The underwater traps of the carnivorous plants of the Utricularia species
catch their preys through the repetition of an "active slow deflation / 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 in 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.Comment: Accepted for publication in Physical Review
