A Brief Reflection on Fluid Mechanics and Undergraduate Chemical Engineering
Back in the fall of 2006, I took transport phenomena at my undergraduate university in Florida. I had little idea of what the course was about; people had asked me before if it was a course on automobile traffic flow or supply chain management. However, upon skimming the course text and listening to the professor’s first lecture, it became apparent that the course had nothing to do with daily commutes and everything to do with the mathematical modeling of fluids and the transfer of heat. While most of my classmates could not wait for that semester to be over, I remember that course fondly and with appreciation. The mathematics encountered in that course were far above what I expected to encounter in chemical engineering, but that which does not kill us makes us stronger.
What’s the Big Deal about Modeling Fluid Flows?
To boil down our motivation, fluids are commonly encountered in mass industrial production, and often these fluids exhibit peculiar properties that make them difficult to process. This motivates the discovery of a general theory for predicting their behavior under general circumstances. There are other situations where the prediction of fluid flows is of direct practical importance, such as the modeling and prediction of the weather and tides.
Think about fluids you encounter in your daily live other than water. How might their properties confound industrial production? Shampoo is a good example, as well as products such as toothpaste and Greek yogurt. Volumes have been written on properties of various oils and their usage in the lubrication of metal-metal contacts. The main fluid we deal with in our everyday lives, water, is a Newtonian fluid of low viscosity. However, many fluids deviate severely from Newtonian character, and can exhibit highly nonlinear responses to applied stress, as well as memory effects. This is especially true of liquids that have dissolved within them macromolecules of high molecular weight, such as polymers or proteins. Likewise for liquids such as blood, which have a high content of small particles within them. Suspensions of biological material in general can exhibit non-Newtonian behavior. It would be excessively pedantic to list all of the possible types of non-Newtonian fluid here; suffice to say, there are many of them, and general modeling of their flows is an open research problem.
The Hard Part – Fluids are Complicated!
Most people have little conception as to how difficult the modeling of fluids in general is. The first theories ignored the property of viscosity and instead focused exclusively on zero-resistance (“inviscid”) flow. While there is some use to these equations, their shortcomings are rapidly brought to bear when modeling flows with any significant viscous effects.
In order to model viscous fluid flow, two equations are needed: the continuity equation, and the Navier-Stokes equation. These equations are, in general, nonlinear partial differential equations for which no general solution is known. However, there have been many advances made in the numerical solution of flow fields. This intersecting branch of physics, engineering, and computer science, called computational fluid dynamics, concerns itself with direct solution of the governing equations for a given fluid flow. The advances have culminated in off-the-shelf software, such as FLUENT, which can even model non-Newtonian fluids.
Check out this collection of fascinating films here. Here is one of the videos, a video on Flow Visualization:
In the days that these videos were made (circa 1960), there was no FLUENT, and computers were low-powered, cumbersome devices that would be totally inadequate for flow calculation. Instead of simulating flows, the scientists in these videos had to observe flows directly in the laboratory using experimental apparatus. The video on flow visualization shows many clever techniques used to observe the flow field without disturbing it. The scientists also were unable to solve the nonlinear partial differential equations governing the flow, and thus had to rely on sharp scientific intuition, as well as dimensionless numbers.