  Photoresponsive surfactants provide a unique microfluidic driving mechanism.
Since their molecular shapes change under illumination and thereby affect
surface tension of fluid interfaces, Marangoni flow along the interface occurs.
To describe the dynamics of the surfactant mixture at a planar interface, we
formulate diffusion-advection-reaction equations for both surfactant densities.
They also include adsorption from and desorption into the neighboring fluids
and photoisomerization by light. We then study how the interface responds when
illuminated by spots of light. Switching on a single light spot, the density of
the switched surfactant spreads in time and assumes an exponentially decaying
profile in steady state. Simultaneously, the induced radial Marangoni flow
reverses its flow direction from inward to outward. We use this feature to set
up specific feedback rules, which couple the advection velocities sensed at the
light spots to their intensities. As a result two neighboring spots switch on
and off alternately. Extending the feedback rule to light spots arranged on the
vertices of regular polygons, we observe periodic switching patterns for
even-sided polygons, where two sets of next-nearest neighbors alternate with
each other. A triangle and pentagon also show regular oscillations, while
heptagon and nonagon exhibit irregular oscillations due to frustration. While
our findings are specific to the chosen set of parameters, they show how
complex patterns at photoresponsive fluid interfaces emerge from simple
feedback coupling.
