Elastohydrodynamics of three-dimensional chemically active filaments

Active deformable filaments exhibit a large range of qualitatively different three-dimensional dynamics, depending on their flexibility, the strength and nature of the active forcing, and the surrounding environment. We investigate the dynamic behaviour of elastic, chemically propelled phoretic filaments, combining two existing models; a local version of slender phoretic theory, which determines the resulting slip flows for chemically propelled filaments with a given shape and chemical patterning, is paired with a computationally efficient method for capturing the elastohydrodynamics of a deformable filament in viscous flow to study the chemoelastohydrodynamics of filaments. As the activity increases, or equivalently the filament stiffness decreases, these filaments undergo buckling instabilities that alter their behaviour from rigid rods. We follow their behaviour well beyond the buckling threshold to find a rich array of dynamics. Through two illustrative examples, we conduct initial-value simulations that show that as the stiffness of the filament is decreased, the dynamic behaviour moves from rigid motion to planar buckling, through an out-of-plane transition, eventually reaching diffusive-like behaviours for very deformable filaments.