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

δP = 10218/20 × 10-6 Pa = 79.4 kPa

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 v s 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 × v s = 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 × v s = 4 × (0.04 m)2 × 2022 W/m2 = 40.65 W

Assuming the pulse lasts one mS, then the total energy radiated is

E = 40.65 joules/sec × 0.001 sec = 0.041 joules

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.