Cavitation in water/liquids is a very effective way of generating shock waves1, due to the rapid accelerations/decelerations of the bubble interface during its collapse stage. Cavitation-related phenomena may even appear in nature, in animal species; for example dolphins cannot swim faster than 15 m/s due to cavitation formation2, which causes pain. On the other hand, the lack of pain receptors on the fins of fish belonging to the scombrid family2 (e.g. mackerels, tunas, etc.) allows them to exceed the cavitation free-limit and cavitation-induced damage has been observed on their bodies. Apart from the hindrance that cavitation may cause to swimming fish, other animal species have evolved to exploit the generation of shock waves through cavitation to stun or kill prey. Examples of such animals are snapping shrimps (belonging to the family of Alpheidae) and mantis shrimps (belonging to the family of Odontodactylidae).

Mantis shrimps have two hammer-like or club-like raptorial appendages, which they use to strike with extreme force their prey, such as e.g. small crustaceans or molluscs. High speed imaging revealed that cavitation may form between the hammer-like appendage and the target3,4. It is speculated that the mechanism of cavitation formation is due to the strong depressurization of water due to the Bernoulli principle3, i.e. as the fluid moves at high speed, its static pressure drops. Moreover, it is likely that cavitation is enhanced by vortex formation and the hammer rebound after the impact on the target surface3. However, there are indications that cavitation in the case of the mantis shrimp may be an unwanted effect. Detailed inspection revealed that cavitation does not only damage the target, but the mantis shrimp’s appendages as well4. Over time, the appendage surface becomes pitted and damaged, though frequent moulting of the mantis shrimp replaces the damaged smashing surface. The aforementioned discussion indicates that perhaps in the case of mantis shrimp, cavitation appears to be a side-effect of the percussion, with negative aspects that the shrimp has evolved to handle. On the other hand, it seems that the pistol shrimp is the sole species evolved to actively use cavitation itself as a weapon to kill/stun its prey. The mechanism of cavitation formation in pistol shrimp claws will be analyzed in the present work, focusing on the fluid mechanics aspects of its operation.

Snapping shrimps, known also as pistol shrimps, have two specially shaped claws, one of which is enlarged and is capable of forming cavitation bubbles5,6. Claws are expendable; if the large claw is amputated, the smaller claw will grow to replace the missing limb, whereas a new minor claw will grow in the place of the large claw7. The claw consists of two parts, the dactyl and the propus5. On the dactyl there is a protrusion (it will be referred as plunger hereafter) which fits into a complementary socket of the propus, see also Fig. 1. When the claw is fully open, water fills the socket of the propus. Then, when the claw closes rapidly, the plunger displaces water from the socket volume. Water escapes through a narrow anterior groove formed between the plunger and the propus, as shown in Fig. 1. The water expelled from the socket through the groove, creates a vortex ring5 in a similar way as an air vortex cannon8. Note that the shrimp claw is a complicated 3D shape and the expelled jet is not aligned at the same plane as the rest of the claw, thus it is not obstructed by the dactyl tip9. Hess et al.5 introduced the concept of formation number to explain the maximization of momentum transfer from the jet to the vortex. The jet velocity has been estimated by Versluis et al.10 to be ~25 m/s, using high speed imaging of an actual pistol shrimp claw closing. Such a velocity may lead to pressure drops of ~3.105 Pa, which is enough to vaporise water locally10 forming a cavitation bubble. Additionally, a simplified numerical investigation, based on the assumption of spherical cavitation bubble solved with the Rayleigh-Plesset equation, indicated pressure levels during collapse of even 2000 bar10. Furthermore, a study by Lohse et al.6 suggests that luminescence phenomena may be observed at the collapsing bubbles formed by pistol shrimps.

Figure 1 (a) Snapping shrimp claw components: d corresponds to dactyl, p to plunger and s to socket5. (b) Closed claw; the passage through which flow is expelled is visible5. (c) Render of the simplified claw geometry used in the present study and in previous experimental investigations5. Full size image

While the aforementioned list of experimental work5,6,10 aimed to investigate the phenomena being involved in the operation of the pistol shrimp claw, still the mechanism of cavitation formation is not described and well understood. In particular, the work of Versluis et al.10 examined the macroscopic cavitation formation from the claw and employed a simplified numerical model based on the assumption of spherical bubble shape and relying on parameter fitting to explain cavitation formation. In their work they recognised the lack of detailed flow field and pressure data in the vicinity of the closing claw. The work of Lohse et al.6 discussed the light emission from collapsing bubbles generated by pistol shrimps, hinting the extreme pressure/temperature conditions during collapse. Not much explanation was provided on the cavitation mechanism or flow field though. Finally, the work of Hess et al.5 was an experimental study aiming to describe the flow pattern during claw closure by analyzing an enlarged dimensions claw, which was based on a real pistol shrimp claw, scanned using X-ray Computational Tomography (CT). While vortex formation was demonstrated, the enlarged dimensions of the claw geometry did not permit observations of cavitation.

