The Physics of Making "Smoothies"

Frame from a video on the referenced article. Note the
cloudy region in the bottom of the liquid near the blades.
This is caused by minute bubbles created by cavitation at
the tips of the blades. The brown layer on top of the water
is oil.

Thanks to a colleague for pointing out an interesting article on shock waves in food blenders! Mathematician-turned-chef Chris Young and colleagues have collaborated in a series of articles to explain the science behind various cooking techniques. In this article, Young explains how the blades in the blender cut food up into small pieces, but then that the real work is done by small bubbles created by the blades through a process known as "cavitation."

Cavitation occurs when the pressure in a liquid drops below the equilibrium vapor pressure. It is a common occurrence in industrial settings, such as around the tips of rotating blades. Pressure drops occur in a variety of settings ranging from the flow of rivers around and over objects to flow in nozzles, to the wiggling of the tails and fins of swimming animals, and cavitation is a possibility in any of these settings. A bubble formed by cavitation is unstable. When such bubbles collapse, often asymmetrically, a tiny jet is formed. When these jets impinge on either the opposite sides of the bubble walls or on an adjacent surface, very high pressures, thousands of times atmospheric pressure, can occur. These jets erode the adjacent surfaces, causing structural damage.  Cavitation around the tips of dolphin or tuna tails may limit the speed with which these animals can swim! Cavitation is also a major problem at spillways from dams, and played a role in the near-failure of the bypass tubes during a major flood crisis at Glen Canyon Dam in 1983.

Exploding lava bubble at Etna

Exploding lava bubble at Mount Etna
Photo copyrighted by Tom Pfeiffer
from Volcano Discovery

Audible booms, sometimes very audible, occur at a number of volcanoes around the world. In a previous post, I discussed a variation on this ("flashing arcs") for the "James Bond" volcano, Shinmoedake,  and the Matua, Siberia, eruption. Also, more on shock waves here in the context of China's new fighter jet!

Here, the photographer captured the source of one such boom, a lava bubble (what is the scale??) bursting from the lava lake at Mount Etna.

In text accompanying the photo at the left, the photographer reported that "a loud detonation and a strong shock wave that felt like a punch into the stomach when observed from 300 meters distance, accompanies these bursts. Even at 10 km distance, windows rattle."

Audible booms or atmospheric shock waves are produced when something pushes suddenly on the atmosphere. This is most easily illustrated with a one-dimensional experiment called a "shock tube."  These were developed to explore the effects of bombs on the atmosphere, but have been widely used to investigate basic science problems such as chemical kinetics, and basic properties of gases as a function of pressure and temperature.

Schematic of a shock tube experiment.
Source is here; use is permitted for any purpose.

A diaphragm, which is usually a piece of aluminum, is placed in the tube.  One region of the shock tube is taken up to a high pressure compared to the other region, and then the diaphragm is burst, either mechanically or sometimes with an electric wire. As shown in the upper part of this diagram, a wave, the shock wave, propagates into the low-pressure region. It "carries the message" that the diaphragm has burst into the low pressure region. At the same time, another wave, the expansion fan, propagates into the high-pressure region.  It "carries the message" that the diaphragm has burst into the high pressure section of the tube. The interface between the high and low pressure regions is called the "contact surface", and it moves downstream after the diaphragm is burst. Both waves reflect off the ends of the tube, and the flow becomes very complicated after that. 

The bursting bubble at Mount Etna is a spherical version of a shock tube.  In this case, the "diaphragm" was a coating of lava.  The motion of the "contact surface" is beautifully visible as the red hot lava fragments! Congratulations to the photographer!

A shocking James Bond volcano breaks windows 8 km away!

Shinmoedake volcano started eruptng about January 26, and it now joins a few other volcanoes in the world as one capable of producing atmospheric shock waves.  Turn up your speakers (well, not too far), play the video on this site, and listen to the shock just a couple of seconds into the video!  Assuming that the camera is in the town of Miyazaki, it took the shock about 25 seconds to cover the 8 km (5 mi) from the volcano to the town. So, the process that created the shock occurred well before the eyewitness turned on the recording device. The shock broke hundreds of windows. After I wrote this, I discovered another video that starts earlier and captures the whole eruption sequence; fortunately, my calculation of the shock travel time above seems to be right on!

Added on Feb. 7.  In this video, you can see the air shock sweeping rapidly down the flank of the volcano in the first few seconds, and you can hear the shock at about 33 seconds.

Set from the "You Only Live Twice"

This volcano, in a quieter time in 1967, was the location of the notorious villan, Blofield, and his SPECTRE organization in the movie "You only live Twice", and thus the name that is now appearing in the press, the James Bond volcano.

The shock wave that produced the boom you heard in the video did not have a visible presence, only audible. However, visible shock waves at volcanoes were first described at Mount Vesuvius by F.A. Perret who called them "flashing arcs."  In his article in the American Journal of Science (volumes 183-184, Article XXXII, pp. 329-333, 1912).  From that article: "The frequency of the explosions varied from approximately one every three or four seconds to at least three per second.  Although powerful, they were verysharp and sudden in their nature, and at the instant of each--but before it could be sensed by the eye or ear--a thin, luminous arc flashed upward and outward from the crater and disappeared in space.  Then came the sound of the explosion and the projection of gas and detritus above the lip of the crater.  The motion of translation of the arcs, while very rapid in comparison with that of the detritus, was not above the limits of easy observation and there could be no doubt as to the reality of the phenomenon, which was repeated some hundreds of times.  ...of the actual phenomenon, the beauty of which lies in the delicate luminosity, the elegance and perfection of form, and the grace and vivacty of the arcs amid the contrasting color and relatively sluggish movement of their surroundings."

F.A. Perret at Campi Flagrei, Italy, possibly 1906-1907
photo is from
http://historyofgeology.blogspot.com/p/about_02.html

Ah, wouldn't it be nice if some of our peer reviewed journals today allowed us to regain some of this style of writing!

Perret travelled to volcanoes around the world, but it was not until four years later that he saw them again, this time at Vesuvius.  After proposing that the arcs were related to sound waves, he concluded "...the flashing arcs may be considered one of the most beautiful of all volcanic phenomena."

This posting got me to a wonderful blog by David Bressen on the history of geology, and I'll refer you there "for the rest of the story".  The discussion of Perret that accompanies the picture above is on the January 18, 2011, blog.

Other volcanoes that have shocks are Ngauruhoe (New Zealand), Sakurajima (Japan), Matua (Siberia), and, just last summer, Eyjafjallajokull.