A model for predicting the current, concentration, and potential distributions in a thin-gap channel flow is presented. The model does not invoke the thin diffusion layer assumption or the assumption of straight current lines, and it allows for multiple reactions. The model, however, does not include the effect of migration; thus, it is only valid for systems with excess supporting electrolyte. This model can be used for the design and scale-up of channel flow electrochemical reactors. Results are presented for a single reaction to show the effects of interacting diffusion boundary layers and of the axial component of current.

Swarms of coupled mobile agents subject to inter-agent wireless communication delays are known to exhibit multiple dynamic patterns in space that depend on the strength of the interactions and the magnitude of the communication delays. We experimentally demonstrate communication delay-induced bifurcations in the spatiotemporal patterns of robot swarms using two distinct hardware platforms in a mixed reality framework. Additionally, we make steps toward experimentally validating theoretically predicted parameter regions where transitions between swarm patterns occur. We show that multiple rotation patterns persist even when collision avoidance strategies are incorporated, and we show the existence of multi-stable, co-existing rotational patterns not predicted by usual mean field dynamics. Our experiments are the first significant steps toward validating existing theory and the existence and robustness of the delay-induced patterns in real robotic swarms.

A convenient representation of the solution to the asymmetric Graetz problem in channel flow is presented. The asymmetric Graetz problem in channel flow is similar to the classical Graetz problem of heat or mass transfer to a fluid flowing in a round duct. In the classical problem, the tube wall undergoes a step change in. concentration at a given axial position. In the asymmetric Graetz problem, the duct is flat, and the concentration step occurs at only one channel wall. It is shown how this solution to the asymmetric Graetz problem may be used in a superposition integral to determine the wall flux in problems where the arbitrary channel wall concentrations differ on the two walls .