The fern cavitation catapult: mechanism and design principles

Abstract

Leptosporangiate ferns have evolved an ingenious cavitation catapult to disperse their spores. The mechanism relies almost entirely on the annulus, a row of 12 -25 cells, which successively: (i) stores energy by evaporation of the cells' content, (ii) triggers the catapult by internal cavitation, and (iii) controls the time scales of energy release to ensure efficient spore ejection. The confluence of these three biomechanical functions within the confines of a single structure suggests a level of sophistication that goes beyond most man-made devices where specific structures or parts rarely serve more than one function. Here, we study in detail the three phases of spore ejection in the sporangia of the fern Polypodium aureum. For each of these phases, we have written the governing equations and measured the key parameters. For the opening of the sporangium, we show that the structural design of the annulus is particularly well suited to inducing bending deformations in response to osmotic volume changes. Moreover, the measured parameters for the osmoelastic design lead to a near-optimal speed of spore ejection (approx. 10 m s -1 ). Our analysis of the trigger mechanism by cavitation points to a critical cavitation pressure of approximately 2100 + 14 bar, a value that matches the most negative pressures recorded in the xylem of plants. Finally, using high-speed imaging, we elucidated the physics leading to the sharp separation of time scales (30 versus 5000 ms) in the closing dynamics. Our results highlight the importance of the precise tuning of the parameters without which the function of the leptosporangium as a catapult would be severely compromised.

Creasing in evaporation-driven cavity collapse

“…13 In the plant kingdom, structures in organ-based plants couple water flux to geometric changes in order to achieve motion without muscle. 14,15 The latter coupling is found in hygromorphs; 16,17 surface tension propulsion; 18 and drying-associated, hydrostatic-pressuredriven energy storage that precedes failure 19 or cavitation 15,20 events. As a result of the large deformations in these soft systems, creases are observed at the inner liquid-solid interface.…”

How water flow, geometry, and material properties drive plant movements

“…Plant movements can be grouped into swelling/shrinking (hydraulic), snap buckling and explosive fracture (elastic instabilities) (Skotheim and Mahadevan, 2005). Another way of thinking of this is whether or not energy storage is required, as has been elegantly described in Llorens et al (Llorens et al, 2016). The energy required to move a part of the plant is equal to the work done by this movement: work = force x distance.…”

“…12 analyse under which conditions which strategy is best suited. For the fern cavitation catapult described in Llorens et al (Llorens et al, 2016), the motor is driven by evaporation which stores elastic energy in the annular cells leading to 'water tension'. This extraordinary metastable state of negative absolute water pressure (Herbert et al, 2006;Menzl et al, 2016), which is key for water transport through the xylem, is prone to cavitation which provides a latch mechanism (Llorens et al, 2016).…”

Curvature-based, time delayed feedback as a means for self-propelled swimming

“…The reduction of the swimmer beam equation to this low dimensional ODE might be justified by investigating the dynamics of an oscillating mode of the system, in the spirit of [52]. The stability regions of equation (8) may be readily determined using standard techniques [53,54].…”