Efficiency of Surface-Driven Motion: Nanoswimmers Beat Microswimmers

Abstract

Surface interactions provide a class of mechanisms which can be employed for propulsion of microand nanometer sized particles. We investigate the related efficiency of externally and self-propelled swimmers. A general scaling relation is derived showing that only swimmers whose size is comparable to, or smaller than, the interaction range can have appreciable efficiency. An upper bound for efficiency at maximum power is 1/2. Numerical calculations for the case of diffusiophoresis are found to be in good agreement with analytical expressions for the efficiency.

Dynamics and efficiency of a self-propelled, diffusiophoretic swimmer

“…Eqns. (34,35) with fixed concentrations far away of the swimmer are employed for numerical solution of Eqns. (20)(21)(22)(23)(24).…”

“…The discrepancy emphasizes the importance of the hydrodynamic dissipation for the efficiency. This point found particular emphasize in our previous theoretical work were we have examined the hydrodynamic efficiency for generic surface driven swimmers 35 . The hydrodynamic efficiency provides an upper bound on the overall efficiency while it does not include dissipative effects related to building up the chemical gradient driving the swimmer.…”

“…The boundary conditions at the surface of the swimmer, Eqns. (34,35), couple different coefficients of the expansion Eq. (41) and one has…”

The efficiency of self-phoretic propulsion mechanisms with surface reaction heterogeneity

“…The efficiency of the current artificial self-propulsion mechanisms is widely considered to be low for micron-size particles [34][35][36][37]. Understanding where the conversion bottleneck lies and how biological swimmers manage to be more efficient is instrumental in achieving real world applications.…”

“…[34]. The concept of the efficiency of swimming has since been investigated by Sabass and Seifert, who showed that nanoparticles are far more efficient at self-propulsion than micron sized colloids [35] and examined this quantity the context of self-electrophoresis [36]. More recently, Wang et al [37] performed an analysis of the efficiency of various types of swimmers.…”