Shaping the gradients driving phoretic micro-swimmers: influence of swimming speed, budget of carbonic acid and environment

Abstract

Abstract pH gradient-driven modular micro-swimmers are investigated as a model for a large variety of quasi-two-dimensional chemi-phoretic self-propelled entities. Using three-channel micro-photometry, we obtain a precise large field mapping of pH at a spatial resolution of a few microns and a pH resolution of $$\sim 0.02~\hbox {pH}$$ ∼ 0.02 pH units for swimmers of different velocities propelling on two differently charged substrates. We model our results in terms of solutions of the three-dimensional advection–diffusion equation for a 1:1 electrolyte, i.e. carbonic acid, which is produced by ion exchange and consumed by equilibration with dissolved $$\hbox {CO}_{2}$$ CO 2 . We demonstrate the dependence of gradient shape and steepness on swimmer speed, diffusivity of chemicals, as well as the fuel budget. Moreover, we experimentally observe a subtle, but significant feedback of the swimmer’s immediate environment in terms of a substrate charge-mediated solvent convection. We discuss our findings in view of different recent results from other micro-fluidic or active matter investigations. We anticipate that they are relevant for quantitative modelling and targeted applications of diffusio-phoretic flows in general and artificial micro-swimmers in particular. Graphic Abstract