Lava flows come in many varieties but one of the most captivating is the pāhoehoe flow, meaning “smooth, unbroken lava” in the native Hawaiian. This type of basaltic lava features a smooth or undulating surface formed by the fluid lava beneath a cooler, congealing surface crust. They often feature low viscosity (by the standards of lava) and very high temperatures between 1100 and 1200 degrees Celsius. Here the flow shows features of viscous fluids like honey, including rope-coiling motions.
Tag: viscous flow
Viscous Fluid Falling on a Moving Belt
In this video a very viscous (but still Newtonian) fluid is falling in a stream onto a moving belt. Initially, the belt is moving quickly enough that the viscous stream creates a straight thread. As the belt is slowed, the stream begins to meander sinusoidally and ultimately begins to coil. Aside from some transient behavior when the speed of the belt is changed very quickly, the behavior of the thread is very consistent within a particular speed regime. This is indicative of a nonlinear dynamical system; each shift in behavior due to the changing speed of the belt is called a bifurcation and can be identified mathematically from the governing equation(s) of the system. (Video credit: S. Morris et al)
Viscous Fingers
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.
Reader Question: Froude vs. Reynolds
@spooferbarnabas asks: I was wondering what the difference is between Froude’s number and Reynold’s number? they seem very similar
Fluid dynamicists often use nondimensional numbers to characterize different flows because it’s possible to find similarity in their behaviors this way. The Reynolds number is the most common of these dimensionless numbers and is equal to (fluid density)*(mean fluid velocity)*(characteristic length)/(fluid dynamic viscosity). The Reynolds number is considered a ratio of total momentum (or inertial forces) to the molecular momentum (or viscous forces). A small Reynolds number indicates a flow dominated by viscosity; whereas a flow with a large Reynolds number is considered one where viscous forces have little effect.
The Froude number, in contrast, focuses on resistance to flow caused by gravitational effects, not molecular effects. It is defined as (mean fluid velocity)/(characteristic wave propagation velocity). Initially, it was developed to describe the resistance of a model floating in water when towed at a given speed. As the boat’s hull moves through the water, it creates a wave that travels forward (and backward in the form of the wake), carrying information about the boat–much like pressure waves travel before and behind a subsonic aircraft. The speed of the wave created by the boat depends on gravity (see shallow water waves). The closer the boat’s speed comes to the water wave’s speed, the greater the resistance the boat experiences. In this respect, the Froude number is actually analogous to the Mach number in compressible fluids.
I hope that helps explain some of the differences!
Reader Question: National Committee for Fluid Mechanics Films
lazenby asks: Have you seen these guys? http://web.mit.edu/hml/ncfmf.html
Yes, absolutely! Those videos, which date from the 1960s, are so useful that they’re still shown to undergraduates today. (Or at least they showed several of them to us when I was junior!) They can seem a bit slow by current standards, but the films are full of great demonstrations of basic fluid mechanics. If the links on that page don’t work (or, if like me, you can’t stream RealPlayer), a lot of the videos can also be found on YouTube by searching for individual titles. The Low Reynolds Number Flow video is one of my favorites because it’s hosted by G. I. Taylor, one of the the most prolific and influential fluid mechanicians of the 20th century.
Ants as a Fluid
The collective behavior of ants can mirror the flow of a viscous fluid. It would be interesting to see if any such parallels carry over to the flocking of birds or schooling of fish. The latter two behaviors are thought to increase aero- and hydrodynamic efficiency for the group. #
Viscous Fingers
This photo shows the Saffman-Taylor instability in a Hele-Shaw cell. Here a viscous fluid has been placed between two glass plates and a second less viscous fluid inserted, resulting in a finger-like instability as the less viscous fluid displaces the more viscous one. This is an effect that can be easily explored at home using common liquids like glycerin, water, dish soap, or laundry detergent. #
Oil Chandeliers
What you see above is a composite of images of an oil droplet falling into alcohol from two different heights. The top row of images is from a height of 25 mm and the bottom from a height of 50 mm. The first droplet forms an expanding vortex ring which breaks down via the Rayleigh-Taylor instability due to its greater density than the surrounding alcohol. The second droplet impacts the alcohol with greater momentum and is initially deformed by viscous shear forces. Eventually it, too, breaks down by the Rayleigh-Taylor mechanism. This image is part of the 2010 Gallery of Fluid Motion. # (PDF)
Swimming in Corn Syrup
Highly viscous laminar flows exhibit kinematic reversibility, meaning: if you move the fluid one direction and then execute the same motion in the opposite direction, every fluid particle will return to its initial, undisturbed position. Above, you see a swimming device attempting to move through corn syrup by flapping. Because of this kinematic reversibility, it cannot propel itself. For the same reason, many microscopic organisms do not utilize flapping to move.
Effects of Viscosity
[original media no longer available]
Today’s video demonstrates the effect of viscosity, which measures a fluid’s resistance to deformation. On the left is a column of highly viscous fluid; the fluids become less viscous as one moves right. When a jet of dye is released into the highly viscous fluid, the jet is very slow to penetrate, whereas, in the rightmost column, the dye expands quickly into a turbulent jet. Between these extremes, we see a laminar dye jet entering the liquid. The mushroom-like shape the laminar jet takes is the result of the Rayleigh-Taylor instability, which occurs when a denser fluid is on top of a lighter fluid in a gravitational field.
