SUMMARY The American cockroach, Periplaneta americana, is reported to follow walls at a rate of up to 25 turns s–1. During high-speed wall following, a cockroach holds its antenna relatively still at the base while the flagellum bends in response to upcoming protrusions. We present a simple mechanosensory model for the task-level dynamics of wall following. In the model a torsional, mass-damper system describes the cockroach's turning dynamics, and a simplified antenna measures distance from the cockroach's centerline to a wall. The model predicts that stabilizing neural feedback requires both proportional feedback (difference between the actual and desired distance to wall) and derivative feedback (velocity of wall convergence) information from the antenna. To test this prediction, we fit a closed-loop proportional-derivative control model to trials in which blinded cockroaches encountered an angled wall (30° or 45°) while running. We used the average state of the cockroach in each of its first four strides after first contacting the angled wall to predict the state in each subsequent stride. Nonlinear statistical regression provided best-fit model parameters. We rejected the hypothesis that proportional feedback alone was sufficient. A derivative (velocity) feedback term in the control model was necessary for stability.

Inertial focusing in microfluidic channels has been extensively studied experimentally and theoretically, which has led to various applications including microfluidic separation and enrichment of cells. Inertial lift forces are strongly dependent on the flow velocity profile and the channel cross-sectional shape. However, the channel cross-sections studied have been limited to circles and rectangles. We studied inertial focusing in non-rectangular cross-section channels to manipulate the flow profile and thus the inertial focusing of microparticles. The location and number of focusing positions are analyzed with varying cross-sectional shapes and Reynolds number. We found that the broken symmetry of non-equilateral triangular channels leads to the shifting of focusing positions with varying Reynolds number. Non-rectangular channels have unique mapping of the focusing positions and the corresponding basins of attraction. By connecting channels with different cross-sectional shapes, we were able to manipulate the accessible focusing positions and achieve focusing of microparticles to a single stream with ∼99% purity.

Direct numerical simulations (DNS) of turbulent boundary layers over isothermally heated walls were performed, and the effect of viscosity stratification on the turbulence statistics and skin friction were investigated. An empirical relation for temperature-dependent viscosity for water was adopted. Based on the free-stream temperature (30°C), two wall temperatures (70°C and 99°C) were selected. In the heated flows, the turbulence energy diminishes in the buffer layer, but increases near the wall. The reduction in turbulence kinetic energy in the buffer layer is accompanied by smaller levels of Reynolds shear stresses and, hence, weaker turbulence production. The enhanced turbulence energy near the wall is attributed to enhanced transfer of energy via additional diffusion-like terms due to the viscosity stratification. Despite the lower fluid viscosity near the wall, dissipation is also increased owing to the augmented near-wall fine-scale motion. Wall heating results in reduction in the skin-friction coefficient by up to 26 %. An evaluation of the different contributions to the skin friction demonstrates that drag reduction is primarily due to the changes in the Reynolds shear stresses across the boundary layer. Quadrant and octant analyses showed that ejections (Q2) and sweeps (Q4) are significantly reduced, a result further supported by an examination of outer vortical structures from linear stochastic estimation of the ejection events and spanwise vortices.

Direct numerical simulation data of turbulent channel flow (Re τ = 930) are used to investigate the statistics of long motions of streamwise velocity fluctuations (u), and the interaction of these structures with the near-wall disturbances, which is facilitated by their associated large-scale circulations. In the log layer, the negative-u structures are organized into longer streamwise extent (>3δ) in comparison to the positive-u counterparts. Near the wall, the footprint of negative-u structures is relatively narrow in comparison to the footprint of positive-u structures. This difference is due to the opposite spanwise motions in the vicinity of the footprints, which are either congregative or dispersive depending on the circulation of the outer roll cells. Conditional sampling of the footprints shows that the spanwise velocity fluctuations (w) are significantly enhanced by the dispersive motions of high-speed structures. On the other hand, the near-wall congregative motions of negative-u structures generate relatively weak w but intense negative-u regions due, in part, to the spanwise collective migration of near-wall streaks. The concentrated near-wall regions of negative-u upwell during the merging of the outer long scales -an effect that is demonstrated using statistical analysis of the merging process. This leads to a reduction of the convection speed of downstream negative-u structures and thus promotes the merging with upstream ones. These top-down and bottom-up interactions enhance the spatial coherence of long negative-u structures in the log region.