Individual and Collective Surfing of Chemically Active Particles

Courant Institute of Mathematical Sciences and Princeton University

We study theoretically the motion of particles located at a liquid-gas interface. These particles release a chemical species that locally changes the surface tension. The consequent gradients in surface tension and the associated Marangoni flow then move the particles along the interface. We call this surfing. First, we consider the surfing of a single spheroidal particle at a semi-infinite interface and derive closed-form expressions for the self-induced surfing speed. Our derivations are based on the Lorentz reciprocal theorem which eliminates the need for developing the detailed flow field. Next, we probe the collective surfing of particles located at the interface of a finite-depth liquid layer. We calculate the linear stability condition of this system and examine the consequences of instability on the flow in the bulk. We also show that for sufficiently deep and shallow fluid layers this system yields the two-dimensional Keller-Segel model for the collective chemotaxis of slime mold colonies.