Fuck Yeah Fluid Dynamics

Celebrating the physics of all that flows. Ask a question, submit a post idea or send an email. You can also follow FYFD on Twitter and Google+. FYFD is written by Nicole Sharp, PhD.

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Posts tagged "viscosity"

A water droplet can rebound completely without spreading from a superhydrophobic surface. The photo above is a long exposure image showing the trajectory of such a droplet as it bounces. In the initial bounces, the droplet leaves the surface fully, following a parabolic path with each rebound. The droplet’s kinetic energy is sapped with each rebound by surface deformation and vibration, making each bounce smaller than the last. Viscosity damps the drop’s vibrations, and the droplet eventually comes to rest after twenty or so rebounds. (Image credit: D. Richard and D. Quere)

The coalescence of two liquid droplets takes less than the blink of an eye, but it is the result of an intricate interplay between surface tension, viscosity, and inertia. The high-speed video above was filmed at 16000 frames per second, yet the initial coalescence of the silicone oil drops is still nearly instantaneous. At the very instant the drops meet, an infinitesimally small neck is formed between the droplets. Mathematically speaking, the pressure and curvature of the droplets diverge as a result of this tiny contact area. This is an example of a singularity. Surface tension rapidly expands the neck, sending capillary waves rippling along the drops as they become one. (Video credit: S. Nagel et al.; research credit: J. Paulsen)

The Kaye effect is particular to shear-thinning non-Newtonian fluids - that is, fluids with a viscosity that decreases under deformation. The video above includes high-speed footage of the phenomenon using shampoo. When drizzled, the viscous liquid forms a heap. The incoming jet causes a dimple in the heap, and the local viscosity in this dimple drops due to the shear caused by the incoming jet. Instead of merging with the heap, the jet slips off, creating a streamer that redirects the fluid. This streamer can rise as the dimple deepens, but, in this configuration, it is unstable. Eventually, it will strike the incoming jet and collapse. It’s possible to create a stable version of the Kaye effect by directing the streamer down an incline. (Video credit: S. Lee)

Everyone has seen drops of liquid falling onto a dry surface, yet the process is still being unraveled by researchers. We have learned, for example, that lowering the ambient air pressure can completely suppress splashing. Viscosity of the fluid also clearly plays a role, but the relationship between these and other variables is unclear. The images above show two droplet impacts in which the viscosity differs. The top image shows a low viscosity fluid, which almost immediately after impact forms a thin expanding sheet of fluid that lifts off the surface to create a crownlike splash. In contrast, the higher viscosity fluid in the bottom image spreads as a thick lamella with a thinner outer sheet that breaks down at the rim. Researchers found that both the high- and low-viscosity fluids have splashes featuring these thin liquid sheets, but the time scales on which the sheet develops differ. Moreover, lowering the ambient pressure increases the time required for the sheet to develop regardless of the fluid’s viscosity. (Image credit: C. Stevens et al.; submitted by @ASoutIglesias)

Reader thesnazz asks:

Is there a difference between surface tension and viscosity, or are they two manifestations of the same process and/or principles? If you know a given fluid’s surface tension, can you predict its viscosity, and vice versa?

This is a good question! To answer it, let’s think about where surface tension and viscosity come from. Like many concepts in fluid dynamics, these quantities describe for a whole fluid the properties that arise from interactions between molecules.

To prevent this becoming overly long, I’m going to tackle this over a couple posts. Today, I’ll talk about viscosity. 
One way to describe a fluid’s viscosity is as a measure of its resistance to deformation. Another way to think of it is how easily momentum is transmitted from one part of the fluid to another. The diagram above is the classic representation. A layer of fluid is sandwiched between two flat plates. If the top plate moves, friction requires that the fluid particles in contact with the plate get dragged along. This shears the fluid just below that and drags it along, but not quite as much. Those fluid particles do the same to their neighbors and so on down to the stationary second plate, where the fluid is at rest. 
Viscosity is the property that determines how much those neighboring fluid particles move; the more viscous the fluid, the more the neighboring bits of fluid resist getting pulled along. This is a property that’s inherent to a fluid. It comes from how the molecules of the fluid interact with one another, but there are no simple expressions to calculate the viscosity of a liquid or a gas from the individual interactions of its molecules. Instead we experimentally measure viscosity values and use empirical formulas to approximate how viscosity changes with temperature and other effects. (Image credit: Wikimedia)

Reader thesnazz asks:

Is there a difference between surface tension and viscosity, or are they two manifestations of the same process and/or principles? If you know a given fluid’s surface tension, can you predict its viscosity, and vice versa?

This is a good question! To answer it, let’s think about where surface tension and viscosity come from. Like many concepts in fluid dynamics, these quantities describe for a whole fluid the properties that arise from interactions between molecules.

To prevent this becoming overly long, I’m going to tackle this over a couple posts. Today, I’ll talk about viscosity. 

