No many-scallop theorem: Collective locomotion of reciprocal swimmers

Abstract

To achieve propulsion at low Reynolds number, a swimmer must deform in a way that is not invariant under time-reversal symmetry; this result is known as the scallop theorem. We show here that there is no many-scallop theorem. We demonstrate that two active particles undergoing reciprocal deformations can swim collectively; moreover, polar particles also experience effective long-range interactions. These results are derived for a minimal dimers model, and generalized to more complex geometries on the basis of symmetry and scaling arguments. We explain how such cooperative locomotion can be realized experimentally by shaking a collection of soft particles with a homogeneous external field.

References in corpus (6)

• A Simplest Swimmer at Low Reynolds Number: Three Linked Spheres
• Nonequilibrium Fluctuations, Travelling Waves, and Instabilities in Active Membranes
• Analytic results for the three-sphere swimmer at low Reynolds number
• Nonequilibrium steady states in a vibrated-rod monolayer: tetratic, nematic and smectic correlations
• Mechanical Response of a Small Swimmer Driven by Conformational Transitions
• Dumb-bell swimmers

Cited by in corpus (31)

• The hydrodynamics of swimming microorganisms
• Life around the scallop theorem
• Synchronization and Collective Dynamics in a Carpet of Microfluidic Rotors
• Hydrodynamic Collective Effects of Active Protein Machines in Solution and Lipid Bilayers
• Minimal Model for Hydrodynamic Synchronization
• Enhanced diffusion by reciprocal swimming
• Pulling and Pushing a Cargo With a Catalytically Active Carrier
• Swimmer-tracer scattering at low Reynolds number
• Stochastic Low Reynolds Number Swimmers
• Emergent self-propulsion at low Reynolds number
• The long-time dynamics of two hydrodynamically-coupled swimming cells
• Dynamics and interactions of active rotors
• Kinematics of a simple reciprocal model swimmer at intermediate Reynolds numbers
• Noisy swimming at low Reynolds numbers
• Surface microswimmers, harnessing the interface to self-propel
• Magnetically powered metachronal waves induce locomotion in self-assemblies
• CUDA simulations of active dumbbell suspensions
• Coherent Hydrodynamic Coupling for Stochastic Swimmers
• Dynamics of groups of magnetically driven artificial microswimmers
• Defect Loops in Three-Dimensional Active Nematics as Active Multipoles
• A general perturbative approach for bead-based microswimmers reveals rich self-propulsion phenomena
• Passive swimming in low Reynolds number flows
• Polarisation of cells and soft objects driven by mechanical interactions: Consequences for migration and chemotaxis
• Simulations of supercooled water under passive or active stimuli
• Generalized Scallop Theorem for Linear Swimmers
• Effective swimming strategies in low Reynolds number flows
• Shaking-induced motility in suspensions of soft active particles
• Comparison of time reversal symmetric and asymmetric nano-swimmers oriented with an electric field in soft matter
• Low Reynolds number hydrodynamics of asymmetric, oscillating dumbbell pairs
• Simulation of a flat folding nano-swimmer confined in a nanopore
• Pairwise and collective behavior between model swimmers at intermediate Reynolds numbers