liquids

elongation rate = ——

volume conserved: decreasing thickness, increasing area

Figure 8.2 Schematic representation of the thinning of fluid elements due to extensional flow can be brought about only by molecular diffusion. In the case of liquids of high viscosity, this is a slow process.

In laminar flow, a similar mixing process occurs when a liquid is sheared between two rotating cylinders. During each revolution, the thickness of an initially radial fluid element is reduced, and molecular diffusion takes over when the fluid elements are sufficiently thin. This type of mixing is shown schematically in Figure 8.3 in which the tracer is pictured as being introduced perpendicular to the direction of motion. It will be realized that, if an annular fluid element had been chosen to begin with, then no obvious mixing would have occurred. This emphasises the importance of the orientation of the fluid elements relative to the direction of shear produced by the mixer.

line of minor tracer

Figure 8.3 Laminar shear mixing in a coaxial cylinder arrangement

Finally, mixing can be induced by physically dividing the fluid into successively smaller units and then re-distributing them. In-line mixers for laminar flows rely primarily on this mechanism, as shown schematically in Figure 8.4.

Thus, mixing in liquids is achieved by several mechanisms which gradually reduce the size or scale of the fluid elements and then re-distribute them. If, for example, there are initial differences in concentration of a soluble material, uniformity is gradually achieved, and molecular diffusion becomes compo line of minor tracer compo

Figure 8.3 Laminar shear mixing in a coaxial cylinder arrangement initial orientation after 3 rotations no mixing initial orientation after 3 rotations no mixing

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