Periodic Orbits of Active Particles induced by Hydrodynamic Monopoles

Abstract

Terrestrial experiments on active particles, such as Volvox, involve gravitational forces, torques and accompanying monopolar fluid flows. Taking these into account, we analyse the dynamics of a pair of self-propelling, self-spinning active particles between widely separated parallel planes. Neglecting flow reflected by the planes, the dynamics of orientation and horizontal separation is symplectic, with a Hamiltonian exactly determining limit cycle oscillations. Near the bottom plane, gravitational torque damps and reflected flow excites this oscillator, sustaining a second limit cycle that can be perturbatively related to the first. Our work provides a theory for dancing Volvox and highlights the importance of monopolar flow in active matter.

arXiv comment6 figures, 2 tables, 5 pages main + 6 S.I

References in corpus (17)

• The hydrodynamics of swimming microorganisms
• Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles
• How far from equilibrium is active matter?
• Sedimentation of active colloidal suspensions
• Direct measurement of the flow field around swimming microorganisms
• Dancing Volvox: Hydrodynamic Bound States of Swimming Algae
• Active matter
• Green Algae as Model Organisms for Biological Fluid Dynamics
• Like-charge attraction through hydrodynamic interaction
• Run-and-tumble particles with hydrodynamics: sedimentation, trapping and upstream swimming
• Flow-induced phase separation of active particles is controlled by boundary conditions
• Squirmers with swirl -- a model for $Volvox$ swimming
• Irreducible Representations Of Oscillatory And Swirling Flows In Active Soft Matter
• Universal hydrodynamic mechanisms for crystallization in active colloidal suspensions
• Effective pseudo-potentials of hydrodynamic origin
• Many-body microhydrodynamics of colloidal particles with active boundary layers
• Generalized Stokes laws for active colloids and their applications

Cited by in corpus (6)

• Stability of dancing Volvox
• Controlled Optofluidic Crystallization of Colloids Tethered at Interfaces
• Waves, Algebraic Growth and Clumping in Sedimenting Disk Arrays
• PyStokes: phoresis and Stokesian hydrodynamics in Python
• Fluctuating hydrodynamics of an autophoretic particle near a permeable interface
• Active Caustics