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In the present paper the behavior of a single artificial microswimmer isaddressed, namely an active droplet moving by Marangoni flow. The non-uniformsurface tension distribution underlying the propulsion mechanism of thedroplet, is generated by a non-uniform distribution of surfactant on itssurface. We provide a numerical treatment for the main factors playing a rolein real systems, such as advection, diffusion and the presence of chemicalspecies with different behaviors. The flow field inside and outside the dropletis derived, thus accounting for the two-way coupling between the surroundingfluid and the motion of the swimmer. Mass diffusion is also taken into account.In particular, we consider two concentration fields: the surfactantconcentration in the bulk, i.e. in the liquid surrounding the droplet, and thesurfactant concentration on the surface. The latter is related to the localsurface tension, through an equation of state (Langmuir equation). We examinedifferent interaction mechanisms between the bulk and the surface concentrationfields, namely the case of insoluble surfactants attached to the surface (noexchange between the bulk and the surface) and soluble surfactants withadsorption/desorption at the surface. We also consider the case where the bulkconcentration field is in equilibrium with the content of the droplet. Thenumerical results are validated through comparison with analyticalcalculations. We show that our model can reproduce the typical pusher/pullerbehavior presented by squirmers. It is also able to capture the self-propulsionmechanism of droplets driven by Belousov-Zhabotinsky (BZ) reactions, as well asa typical chemotactic behavior.

Numerical simulation of artificial microswimmers driven by Marangoni flow