Flagellar dynamics of chains of active Janus particles fueled by an AC electric field

Abstract

We study the active dynamics of self-propelled asymmetrical colloidal particles (Janus particles) fueled by an AC electric field. Both the speed and direction of the self-propulsion, and the strength of the attractive interaction between particles can be controlled by tuning the frequency of the applied electric field and the ion concentration of the solution. The strong attractive force at high ion concentration gives rise to chain formation of the Janus particles, which can be explained by the quadrupolar charge distribution on the particles. Chain formation is observed irrespective of the direction of the self-propulsion of the particles. When both the position and the orientation of the heads of the chains are fixed, they exhibit beating behavior reminiscent of eukaryotic flagella. The beating frequency of the chains of Janus particles depends on the applied voltage and thus on the selfpropulsive force. The scaling relation between the beating frequency and the self-propulsive force deviates from theoretical predictions made previously on active filaments. However, this discrepancy is resolved by assuming that the attractive interaction between the particles is mediated by the quadrupolar distribution of the induced charges, which gives indirect but convincing evidence on the mechanisms of the Janus particles. This signifies that the dependence between the propulsion mechanism and the interaction mechanism, which had been dismissed previously, can modify the dispersion relations of beating behaviors. In addition, hydrodynamic interaction within the chain, and its effect on propulsion speed, are discussed. These provide new insights into active filaments, such as optimal flagellar design for biological functions.

Instabilities and Spatiotemporal Dynamics of Active Elastic Filaments

“…(clamped head). Together, equation (14) and the boundary conditions form an eigenvalue problem. Non-trivial solutions only exist for specific values of the complex eigenvalue ω.…”

“…We calculate the eigenvalues by discretizing equation (14) and its boundary conditions using a second-order-accurate finite difference method (see ESM §III.A), then track their behavior as a function of the activity parameter β . Note that they do not depend on γ at all.…”

“…To better understand the relationship between the two situations, it is useful to consider the undamped version of our problem, i.e., replace the anisotropic friction force [ξ t t + ξ ⊥ (1 − t t)] · ∂ t r with an inertial term ρ∂ 2 t r where ρ is the mass density per unit length of the filament. Up to some redefinitions of the dimensionless parameters, this is equivalent to changingθ toθ in equation (2) and ω to ω 2 in equation (14) 46 . The free, pinned, and clamped boundary conditions are unchanged.…”

“…Examples include the buckling of cytoskeletal filaments by molecular motors [2][3][4][5][6][7][8][9] , the sliding deformations of microtubule doublets induced by ATPase dynein in eukaryotic cilia [10][11][12] , and the looping of DNA that is crucial to the normal functioning of the cell. In the synthetic realm, filaments made of connected magnetically responsive colloids driven by external fields [13][14][15][16] or of tailored connected Janus particles 14 may also bend or buckle as they move.…”

Directed assembly of active colloidal molecules

“…In a previous work we have shown how chains of non-polar active colloids can spontaneously oscillate and behave as cilia or flagella, but we did not present a method to assemble those structures [19]. Despite the fact that several methods for the design of complex flagella-like structures have been developed, for example clusters of particles with elastic bonds [8,12], or chains sustained by magnetic fields [20], there is no general procedure to create the type of chains that we have previously studied. The aim of this paper is to describe one such method.…”