Theoretical modeling of catalytic self-propulsion

Self-propelling particles or microswimmers have opened a new field of investigation with both fundamental and practical perspectives. They represent very convenient model objects for experimental studies of active matter, and have implications in nano-robotics, drug delivery, and more. Here, we summarize recent advances in theoretical description of the self-propulsion of catalytic microswimmers that non-uniformly release ions, including its physical origins and the current switch in focus to non-linear effects, geometric tuning and more. In particular, we show that the ionic self-propulsion always includes both diffusiophoretic and electrophoretic contributions, and that non-linear effects are physical causes of a number of intriguing phenomena, such as the reverse in the direction of the particle motion in response to variations of the salt concentration or self-propulsion of electro-neutral particles. We finally suggest several remaining theoretical challenges in the field.