SCALE-UP OF MIXING SYSTEMS
The calculation of power requirements for agitation is only a part
of the mixer design. In any mixing problem, there are several defined
objectives such as the time required for blending two immiscible
liquids, rates of heat transfer from a heated jacket per unit volume of
the agitated liquid, and mass transfer rate from gas bubbles dispersed
by agitation in a liquid. For all these objectives, the process results
are to achieve the optimum mixing and uniform blending.
mixing of fluids
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The process results are related to variables characterizing mixing,
namely geometric dimensions, stirrer speed (rpm), agitator power, and
physical properties of the fluid (e.g., density, viscosity, and surface
tension) or their dimensionsless combinations (e.g., the Reynolds
number, Froude number, and Weber number, ?N2D3
A/?). Sometimes,
empirical relationships are established to relate process results and
agitation parameters. Often, however, such relationships are nonexistent.
Laboratory scales of equipment using the same materials as
on a large scale are then experimented with, and the desired process
result is obtained. The laboratory system can then be scaled-up to
predict the conditions on the larger system.
For some scale-up problems, generalized correlations as shown in
Figures 8-11, 8-12, 8-13, and 8-14 are available for scale-up. However,
there is much diversity in the process to be scaled-up, and as such no
single method can successfully handle all types of scale-up problems.
Various methods of scale-up have been proposed; all based on
geometric similarity between the laboratory equipment and the fullscale
plant. It is not always possible to have the large and small vessels
geometrically similar, although it is perhaps the simplest to attain. If
geometric similarity is achievable, dynamic and kinematic similarity
cannot often be predicted at the same time. For these reasons, experience
and judgment are relied on with aspects to scale-up.
The main objectives in a fluid agitation process are [25]:
• Equivalent liquid motion (e.g., liquid blending where the liquid
motion or corresponding velocities are approximately the same in
both cases).
• Equivalent suspension of solids, where the levels of suspension
are identical.
• Equivalent rates of mass transfer, where mass transfer is occurring
between a liquid and a solid phase, between liquid-liquid phases,
or between gas and liquid phases, and the rates are identical.