Statistical distribution of elevation from a planar interface of phoretically active microparticles

In this article, we study the height distribution of phoretically active microparticles exposed to external flow. Sedimented particles hover under light illumination and experience a stronger shear force proportional to the elevation height of the particle. Due to the natural variation in the phoretic activity of individual particles, their hovering heights also vary, resulting in an observed velocity distribution along the flow streamline. Furthermore, the hovering height results from a many-body problem of long-ranged phoretic effects of individual particles. Indeed, the mean velocity and its distribution depend on particle concentration: as the concentration increases, both the mean velocity and the width of the velocity distribution decrease, until a certain concentration is reached beyond which both remain constant. This results from overlapping chemical product gradient of an individual particle with its neighbors, basically decreasing with increasing concentration - and so the phoretic activity and hovering height. Besides, during the hovering we observe a localized dilution having an impact on the light-induced velocity changes of the microparticles.