Plateau-Rayleigh Instability in a water sheet from a fountain. Photo Credit: f***yeahfluiddynamics.tumblr.com
Here at TeamUV.org, we have often discussed some of the finer intricacies of fluid mechanics (or usually more specifically, fluid dynamics, as opposed to fluid statics). Generally speaking, however, we have looked at fluid flow and behavior from a very macroscopic view, that is we have looked at fluids as they act on the macroscopic length scale, within which objects are practically visible by the naked eye. In the various fields of engineering, most engineers would only need a macroscopic understanding of fluid mechanics in order to perform rather rudimentary calculations and analysis. For example, if an engineer was asked to determine the hydrostatic pressure exerted on a submerged pressure vessel lying on the bottom of the ocean or if they were asked to size (determine pump impeller diameter, pump speed, power input necessary, pump type, capacity/flow rate, etc. for) a pump based off of the known pressure gradient (perhaps it has to force water through a very fine filter while maintaining a certain amount of pressure), elevation change, or required change in speed, a macroscopic view of fluid mechanics would often be sufficient. But is this always the case?
Of course not! The golden rule of engineering regarding what you need to know to perform your job is that there is no golden rule of engineering regarding what you need to know to perform your job. Engineering is a highly dynamic field, with ground-breaking discoveries made continuously…right now, somewhere in the world a scientist or engineer is making a major contribution to the future of STEM. Additionally, engineers (especially mechanical engineers, who have a very large, diverse knowledge base) can be asked to do anything at any given time, and they must be able to figure it out! So to say that the macro scale is the only one an engineer needs to be aware of (especially in the field of fluid mechanics) would be a gross understatement. So where does that leave us? Well now would be a good time to explain what is meant by “length scale” and to share some of the typical ones. After that, we will very briefly roll through some of the fluid effects that exist on smaller length scales, as these highly complex phenomena are beyond the scope of this post.
Orders of magnitude as they apply to the Eiffel Tower viewed from different length scales, demonstrating how different length scales reveal different details. Photo Credit: iupui.edu
A length scale is essentially a parameter for deciphering the characteristic length associated with a phenomena. For example, if we are talking about the atomic scale, we are generally talking about phenomena that occurs in the size range of atoms, on the order of magnitude of pico- to femto-meters (10^-12 or ^-15 m). If we are talking about the microscale, we are talking about things on the order of micrometers (10^-6 m) such as water droplets or the thickness of a human hair. The macroscale would be associated with cars, mountains, you and I, etc. and would be essentially anything in your field of vision, i.e. probably from millimeters on up to kilometers (although the macroscale is not precisely defined). From here, we would likely move on to the astronomic scale, which is generally used to refer to phenomena on the scale of the universe, or Megameters (10^6 or 1,000,000 m) on up. For example, if you were to move from an atomic to micro to macro to larger with regards to your hand, you could envision protons and neutrons in your skin cells and then zoom out to bacteria under a microscope and then zoom out further to your hand itself and then zoom out further to the Earth itself, further to the Milky Way Galaxy, and so on and so on. In fact, if you have a second, you should check out this zoomable tool for visualizing the scales of the universe.
So back to fluid dynamics after a very lengthy detour, why should we care about length scales smaller than the macroscale? Because turbulence (as well as all fluid motion and other physical phenomena in general), is a result of phenomena on smaller length scales. So in order to actually understand the onset of turbulence or how fluids react with each other or with structures, etc. within the framework of deeper understanding, we must understand the microscopic behavior of fluids. Much of this behavior is defined by fluid stability and instabilities, which are not only very interesting to look at, but are the building blocks for the entire field of fluid dynamics as we know it! At this point, I will quickly show some pictures of some of the more common instabilities, but will not go into descriptive detail as scientifically, mathematically, etc. they are extremely complex phenomena that many fluid dynamicists spend their entire careers studying.
Kelvin-Helmholtz Instability simulation. [Media Credit: Wikipedia.org]
Kelvin-Helmholtz Instability made visible by clouds. Photo Credit: UP.edu
Rayleigh-Taylor Instability simulation. Photo Credit: Wikipedia.org
Rayleigh-Taylor Instability seen in dye drops in water. Photo Credit: Colorado.edu
Gortler Vortices on an oscillating cylinder within a flow marked by fluorescent dye. Photo Credit: APS.org
