Effects of hydrodynamic slip and taenidial structure in insect tracheal flows*

Through evolutionary refinement, insects have developed respiratory systems that have been efficiently handling air inside complex microscale tracheal networks for over 480 million years. They do this exceptionally well, as evidenced by the fact that their metabolic range is the highest in the animal kingdom, about 5 times higher than humans’. This exceptional range has been attributed to their unique respiratory systems, which carry oxygen directly to the cells without using blood as an intermediate carrier. One of the unusual features of insect respiration from a fluid dynamics perspective is that insect tracheal flows are often low-Reynolds-number (~0.1), but high-Knudsen-number (0.0001-1). In this work, we investigate the effects of hydrodynamic slip and fine-scale internal tracheal morphology in intratracheal flows in insects. We hypothesize that the helical taenidial structures found on the inner wall of the tracheal tubes determine the structure of the flow field near the wall and play a vital role in transport. We have closely reproduced the internal morphology of the tracheal tubes of the American cockroach, Periplaneta americana, in our computational geometry. To investigate this hypothesis, we designed a series of simulations using the Lattice Boltzmann method (LBM) at a Reynolds number of 0.1. For simplicity of computational analysis, we use a square microchannel and only add taenidial structure to the bottom wall. In the first set of simulations, we removed the taenidial structures and simulated the flow through the microchannel for both no-slip and slip boundary conditions. In the second set of simulations, we introduce the taenidial structures on the bottom wall and compare the simulation results to those without the taenidia. We find that the taenidia significantly affect the flow structure and characterize their contribution.