Active colloidal chains with cilia- and flagella-like motion

Abstract

It has been shown that self-assembled chains of active colloidal particles can present sustained oscillations. These oscillations are possible because the effective diffusiophoretic forces that mediate the interactions of colloids do not respect the action-reaction principle and hence, a Hopfbifurcation is possible even for overdamped dynamics. Anchoring the particles in one extreme breaks the headtail symmetry and the oscillation is transformed into a traveling wave pattern, and thus the chain behaves like a beating cilium. The net force on the anchor, estimated using the resistive force theory, vanishes before the bifurcation and thereafter grows linearly with the bifurcation parameter. If the mobilities of the particles on one extreme are reduced to mimic an elongated cargo, the traveling wave generates a net velocity on the chain that now behaves like a moving flagellum. The average velocity again grows linearly with the bifurcation parameter. Our results demonstrate that simplified systems, consisting only of a few particles with non-reciprocal interaction and head-tail asymmetry, show beating motion and self-propulsion. Both properties are present in many non-equilibrium models thus making our results a general feature of active matter.

Directed assembly of active colloidal molecules

“…For the construction of the cilia-and flagella-like structures described in [19], we considered a simple model of active particles, which do not self-propel on their own, but rather activity emerges as a result of interactions [27]. In presence of concentration inhomogeneities, colloids experience a phoretic drift which is well described by a velocity proportional to the concentration gradient of a relevant solute, multiplied by a mobility coefficient μ, m = -  V c [28].…”

“…The velocity of each colloid, which results from the mutual interaction and with the external field is , with r eq the equilibrium distance of the two colloids (of order 1). We assume as in [19,27] that the radial distance is a hard degree of freedom, which does does not vary even in presence of an external field. Imposing that the relative velocity r = -…”

“…Having demonstrated that we can produce trimers and dimers with a high yield, in a very localized way, for a wide range of parameters, and that these small colloidal molecules can be guided with walls and external potentials without destroying them, we will study a reaction path that produces the colloidal chains with dynamic function we have previously studied [19].…”

“…All the colloidal chains we reported in [19] consist of an integer number of trimers. Thus, each of these structures could be formed by the collision of trimers directed to a reaction zone by the means described in the previous sections.…”

“…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.…”