Unifying fluidic excretion across life from cicadas to elephants

We report on the jetting behavior of cicadas Fidicinoides sp. and Guyalna sp. feeding on non-native Indian almond trees (Terminalia catappa) in the Peruvian Amazon and Chremistica umbrosa in Singapore (SI Appendix). We quantified their jetting behavior in detail as shown in Fig. 1b, which includes the following ($n=$ individual, $N=$ excretion events): Fidicinoides sp.: $n=3$, $N=7$; Guyalna sp.: $n=1$, $N=3$; C. umbrosa: $n=6$, $N=9$. The cicadas generated fine, continuous jets with a diameter $d\sim$160 to 500 $\mathrm{\mu }$m with durations of $\tau \sim$80 to 560 ms (Movie S1). The average speed of the jet for cicadas is around (u$\sim$ 0.6 to 3.16 m/s) and the total volume per excretion event ranges from ($\sim$6 to 574 $\mathrm{\mu }$L). Cicadas employ large cibarial muscles and a specialized digestive system to process significant volumes of xylem fluid—up to $300\times$ their body weight per day (5). Dimensional analysis indicates that inertial forces primarily drive cicada jetting behavior with a Weber number $We=\rho d{u}^2/\gamma \sim$2 to 90, a Reynolds number $Re=\rho du/\mu \sim$100 to 1,900, and a Bond number $Bo=\rho g{d}^2/\gamma \sim$0.003 to 0.08 (Fig. 1C).

Why do cicadas, operating in the same surface-tension-dominated regime as other xylem-sap feeders ($Bo<1$), employ jetting instead of droplet excretion for waste elimination? This is particularly striking given the energetically demanding nature of their diet–xylem sap, which is nutritionally dilute and under negative pressure. We suggest that jetting enables cicadas to efficiently address both these dietary challenges simultaneously.

Cicadas, some of the largest insects in the Hemiptera order, face different physical limitations than their smaller counterparts like sharpshooters (7). This size difference significantly impacts their feeding and excretion mechanics. For instance, the largest cicada species, the empress cicada (Megapomponia imperatoria), is larger than some hummingbirds (8). Such size provides cicadas with lower energetic costs for generating fluidic jets compared to smaller insects, which require higher pressures for fluid flow. Specifically, cicadas require substantially less pressure for excretion due to their larger orifice sizes ($d\sim$160 to 500 $\mathrm{\mu }$m) compared to sharpshooters ($d<$100 $\mathrm{\mu }$m), as the required pressure within their hindgut scales inversely with the square of the orifice diameter and directly with the length of the hindgut $P\propto l/d^2$. Our analysis aligns with Novotny and Wilson’s findings on the allometric scaling of suction feeding pressure in xylem-sap feeding insects (7). Thus, larger xylem-feeding insects like cicadas exert less energy in both feeding and excreting, rendering jetting both energetically efficient and mechanically feasible (9).

Moreover, fluid mechanics principles indicate that cicadas’ use of fluidic jets facilitates expelling larger volumes rapidly ($Q\propto u$), enhancing nutrient extraction efficiency from xylem-sap. This adaptation not only proves energetically efficient but also suits their need to process large volumes of nutritionally poor food. The ability to process larger volumes may also supplement nitrogen, a critical growth element, but one that is scarce in plant xylem ($<$0.01%N) (10). Furthermore, the capacity to ingest and eject large volumes potentially offers cicadas a polyphagous lifestyle, enabling access to a wide range of host plants (7).

Beyond their primary feeding and excretion mechanics, these jet secretions may further serve multifunctional roles. For example, adult cicadas have been reported to spray incoming intruders with their anal jets when disturbed (11), and nymphal cicadas may exploit the copious amount of their watery excretion to agglutinate soil to build underground hallways and chambers, remove mud from integuments (12), and on some rare occasions observed to build aboveground turrets (13).

To bridge knowledge gaps, we conceptualize urination within a framework defined by two key dimensionless numbers in fluid dynamics: the Bond number ($\mathit{Bo}$) and the Weber number ($\mathit{We}$) (Fig. 1C and SI Appendix). Here, $\mathit{Bo}$ acts as a physical scale proxy with respect to capillary length, expressed as ${(d/l_c)}^2$, where $l_c$ is the capillary length ($\sim$2.4 mm for water). The Weber number $\mathit{We}$ describes the fluid’s morphology upon exiting the nozzle, varying from a dripping at low $\mathit{We}$ to a jetting at high $\mathit{We}$ (14). In our work, we simplify jetting as a phenomenon that occurs when inertial forces overcome surface tension forces ($We>1$), leading to a continuous fluid stream.

