Efficiency limits of the three-sphere swimmer

Abstract

We consider a swimmer consisting of a collinear assembly of three spheres connected by two slender rods. This swimmer can propel itself forward by varying the lengths of the rods in a way that is not invariant under time reversal. Although any non-reciprocal strokes of the arms can lead to a net displacement, the energetic efficiency of the swimmer is strongly dependent on the details and sequences of these strokes, and also the sizes of the spheres. We define the efficiency of the swimmer using Lighthill's criterion, i.e., the power that is needed to pull the swimmer by an external force at a certain speed, divided by the power needed for active swimming with the same average speed. Here, we determine numerically the optimal stroke sequences and the optimal size ratio of the spheres, while limiting the maximum extension of the rods. Our calculation takes into account both far-field and near-field hydrodynamic interactions. We show that, surprisingly, the three-sphere swimmer with unequal spheres can be more efficient than the equally-sized case. We also show that the variations of efficiency with size ratio is not monotonic and there exists a specific size ratio at which the swimmer has the highest efficiency. We find that the swimming efficiency initially rises by increasing the maximum allowable extension of the rods, and then converges to a maximum value. We calculate this upper limit analytically and report the highest value of efficiency that the three-sphere swimmer can reach.

arXiv comment7 pages, 3 figures

References in corpus (26)

• The hydrodynamics of swimming microorganisms
• Physics of Microswimmers - Single Particle Motion and Collective Behavior
• A Simplest Swimmer at Low Reynolds Number: Three Linked Spheres
• Life around the scallop theorem
• Finding the ciliary beating pattern with optimal efficiency
• Analytic results for the three-sphere swimmer at low Reynolds number
• Pushmepullyou: An efficient micro-swimmer
• A basic swimmer at low Reynolds number
• Optimal Swimming at low Reynolds numbers
• Universal bound on the efficiency of molecular motors
• Enhanced Diffusion of Enzymes that Catalyze Exothermic Reactions
• Dynamics and efficiency of a self-propelled, diffusiophoretic swimmer
• Kinematics of the most efficient cilium
• The optimal elastic flagellum
• Mechanical Response of a Small Swimmer Driven by Conformational Transitions
• Optimal feeding is optimal swimming for all Péclet numbers
• Realization of the Najafi-Golestanian microswimmer
• Synthetic Mechanochemical Molecular Swimmer
• Efficiency of surface-driven motion: nano-swimmers beat micro-swimmers
• Propulsion of a two-sphere swimmer
• Swimming trajectories of a three-sphere microswimmer near a wall
• Stochastic Low Reynolds Number Swimmers
• Three-Sphere Low Reynolds Number Swimmer with a Cargo Container
• Transition in swimming direction in a model self-propelled inertial swimmer
• Higher-order force moments of active particles
• Effect of fluid inertia on the motion of a collinear swimmer

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