Numerical simulation of artificial microswimmers driven by Marangoni flow

- A level-set method for artificial microswimmers is proposed.
- It addresses active droplets moving by Marangoni flow (e.g. BZ reactions droplets).
- The fluid flow, diffusion, interacting chemical species (surfactants) are included.
- The typical squirmer behavior (pusher/puller/neutral) was reproduced.
- The inception of self-substained motion was retrieved as well as chemotaxis.

In the present paper the behavior of a single artificial microswimmer is addressed, namely an active droplet moving by Marangoni flow. We provide a numerical treatment for the main factors playing a role in real systems, such as advection, diffusion and the presence of chemical species with different behaviors. The flow field inside and outside the droplet is modeled to account for the two-way coupling between the surrounding fluid and the motion of the swimmer. Mass diffusion is also taken into account. In particular, we consider two concentration fields: the surfactant concentration in the bulk, i.e. in the liquid surrounding the droplet, and the surfactant concentration on the surface. The latter is related to the local surface tension, through an equation of state (Langmuir equation). We examine different interaction mechanisms between the bulk and the surface concentration fields, namely the case of insoluble surfactants attached to the surface (no exchange between the bulk and the surface) and soluble surfactants with adsorption/desorption at the surface. We also consider the case where the bulk concentration field is in equilibrium with the content of the droplet. The numerical results are validated through comparison with analytical calculations. We show that our model can reproduce the typical pusher/puller behavior presented by squirmers. It is also able to capture the self-propulsion mechanism of droplets driven by Belousov-Zhabotinsky (BZ) reactions, as well as a typical chemotactic behavior.