The Energy Physics of the Pistol Shrimp
rael-science
The Energy Physics of the Pistol Shrimp
Ronjon Nag
December 11, 2017
Submitted as coursework for PH240,
Stanford University, Fall 2017
What Is a Pistol Shrimp and What Does It Do ?
 |
| Fig. 1: One species of pistol shrimp,
Alpheus cedrici, with an enlarged left claw used for
snapping (Source: Wikimedia
Commons) |
The pistol shrimp is a remarkable creature about 4 cm
in length and 25 grams in weight. Despite its small size, it can move
its claws at a speed of 97 km/hr. The speed of the snap is such that a
bubble is created consisting of vacuum. The internal low pressure causes
a water pulse that immobilizes prey with an associated noise of 218 dB
which is louder than a bullet, and reportedly a temperature of 4800
degrees centigrade which is similar to the surface temperature of the
sun, albeit over a very small area. Additionally, there is a brief flash
of light [1]. A pressure of 80 kPa at a distance of 4 cm from the claw
has been measured, with the water jet traveling at 25 m/sec, enough to
kill a small fish and it is this pressure which is significant for
stunning prey rather than the heat and light.
Approximate Calculation of Energy
Assuming an area of pressure covering 1
cm2, the energy produced can be approximately calculated
by:
| Energy | = | force × distance
= pressure × area × distance |
| = | 80,000 Pa × 0.0001 m2 × 0.04 m
= 0.32 Joules |
At 25 m/sec then we may assume this is generated in
0.04/25 seconds = 0.0016 seconds, then the power generated would be
200 W.
An Alternative Calculation of Energy
We can now compute the power and energy of this sound
pulse. With δP defined as the maximum pressure excursion, and B
is the Bulk Modulus of water, and vs is the speed of sound in
water, the energy density of the wave at a distance r = 4 cm from the
shrimp is
| 1 2 | (δp)2 B | = | (7.94 × 104 Pa)2 2 × 2.35 × 109 Pa | = | 1.35 Pa | = | 1.35 joules/m3 |
The energy flux at r = 4 cm is then
| 1 2 | (δp)2 B | × vs | = | 1.35 joules/m3 × 1498 m/sec | = | 2022 W/m2 |
The total power radiated
is thus approximately
| 4 π r2 × | 1 2 | (δp)2 B | × vs | = | 4 × (0.04 m)2 × 2022 W/m2 | = | 40.65 W |
Assuming the pulse lasts one mS, then the total energy
radiated is
Pistol Shrimp Mechanism
At first the phenomena of such force, noise, high
temperatures and light from such a small living creature appear to
violate the laws of energy conservation, but actually a simple mechanism
allows the organism to alter the surrounding water in a significant
manner. The phenomena is based on Bernoulli's principle, which when the
liquid moves above a certain speed, the pressure within the liquid
decreases. We see this in rivers and liquids flowing through pipes. When
the pressure drops, tiny air bubbles form, and if the pressure builds
back up, the bubbles burst. As described, the implosion causes
compression which can instantly generate enormous heat, called a
aviation effect. In pipes and water propellors, these effects will, over
time, destroy an chip away metal by the continuous blasts of heat
energy.
What is interesting is that the loud noise is not
caused by the snap of the claw closing. Rather the opening of the claw
accelerates a quantity of seawater to a velocity high enough to cause
cavitation which results in a very low pressure area. Where there is a
low pressure bubble, there is a tendency to fill it and the rushing
water moves behind a pressure wave at speeds greater than the speed of
sound in the empty space. This causes an instantaneous energy release
in which temperatures above 4800 degrees Centigrade and enormous
pressure is generated, creating a visible plasma arc, which in turn,
causes another compression, so-called cavitation effects. This results
in a flash of light - the phenomena where sound can produce light is
known as sonoluminescence and accordingly for the benefit of the pistol
shrimp a high-pressure pulse is sent immobilizing nearby prey. The
process may be considered similar to lightning. When lightning occurs,
the air is superheated and instantaneously causes compression of the air
to such a degree such that a very low-pressure area is created resulting
in surrounding being air propelled into a low pressure bubble with very
little resistance. The matter particles rushing to fill the bubble,
exceed the speed of sound, which causes a loud noise which we know as
thunder.
Is There Practical Use For Humans
It is very tempting to wonder if we can utilize the
heat created by such cavitation processes as an energy source. One idea
might be to create a mechanical replica version of the pistol shrimp.
Moving the claws at 97 Km/hr is probably practical, even at large scale.
Its not clear whether such energy production, even if driven by hydro or
heat harvesting, would be more efficient than other methods of energy
production. Also what might be more difficult is maintaining the
integrity of the vacuum bubble for anything more than a tiny size. The
tiny size of bubbles could however perhaps be an advantage in other
applications. The small bubbles could be useful medicine for tumor
destruction for example [3]. Another idea that has been floated has been
a compression engine [4]
© 2017, Ronjon Nag. The author warrants that the work
is the author's own and that Stanford University provided no input other
than typesetting and referencing guidelines. The author grants
permission to copy, distribute and display this work in unaltered form,
with attribution to the author, for non-commercial purposes only. All
other rights, including commercial rights, are reserved to the
author.
References
[1] D. Lohse, B. Schmitz, and M. Versluis, "Snapping
Shrimp Make Flashing Bubbles," Nature 413, 477 (2001).
[2] M. Versluis et al., "How Snapping Shrimp
Snap: Through Cavitating Bubbles," Science 289, 2114 (2000).
[3] M. Ghorbani et al., "Energy Harvesting in
Microscale with Cavitating Flows," ACS Omega 2 6870 (2017).
[4] B. Neal, "Compressor Unit,"
U.S. Patent 2,030,759, 11 Feb 1936.