We simulate the nonlocal Stokesian hydrodynamics of an elastic filament which is active due to a permanent distribution of stresslets along its contour. A bending instability of an initially straight filament spontaneously breaks flow symmetry and leads to autonomous filament motion which, depending on conformational symmetry can be translational or rotational. At high ratios of activity to elasticity, the linear instability develops into nonlinear fluctuating states with large amplitude deformations. The dynamics of these states can be qualitatively understood as a superposition of translational and rotational motion associated with filament conformational modes of opposite symmetry. Our results can be tested in molecular-motor filament mixtures, synthetic chains of autocatalytic particles or other linearly connected systems where chemical energy is converted to mechanical energy in a fluid environment. , their collective behavior tends to be universal and can be understood by appealing to symmetries and conservation laws [5]. This realization has led to many studies of the collective properties of suspensions of hydrodynamically interacting autonomously motile particles [6].There are ample instances in biology, however, where the conversion of chemical to mechanical energy is not confined to a particle-like element but is, instead, distributed over a line-like element. Such a situation arises, for example, in a microtubule with a row of molecular motors converting energy while walking on it. The mechanical energy thus obtained not only produces motion of the motors but also generates reaction forces on the microtubule, which can deform elastically in response. Hydrodynamic interactions between the motors and between segments of the microtubule must be taken into account since both are surrounded by a fluid. This combination of elasticity, autonomous motility through energy conversion and hydrodynamics is found in biomimetic contexts as well. A recent example is provided by mixtures of motors which crosslink and walk on polymer bundles. A remarkable cilia-like beating phenomenon is observed in these systems [7]. A polymer in which the monomeric units are autocatalytic nanorods provides a nonbiological example of energy conversion on linear elastic elements.Though such elements are yet to be realized in the laboratory, active elements coupled to passive components through covalent bonds have been synthesized [2] and may lead to new kinds of nanomachines [3].Motivated by these biological and biomimetic examples, we study, in this Letter, a semiflexible elastic filament immersed in a viscous fluid with energy converting "active" elements distributed along its length. We present an equation of motion for the filament that incorporates the effects of nonlinear elastic deformation, active processes and nonlocal Stokesian hydrodynamic interactions. We use the lattice Boltzmann (LB) method to numerically solve the active filament equation of motion. Our simulations show that a straight active filament is linearly unsta...

Slender bodies capable of spontaneous motion in the absence of external actuation in an otherwise quiescent fluid are common in biological, physical and technological contexts. The interplay between the spontaneous fluid flow, Brownian motion, and the elasticity of the body presents a challenging fluid-structure interaction problem. Here, we model this problem by approximating the slender body as an elastic filament that can impose non-equilibrium velocities or stresses at the fluid-structure interface. We derive equations of motion for such an active filament by enforcing momentum conservation in the fluid-structure interaction and assuming slow viscous flow in the fluid. The fluid-structure interaction is obtained, to any desired degree of accuracy, through the solution of an integral equation. A simplified form of the equations of motion, that allows for efficient numerical solutions, is obtained by applying the Kirkwood-Riseman superposition approximation to the integral equation. We use this form of the equation of motion to study dynamical steady states in free and hinged minimally active filaments. Our model provides the foundation to study collective phenomena in momentum-conserving, Brownian, active filament suspensions.

Non-equilibrium processes which convert chemical energy into mechanical motion enable the motility of organisms. Bundles of inextensible filaments driven by energy transduction of molecular motors form essential components of micron-scale motility engines like cilia and flagella. The mimicry of cilia-like motion in recent experiments on synthetic active filaments supports the idea that generic physical mechanisms may be sufficient to generate such motion. Here we show, theoretically, that the competition between the destabilising effect of hydrodynamic interactions induced by force-free and torque-free chemomechanically active flows, and the stabilising effect of nonlinear elasticity, provides a generic route to spontaneous oscillations in active filaments. These oscillations, reminiscent of prokaryotic and eukaryotic flagellar motion, are obtained without having to invoke structural complexity or biochemical regulation. This minimality implies that biomimetic oscillations, previously observed only in complex bundles of active filaments, can be replicated in simple chains of generic chemomechanically active beads.

To navigate in complex fluid environments, swimming organisms like fish or bacteria often reorient their bodies antiparallel or against the flow, more commonly known as rheotaxis.