Mechanical model of the ultrafast underwater trap ofUtricularia

Abstract

The underwater traps of the carnivorous plants of the Utricularia species catch their prey through the repetition of an "active slow deflation followed by passive fast suction" sequence. In this paper, we propose a mechanical model that describes both phases and strongly supports the hypothesis that the trap door acts as a flexible valve that buckles under the combined effects of pressure forces and the mechanical stimulation of trigger hairs, and not as a panel articulated on hinges. This model combines two different approaches, namely (i) the description of thin membranes as triangle meshes with strain and curvature energy, and (ii) the molecular dynamics approach, which consists of computing the time evolution of the position of each vertex of the mesh according to Langevin equations. The only free parameter in the expression of the elastic energy is the Young's modulus E of the membranes. The values for this parameter are unequivocally obtained by requiring that the trap model fires, like real traps, when the pressure difference between the outside and the inside of the trap reaches about 15 kPa. Among other results, our simulations show that, for a pressure difference slightly larger than the critical one, the door buckles, slides on the threshold, and finally swings wide open, in excellent agreement with the sequence observed in high-speed videos.

A dynamical model for the Utricularia trap

“…As the trap is fully deflated, e ¼ 0.4 mm, and the minimal volume is V min ¼ 0.67 mm 3 [4]. The area of the membrane of the trap S m is approximately given by…”

“…Experiments show that V decays exponentially to a final volume V 0 [4]. The fluid flux has three contributions.…”

“…The trap, which is a biconcave disc, as pictured in figures 1 and 2, can be approximated as a deformable cylinder [4] of diameter L % 1.5 mm and variable height e. The volume is approximated by…”

“…For now, we simply write the balance of fluxes related to the membrane: [7,8]. The membrane elasticity connects the volume loss to the pressure load: the pressure difference DP varies almost linearly with V in experiments and in simulations [4]: . As a consequence, we conclude from (2.3) and (2.4): will be refined as we develop the model of the door displacement ( §2.3).…”

“…Indeed, previous studies focus only on the mechanics of the trap body [3], or on the door [4] but no model was proposed to link those two aspects. Here, we introduce the hydrodynamics in order to couple these two elastic parts.…”