A Hele Shaw cell is little more than two glass plates separated by a thin layer of viscous fluid. The cell serves as a good test bed for viscous, low Reynolds number flows such as those found in microfluidics. Here a less viscous fluid is injected into the center of the cell, causing the finger-like protrusions of the less viscous fluid into the more viscous one via the Saffman-Taylor instability.
Tag: instability
Convection Visualization
Here on Earth a fascinating form of convection occurs every time we put a pot of water on the stove. As the fluid near the burner warms up, its density decreases compared to the cooler fluid above it. This triggers an instability, causing the cold fluid to drift downward due to gravity while the warm fluid rises. Once the positions are reversed, the formerly cold fluid is being heated by the burner while the formerly hot fluid loses its heat to the air. The process continues, causing the formation of convection cells. The shapes these cells take depend on the fluid and its boundary conditions. For the pot of water on the stove and in the video above, the surface tension of the air/water interface can also play a role in modifying the shapes formed. The effects caused by the temperature gradient are called Rayleigh-Benard convection. The surface tension effects are sometimes called Benard-Marangoni convection.
Flow Vis
Place a viscous fluid in the gap between two plates of glass and you have created a Hele Shaw cell. If a less viscous fluid is then injected between the plates, a fascinating pattern of finger-like protrusions results. This is known as the Saffman-Taylor instability. Because of the relative simplicity of the set-up, it’s possible to create such experiments at home using common household fluids like glycerin, dish soap, dyed water, or laundry detergent. (Photo credits: Jessica Rosencranz, Jessica Todd, Laurel Swift et al, Andrea Fabri et al, Tanner Ladtkow et al, Mike Demmons et al, Trisha Harrison, Justin Cohee, and Erik Hansen)
2D Convection
This simulation shows 2D Rayleigh-Benard convection in which a fluid of uniform initial temperature is heated from below and cooled from above. This is roughly analogous to the situation of placing a pot of water on a hot stovetop. (In the case of the water on the stove, the upper boundary is the water-air interface, while, in the simulation, the upper boundary is modeled as a no-slip (i.e. solid) interface.) The simulation shows contours of temperature (black = cool, white = hot). In general, the hot fluid rises and the cold fluid sinks due to differences in density, but, as the simulation shows, the actual mixing that occurs is far more complex than that simple axiom indicates.
Cloud Streets
Cloud streets–long rows of counter-rotating air parallel to the ground in the planetary boundary layer–are thought to form as a result of cold air blowing over warm waters while caught beneath a warmer layer of air, a temperature inversion. As moisture evaporates from the warmer water, it creates thermal updrafts that rise through the atmosphere until they hit the temperature inversion. With nowhere to go, the warmer air tends to lose its heat to the surroundings and sink back down, creating a roll-like convective cell. (Photo credits: NASA Terra, NASA Aqua, and Tatiana Gerus)
Atomization
Atomization–breaking a flowing liquid into a fine spray–is important for fuel injection in a variety of engines, including automobiles, jet engines, ramjets, scramjets, and rockets. The more effectively a liquid fuel can be dispersed as a spray in an engine, the more efficient and stable the combustion will be. The apparatus in this high-speed video injects an annular water sheet with concentric jets of air on either side of the water. The video series shows the effects of increasing the outer and inner air velocities relative to the water on the breakup of the liquid. What to the naked eye looks like a deluge, high-speed video reveals as a complex undulating structure.
Jet Breakup
As a laminar column of water falls, slight perturbations cause waviness in the stream. Whenever the radius of the stream decreases, the pressure due to surface tension increases, causing fluid to flow away from the area of smaller radius. This outflow decreases the radius further and drives the stream to break into droplets. The mechanism is called the Plateau-Rayleigh instability. (Photo credit: Mahmoudreza Shirinsokhan)
Toroidal Vortex
When instabilities exist in laminar flow, they do not always lead immediately to turbulence. In this video, a viscous fluid fills the space between two concentric cylinders. As the inner cylinder rotates, a linear velocity profile (as viewed from above) forms; this is known as Taylor-Couette flow. If any tiny perturbations are added to that linear profile–say there is a nick in the surface of one of the cylinders–the flow will develop an instability. In this type of flow, an exchange of stabilities will occur. Rather than transitioning to turbulence, the fluid develops a stable secondary flow–the toroidal vortex highlighted by the dye in the video. If the rotation rate is increased further other instabilities will develop.
The Dance of Jets and Droplets
Placing a prism upside down in a bath of silicone oil creates a trapped bubble of air inside the prism. When oscillated above a critical amplitude, the corners of the prism, the oil, and the air perform an intricate dance of bubbles, singularities, jets, and droplets. Read more in the research paper. #
Spiky Ferrofluid
Ferrofluids consist of ferromagnetic nanoparticles suspended in a fluid. When subjected to strong magnetic fields, they develop a distinctive peak-and-valley formation due to the normal-field instability. The shape is a result of minimizing the magnetic energy of the fluid. Both gravity and surface tension resist the formation of these peaks. Ferrofluids, in addition to appearing in art exhibits, can be used as liquid seals, MRI contrast agents, and loudspeaker cooling fluids. (Photo credit: Maurizio Mucciola)