One way to describe a fluid’s viscosity is as a measure of its resistance to deformation. Another way to think of it is how easily momentum is transmitted from one part of the fluid to another. The diagram above is the classic representation. A layer of fluid is sandwiched between two flat plates. If the top plate moves, friction requires that the fluid particles in contact with the plate get dragged along. This shears the fluid just below that and drags it along, but not quite as much. Those fluid particles do the same to their neighbors and so on down to the stationary second plate, where the fluid is at rest.

Viscosity is the property that determines how much those neighboring fluid particles move; the more viscous the fluid, the more the neighboring bits of fluid resist getting pulled along. This is a property that’s inherent to a fluid. It comes from how the molecules of the fluid interact with one another, but there are no simple expressions to calculate the viscosity of a liquid or a gas from the individual interactions of its molecules. Instead we experimentally measure viscosity values and use empirical formulas to approximate how viscosity changes with temperature and other effects. (Image credit: Wikimedia)

The dimensionless Reynolds number is a key concept in fluid dynamics, allowing scientists to distinguish regimes of flow between differing geometries and even different fluids. This video gives a great primer on the subject by examining the physics of swimming for a sperm versus a sperm whale. The Reynolds number is essentially a ratio between inertial forces (driven by velocity and size) and viscous forces, and its value can indicate how important different effects are. Sperm and other microbes live at very small Reynolds numbers, meaning that viscosity dominates as the force they must overcome to move. For more on the low Reynolds number world, check out how brine shrimp swim and what happens if a microbe tries to flap its tail. (Hint: it goes nowhere, and this is why.) (Video credit: A. Bhatia/TED Ed; via Jennifer Ouellette)

To round out our series on fluid dynamics in the Ig Nobel Prizes (which are not the same thing as the actual Nobel Prizes), here are some of the other winners. Last year Mayer and Krechetnikov won for a study on coffee sloshing when people walk. We’ve mentioned the pitch-drop experiment measuring the viscosity of an extremely viscous fluid a couple times; Mainstone and Parnell won a 2005 Ig Nobel for that (on-going) work. Another 2005 prize went to Meyer-Rochow and Gal for calculating the pressures involved in penguin defecation. (Yes, seriously.) A avian-related award was also handed out to B. Vonnegut for estimating tornado wind speeds by their ability to strip a chicken of its feathers. And, finally, for those looking to interest undergraduate lab students in mathematics and fluid dynamics, I suggest following the lead of 2002 winner A. Leike who demonstrates laws of exponential decay with beer head. (Photo credit: S. Depolo)

Does a person swim faster in water or syrup? One expects the more viscous syrup would offer a swimmer greater resistance, but, at the same time, it could also provide more to push against. Gettelfinger and Cussler put this to a test experimentally with competitive and recreational swimmers in a pool of water and in one with a fluid measuring roughly twice the viscosity of water. Their results showed no significant change in swimming speed. When you consider that human swimming is highly turbulent, however, the result makes sense. In fluid dynamics, the dimensionless Reynolds number represents a ratio between inertial forces and viscous forces in a flow. The researchers estimate a Reynolds number of a typical human in water at 600,000, meaning that inertial effects far outweigh viscous effects. In this case, doubling the viscosity only reduces the Reynolds number by half, leaving it still well inside the turbulent range. Thus, swimming in syrup has little effect on humans. The Mythbusters also tackled this problem, with similar conclusions. This is a continuation of a series on fluids-related Ig Nobel Prizes. (Photo credit: Mythbusters/Discovery Channel; research credit: B. Gettelfinger and E. L. Cussler, winners of the 2005 Ig Nobel Prize in Chemistry)

A thin spout of water is drawn up through a layer of oil in the photo on the right. This simple version of the selective withdrawal experiment is illustrated in Figure A, in which a layer of viscous oil floats above a layer of water. A tube introduced in the oil sucks fluid upward. At low flow rates, only the oil will be drawn into the tube, but as the flow rate increases (or the tube’s height above the water decreases), a tiny thread of water will be pulled upward as well. The viscous outer fluid helps suppress instabilities that might break up the inner fluid, and their relative viscosities determine the thickness of the initial spout. In this example, the oil is 195 times more viscous than the water. (Photo credit: I. Cohen et al.)

In water and other Newtonian fluids, a rising bubble is typically spherical, but for non-Newtonian fluids things are a different story. In non-Newtonian fluids the viscosity—the fluid’s resistance to deformation—is dependent on the shear rate and history—how and how much deformation is being applied. For rising bubbles, this can mean a teardrop shape or even a long tail that breaks up into fishbone-like ligaments. The patterns shown here vary with the bubble’s volume, which affects the velocity at which it rises (due to buoyancy) and thus the shear force the bubble and surrounding non-Newtonian fluid experience. (Video credit: E. Soto, R. Zenit, and O. Manero)