A general perturbative approach for bead-based microswimmers reveals rich self-propulsion phenomena

Studies of model microswimmers have significantly contributed to the understanding of the principles of self-propulsion we have today. However, only a small number of microswimmer types have been amenable to analytic modeling, and further development of such approaches is necessary to identify the key features of these active systems. Here we present a general perturbative calculation scheme for swimmers composed of beads interacting by harmonic potentials and via hydrodynamics, driven by an arbitrary force protocol. The approach can be used with mobility matrices of arbitrary accuracy, and we illustrate it with the Oseen and Rotne?Prager approximations. We validate our approach by using 3 bead assemblies and comparing the results with the numerically obtained full-solutions of the governing equations of motion, as well as with existing analytic models for the linear and the triangular swimmer geometry. While recovering the relation between the force and swimming velocity, our detailed analysis and the controlled level of approximation allow us to find qualitative differences already in the far field flow of the devices. Consequently, we are able to identify a behavior of the swimmer that is richer than predicted in previous models. Given its generality, the framework can be applied to any swimmer geometry, driving protocol and bead interactions, as well as in problems involving many swimmers.