# Analogies and Problem-Solving

Dec. 15, 2002

Have you ever solved a processing problem using an analogy? If you have not, you might want to give it a try. It could be easier than you think.

An analogy can be defined as an inference that if two or more things agree with one another in some respects, they probably will agree in others. For example, atomic size is like the growth rings of a tree ," atomic radius increases as more energy levels are added.

An analogy, therefore, can be used when two processes or systems are similar to each other. By understanding one process, engineers can better understand the other process. Through process understanding, process problems are solved.

Undergraduate students often are taught that the transport of heat and the transport of mass are similar or analogous to each other. In fact, the correlations used to calculate heat and mass transfer coefficients in many processes are similar in appearance. This analogy is a simple one and easy to understand. Other analogies might not be so obvious.

A host of analogies are waiting to be discovered. Because biotechnology is an up-and-coming area, an analogy in this area might provide another useful example. You could say that biological cells are like liquid drops. Both contain a liquid. Cell mass is similar to a watery liquid. The cell wall is analogous to surface tension of a drop.

How does this help? In biotechnology processes, cells often have to be harvested and broken open to separate biological material. Unfortunately, little definitive study has been made of cell breakage phenomena, and debates about the locations of cell breakage process equipment continue. However, significant information about how drops break up is available. The equilibrium drop size is the size of the drop that is reached on breakage. Very few drops are larger than this drop. This equilibrium drop size is correlated with the Weber Number.

Various constants are possible in the correlation and other effects; however, the major effect is surface tension. If the equipment Weber Number for a drop is not high enough, then the drops will not break up. Analogously, in the same equipment, if the Weber Number for a cell is not high enough, then the cell will not break up. Harvesting and cell breakage require a certain Weber Number level to be obtained in the equipment, helping specify the operating conditions necessary for harvesting cells.

Analogies often have the same length, time and velocity scales. However, analogies do not contain complete identity. For example, drops do not have a uniform size. However, cells generally do.

Another very common analogy states that free-flowing powders behave like liquids. This analogy is useful when considering spills. A free-flowing powder spill, in many ways, is like similarly to a low-viscosity liquid spill.

Spillage information can be estimated for powders from information about liquid spillage. Computer simulations of liquid flow can be used to model free-flowing powder behavior.

Unfortunately, this analogy breaks down in other areas. Liquids pumps are not very useful for pumping free-flowing powders. Blowers are more useful for these powders.

Analogies also are helpful in determining whether or not proposed solutions to problems will work. They keep you from wasting your time on unlikely solutions. For example, compacting solids are not like water. Therefore, compacting solids and water require different handling methods.

Analogies also help in making jumps between equipment, which can save a lot of time and effort. For example, although little study has been made of heat transfer in agitated tanks, considerable information and correlations about heat transfer in pipes are available. To save time and effort, researchers often assume that the heat transfer in a pipe is similar to heat transfer through a vessel wall in an agitated tank. They do not develop an independent correlation for an agitated tank. Instead they use the correlations developed for pipes. As a result, the correlations for the heat transfer coefficients in pipes and agitated tanks appear to be the same. The various dimensionless groups and exponents are the same. Only the lead constant in the correlation is different.

Analogies help organize your thinking and improve the understanding of the physics and chemistry behind processes that are not well understood. Analogies initially are guesses in such situations. Guesses and analogies often are necessary when nothing else is available.

Tatterson is a technical editor for

Chemical Processing. He is a professor at North Carolina A&T State University in Greensboro. Contact him at gbt@ncat.edu. He also teaches short courses for the Center for Professional Advancement, www.cfpa.com.

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