Phototactic three-dimensional motion of active Janus particles

We study the dynamics of active Janus particles that self-propel in solution by light-activated catalytic decomposition of chemical "fuel." In experiments, the particles, illuminated from below, swim upward against gravity. Using holographic microscopy, we track the three-dimensional positions of particles at different incident light intensities. A statistical analysis reveals a nonlinear dependence of the mean vertical velocity on intensity. Theoretically, we develop a model of a photo-active self-phoretic particle that accounts for "self-shadowing" of the light by the opaque catalytic face of the particle. We find that self-shadowing can drive "phototaxis" (rotation of the catalytic cap towards the light source) or "anti-phototaxis," depending on the properties of the particle. Incorporating the effect of thermal noise, we show that the distribution of particle orientations is captured by a Boltzmann distribution with a nonequilibrium effective potential. Furthermore, the mean vertical velocity of phototactic (anti-phototactic) particles exhibits a superlinear (sublinear) dependence on intensity. Overall, our findings show that photo-active particles exhibit a rich "tactic" response to light, which could be harnessed to program complex three-dimensional trajectories.