The present work focuses on the fluid mechanics aspects of cavitation formation, growth and collapse, by resolving the flow field around the claw using numerical simulations. The flow field is something that was not analyzed in previous studies, due to experimental limitations. In particular, investigations involving actual pistol shrimps, have constraints in shrimp handling, in the experiment environment and conditions, thus inherently limiting the applicable measurement techniques. High speed photography becomes problematic, since high frame rates are required (of the order of 106 fps), lighting and focusing becomes difficult (the animal may move in a not very controllable manner). The pressure signal recorded from the hydrophone may be excessively smoothed or underestimated by the sensor bandwidth10. Moreover, the complexity of the geometry of the claw and the uniqueness of each individual animal, hinder systematic and repeatable study. On the other hand, experimental replicas of pistol shrimp claws lack in reproducing the conditions of cavitation formation; for cavitation to occur, one needs a high speed moving object (the plunger). It is difficult to construct such a plunger in real size dimensions, moving at real closure speed, plus there are difficulties in the experimental techniques (similar to those mentioned above, i.e. high speed imaging, focusing/lighting etc.). This is the reason why Hess et al.5 resorted to enlarged and non-cavitating conditions.

A general remark in both cases is that experimental techniques such as high speed photography, or pressure signal measurements provide only partial views of the flow pattern and underlying mechanisms. High speed photography can show the existence of cavitation only, but not the actual density of the fluid. Hydrophones may provide information of the pressure signal at a given point, but not everywhere. Particle-Image-Velocimetry (PIV) cannot provide insight in cavitating regions, since the cavitation cloud obstructs the view. The advantage of a well-defined and converged simulation is that it provides a well controlled environment for conducting studies, without limitations of measuring techniques, since they are not necessary (no need for high-speed imaging, Particle-Image-Velocimetry), the flow field is directly accessible in a quantitative manner everywhere. Also there are much less limitations in the simulated conditions and geometry, ensuring repeatability and control. With the above, it is not implied that simulation is the only viable method in conducting research; it is clear that simulation may have pitfalls (hence the clarification “well-defined and converged”). It is also clear that developing simulation tools requires experimentation and theoretical developments to formulate modelling techniques and validate numerical results.

The present work in an attempt to demonstrate the fundamental flow effects occurring at the claw of a pistol shrimp, the mechanism of cavitation generation, shape and collapse. The claw geometry used is based on the simplified model of Hess et al.5. The reason for resorting to a simplified model is mainly related to validation. There are experimental data available5 that can be used to test the numerical methodology (see also supplementary material 3 and 4) and validate the predictive capability of the model before further investigating cavitating conditions. Additionally, the simplified geometry offers the possibility of repeatability in any further research; the geometry is provided as supplementary material (see also supplementary material 12) in Parasolid Computer-Aided Design (CAD) format that can be used by experimentalists to construct their own models, or researchers to develop and test numerical techniques. Note that the methodology employed is applicable for any arbitrary shape, should it be available in a clean Computer-Aided Design (CAD) format.

It is highlighted that in the frame of this work, instead of relying on modelled parameters/fitting, as was the case in the work of Versluis et al.10, the whole claw and the surrounding fluid are simulated with Computational Fluid Dynamics (CFD). Thus, the present work is the first to simulate the actual flow field inside and outside the claw, demonstrating the flow physics, the cavitation structure and providing additional insight in relation to experiments, since the inherent limitations of the latter are avoided. Despite the simplifications in the claw geometry, the main mechanisms of cavitation generation and collapse are replicable and similar magnitude of jet velocity is found as in experiments involving real pistol shrimps. Briefly stated here, the claw closure produces a high speed jet. The high speed jet induces vortex roll-up, which in turn leads to a strong pressure drop inside the core of the vortex. If the jet velocity is high enough, a pressure drop of even ~105 Pa can be produced, which is enough to vaporize water locally, forming a toroidal cavitation ring. The toroidal cavitation ring oscillates, expanding and collapsing; at the instance of the ring collapse, very high pressures are produced, due to the sudden deceleration of the surrounding liquid.

The simulation of vortex cavitating flows is rather challenging, since high resolution and low numerical dissipation are required to accurately track the vortex11. Additionally, cavitating flows are rather difficult to describe and model, due to large pressure and density ratios; in the present simulations, density varies from 998.2 kg/m3 (pure liquid) to 0.017 kg/m3 (pure vapour) and pressure varies from ~2000 Pa (liquid/vapour mixture) up to 100.105 Pa (pressure peaks). These variations have serious implications in the nature of the flow. Strong density variations imply prevalence of compressibility effects, such as low speed shock waves in the bubbly mixture12 and pressure pulses in areas of cavitation collapse. Indeed, cavitating flows are known to have a vast variation in the speed of sound, ranging from 0.01 m/s for liquid/vapour mixture up to 103 m/s for pure liquid13,14. Cavitation-related computational techniques involve fully Eulerian compressible techniques (selectively15,16,17) or Eulerian-Lagrangian methods (selectively18,19,20). Research on cavitation has many practical applications, ranging from fuel injection systems21,22, ship propellers23 and pumps24,25 to even drug delivery26 and cancer treatment27. The present research could further promote new and efficient designs in water cleaning/purification devices28,29, material processing and chemical engineering30.