264 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Ti•.•. 2.--Mxx• PRocv. ssv. s Mass Transfer Physical Dispersion Extraction Liquid-Liquid Emulsions Dissolving, leaching Solid-Liquid Suspension Absorption Gas-Liquid Foams Heat Transfer Heat Transfer Blending Blending Because of the diverse nature of each of these operations it is not possible to state general principles about mixing operations that would apply to all of these categories. On the other hand, within a given category, such as solid-liquid suspension, there are many mixing principles that are com- mon to most of the processes in this area. Scale-up is the effect of tank size on a particular mixing classification. For a specific process, which may include several steps or classifications, scale-up must consider the effect of tank size on each of these steps to arrive at an over-all scale-up effect. Pilot planting is taking a given mixing operation and endeavoring to find out two essential pieces of information: 1. What is the relative magnitude of the various steps in the process ? 2. What are the effects of the major mixing variables ? There are three methods of arriving at the design of a mixer fo,- full scale processes. These are as follows: 1. Complete knowledge on previous successful installations is available and practically no experimental work is required. 2. The controlling step in the process is known, but one data point is needed to set the level of mixing required in the process. In this case, one or two runs on a laboratory scale in a single tank size, or perhaps even a small amount of data on an existing production unit. 3. The process is entirely new, and a complete pilot plant study must be made. In this case, as a general rule, runs at three or four different speeds in a given tank size would yield suitable information about the process mechanism and would also indicate whether additional runs are needed to isolate some particular important mixing variables. Runs in a second tank size may be needed. The extent of the pilot plant program should never usually exceed the cost of providing for an additional safety factor in a unit which would be designed without the benefit of extensive pilot plant information. BENCH SCALE EQUIPMENT On small bench scale work, data are often obtained for considerations other than mixing. Many times it is desired to eliminate mixing as a vari- able and study other factors in the process. The use of high speed laboratory equipment running at speeds up to

SCALE-UP CONSIDERATIONS IN COSMETIC MANUFACTURE 265 IO(] c 0.001 0.01 0.1 1.0 HORSEPOWER/GALLON Figure 5.--Effect of horsepower level on process result. 10,000 r.p.m. gives a mixing fluid regime that involves extremely large size mixers when projected to production scale equipment. If these power levels are required, then there is justification for pursuing the design of these large size mixers for production scale equipment. If power levels considerably less than those used in the high speed laboratory unit will give satisfactory results, then laboratory work should be done to find out just what effect horsepower has on the process. 'Referring to Fig. 5, if the mixer is operating in the range of 0.5 horse- power per gallon, we cannot tell which of the curves, A, B or C, holds. We must reduce the horsepower to find out where the threshhold horsepower is to give the highest process result. There are two important characteristics of a high speed laboratory mixer. It is not uncommon to have power levels as high as 0.5 horsepower per gallon and to have extremely high fluid shear rates. When it is essential to maintain a high value for either one of these two quantities on the full scale unit, then consideration of high horsepower, high speed production units is justified. Many times in unbaffled or round bottom flasks, impellets which are not similar to those used in production size equipment are used in the labora- tory. This brings up several uncertainties in the usefulness of the data. The use of an unbaffled tank makes the calculation of power consumption uncertain. The use of impeller5 which do not have a Reynolds number-- Power number curve brings in a second source of error.