The stationary-state distribution function of confined active Brownian particles (ABPs) is analyzed by computer simulations and analytical calculations. We consider a radial harmonic as well as an anharmonic confinement potential. In the simulations, the ABP is propelled with a prescribed velocity along a body-fixed direction, which is changing in a diffusive manner. For the analytical approach, the Cartesian components of the propulsion velocity are assumed to change independently; active Ornstein-Uhlenbeck particle (AOUP). This results in very different velocity distribution functions. The analytical solution of the Fokker-Planck equation for an AOUP in a harmonic potential is presented and a conditional distribution function is provided for the radial particle distribution at a given magnitude of the propulsion velocity. This conditional probability distribution facilitates the description of the coupling of the spatial coordinate and propulsion, which yields activity-induced accumulation of particles. For the anharmonic potential, a probability distribution function is derived within the unified colored noise approximation. The comparison of the simulation results with theoretical predictions yields good agreement for large rotational diffusion coefficients, e.g. due to tumbling, even for large propulsion velocities (Péclet numbers). However, we find significant deviations already for moderate Péclet number, when the rotational diffusion coefficient is on the order of the thermal one.
SignificanceTurbulent fluid motion is widespread in nature and is observed across diverse length and time scales, ranging from high-Reynolds number hydrodynamics to active fluids, such as bacterial suspensions and cytoskeletal extracts. It is recognized as one of the unsolved challenges in theoretical physics. Here, we explore out-of-equilibrium magnetic colloidal particles at liquid interfaces that exhibit complex collective behavior, resulting in emergence of an active spinner phase. Self-assembled spinners (active spinning without self-propulsion) induce vigorous vortical flows, demonstrating the properties of a 2D hydrodynamic turbulence. Our findings provide insight into the behavior of active spinner liquids and ways to control the collective dynamics and transport in active colloidal materials.
Ensembles of actuated colloids are excellent model systems to explore emergent out-of-equilibrium structures, complex collective dynamics, and design rules for the next generation materials. Here, we demonstrate that ferromagnetic microparticles suspended at an air-water interface and energized by an external rotating magnetic field spontaneously form dynamic ensembles of synchronized spinners in a certain range of the excitation field parameters. Each spinner generates strong hydrodynamic flows, and collective interactions of the multiple spinners promote a formation of dynamic lattices. On the basis of experiments and simulations, we reveal structural transitions from liquid to nearly crystalline states in this novel active spinner material and demonstrate that dynamic spinner lattices are reconfigurable, capable of self-healing behavior and that the transport of embedded inert cargo particles can be remotely tuned by the parameters of the external excitation field. Our findings provide insights into the behavior of active spinner materials with reconfigurable structural order and tunable functionalities.
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