The $\mathit{Bo}$–$\mathit{We}$ framework has rationalized scaling mechanisms for animal drinking (1) and walking on water (15). In our current study, we apply it to categorize urination into four quadrants, establishing a correlation between size and fluid ejection mechanism across eight orders of magnitude in $\mathit{Bo}$ and $\mathit{We}$. Large mammals occupy the $Bo>1$, $We>1$ quadrant, where inertial forces ($P\sim \rho u^2$) dominate, driven by bladder pressure and gravitational forces ($P\sim \rho gl$). At extremely high values ($Bo>>1,We>>1$), fluids may exit as sheets, as in elephants and cows, where gravity drives inertial flows. Given the constant bladder pressure exerted by larger organisms, the effective fluid driving pressure remains constant, leading to scale-invariant flow speeds around $0.1<u<1$ m/s and a constant urinary time for animals larger than $3\text{kg}$ (3).

Insects and small mammals typically fall into the $Bo<1$, $We<1$ quadrant, where surface tension dominates. Here, surface tension leads to droplet formation and may cause capillary adhesion to surfaces, posing significant challenges for small organisms to get rid of their excreta. Overcoming these capillary forces requires additional mechanisms, like exploiting surface tension properties (e.g., droplet catapulting in sharpshooter insects, kicking in aphids, maternal licking in mice) or reducing its effect (e.g., hydrophobic coating in gall aphids) (3, 4). The predominant fluid forces are due to surface tension $P\sim \gamma /d$ and viscosity $P\sim ul/d^2$ (internal laminar flow) (4).

Invertebrates like cicadas, bumblebees, and butterflies, characterized by $Bo<1$, $We>1$, demonstrate high-speed inertial jets for excretion, differing significantly from similarly sized mammals’ strategies (e.g., bats, mice). Cicadas, notably the smallest known animals for jet excretion, exhibit higher volume and frequency due to their high-volume xylem-sap diet (7, 10). No organisms have been identified in the $Bo>1$, $We<1$ quadrant, which indicates exclusive reliance on gravitational forces for droplet-based excreta removal. This quadrant implies droplet buildup due to capillary pressure ($P\sim \gamma /d$), with dripping occurring when drops exceed the capillary length scale $l_c$ and capillary adhesion. In a small organism hypothetically using this mechanism, the lack of excreta control could lead to self, conspecific, or habitat fouling. It is important to note that fluid ejection from the jetting quadrants ($We>1$) may transition to this quadrant toward the end of fluid ejection (as driving pressure diminishes), with gravity managing the movement of fluid droplets (e.g., dribbling).

Cicadas, with their enigmatic nature, have long fascinated both artists and scientists, from Homer to Darwin. These insects challenge numerous paradigms in biology: they possess some of the longest developmental periods of up to 17 y, rank among the largest insects with wingspans of up to 8 cm that rival small hummingbirds, and produce sounds as loud as chainsaws (100 dB), making them the loudest insects (8). Our study adds to this list by revealing cicada’s ability to excrete powerful fluidic jets, contrasting the droplet formation observed in other Hemipteran-like sharpshooters. This jetting capability allows efficient processing of their nutritionally sparse xylem-sap diet and places them as the smallest known animals to form high-speed jets in a surface tension-dominated regime ($Bo<1$).

With their high population densities during emergence, the ecosystem impact of their fluid excretion is both substantial and largely unknown, presenting unexplored prospects for biomonitoring and bioinspired engineering. Future research directions involve addressing the challenges in studying cicadas in laboratory conditions. While this study relies on observations and analyses in natural settings, culturing cicadas in labs has proven difficult to date, leaving a gap in our comprehensive understanding of their feeding energetics and fluid expulsion mechanisms particularly during their developmental stages, which are typically subterranean.

The dimensional $\mathit{Bo}$–$\mathit{We}$ framework, covering eight orders of magnitude, provides insights into the dynamics of urination, ranging from dripping to jetting, across various species. It not only emphasizes cicadas as one of the smallest organisms capable of producing high-speed excretory jets but also suggests that in the future, it could open avenues to explore diverse fluid ejection behaviors in other organisms, extending beyond excretion to functions such as hunting, defense, and dispersal. This framework offers a forward-looking perspective to understand fluid excretions across scales, underscoring the remarkable adaptability and efficiency of biological systems.

We thank Allen Sanborn, Tatiana Rischel, Chris Simon, and Jacob Harrison for their help in identifying the species of Peruvian Cicadas. We thank Andrea Clark for conducting the MicroCT scans. We thank Tzi Ming Leong for his contributions to cicada documentation in Singapore. We thank Prateek Sehgal for his help with data collection and analysis and David Hu and Sunghwan Jung and the entire Bhamla Lab for their valuable insights. Funding acknowledgments: NIH MIRA Grant R35GM142588 (M.S.B.); NSF Grant POLS-2310691 (M.S.B.); NSF CAREER IOS-1941933 (M.S.B.); and the OpenPhilanthropy Project (M.S.B.).