Flagellum-driven cargoes: Influence of cargo size and the flagellum-cargo attachment geometry

The beating of cilia and flagella, which relies on an efficient conversion of energy from ATP-hydrolysis into mechanical work, offers a promising way to propel synthetic cargoes. Recent experimental realizations of such micro-swimmers, in which micron-sized beads are propelled by isolated and demembranated flagella from the green algae Chlamydomonas reinhardtii (C. reinhardtii), revealed a variety of propulsion modes, depending in particular on the calcium concentration. Here, we investigate theoretically and numerically the propulsion of a bead as a function of the flagellar waveform and the attachment geometries between the bead and the flagellum. To this end, we take advantage of the low Reynolds number of the fluid flows generated by the micro-swimmer, which allows us to neglect fluid inertia. By describing the flagellar waveform as a superposition of a static component and a propagating wave, and using resistive-force theory, we show that the asymmetric sideways attachment of the flagellum to the bead makes a contribution to the rotational velocity of the micro-swimmer that is comparable to the contribution caused by the static component of the flagellar waveform. Remarkably, our analysis reveals the existence of a counter-intuitive propulsion regime in which an increase in the size of the cargo, and hence its drag, leads to an increase in some components of the velocity of the bead. Finally, we discuss the relevance of the uncovered mechanisms for the fabrication of synthetic, bio-actuated medical micro-robots for targeted drug delivery.