(426e) Development of a Mixing Index Provides a Means to Solve Many Industrial Mixing Problems

Industrial mixing success is measured by practical and economical product production, not by extensive description of mixing behavior. Most often the cost and time required for a scientific research project to find the best mixing option is not feasible. The majority of industrial mixer applications are for formulation processes that combine and blend components, as opposed to complicated chemical reactions with multiple possible products. The ability to conveniently quantify mixing intensity can be an effective path to improving or solving many process problems.

A further limitation to most industrial mixing processes is the requirement to use existing mixing equipment. A new mixer is rarely an option for process improvement or even new product production. The successful use of existing equipment often depends on the ability to predict the capabilities of the mixer for the planned product or modified process. A 1 to 10 Scale of Agitation for liquid mixing intensity was introduced in a series of articles published in Chemical Engineering in 1975 and 1976. That intensity scale was linked to a "bulk fluid velocity" and applied to the selection of mixing equipment. Because the concept focused on new mixing equipment, it was presented in a way that was difficult to apply to existing equipment. A convenient and consistent method for predicting mixing intensity for turbine style mixers in liquid applications has been developed to facilitate the evaluation of mixing equipment.

The concept of a 1 to 10 scale of mixing intensity has been reduced to the straightforward calculation of a Mixing Index. This index is based on otherwise obvious variables that influence mixing success, including liquid volume, impeller diameter, rotational speed, and impeller power number. The Mixing Index (MI) can be calculated using the following formula for turbulent conditions: (equation - see uploaded file)
The expression for MI can be rearranged to solve for a rational speed based on an impeller diameter and volume or solved for an impeller diameter at a speed and volume. The simple expression can be used for either evaluation of existing mixing conditions or mixer design based on the selection of other variables. The expression needs a correction factor for reduced impeller pumping at higher viscosity. The correction factor can be used over a typical range of Reynolds numbers for turbine mixers.

The calculation of a MI with a value between 1 and 10 can be compared with CFD images or used for scale-up calculations. A non geometric scale-up example and associated CFD plots will be used to demonstrate the ability of the MI to calculate or compare mixer capabilities. The basic equation can be used to adjust for different volumes and with different impeller types. Scale-up can even keep multiple mixing variables constant by solving multiple equations with multiple unknowns.

While not sophisticated or precise, the MI gives a sufficient estimate of mixing intensity for many industrial applications. It successfully parallels other methods of mixer evaluation and can be applied using spreadsheet calculations and basic engineering skills. Like any other method for solving mixing problems, the MI has its limitations, but it does provide a flexible method for getting estimates of mixing capacities quickly and cost effectively.