A three-dimensional morphoelastic model for self-oscillations in polyelectrolyte hydrogel filaments

TL;DR

This paper develops a 3D morphoelastic model for polyelectrolyte hydrogel filaments in fluid environments under electric fields, revealing complex oscillatory behaviors and instabilities relevant for biomimetic applications.

Contribution

It introduces a novel 3D morphoelastic framework capturing electric-field-induced curvatures and hydrodynamics, advancing the modeling of hydrogel filament dynamics.

Findings

Filament exhibits flutter instability beyond a critical electric field strength.

Instability leads to either planar or complex 3D oscillations depending on parameters.

Numerical simulations show secondary bifurcations to large amplitude motions.

Abstract

We introduce a three-dimensional model for polyelectrolyte hydrogel filaments operating in a fluid environment under an electric field. The formulation builds on a morphoelastic framework for inextensible and unshearable rods, such that the filament's activity is encoded in electric-field-induced spontaneous curvatures, while hydrodynamic interactions are captured via a local approximation of Stokes flows. We employ this framework to investigate the prototypical case of a filament with elliptic cross-section clamped at its base. Under a constant and uniform electric field aligned with its axis, the filament undergoes flutter instability beyond a critical field strength, as revealed by a linear stability analysis. Depending on the model parameters, the instability is characterized by either two- or three-dimensional self-sustained oscillations. We further examine this behaviour through numerical simulations in the post-critical regime, showing that flutter may develop into large amplitude planar oscillations or more complex three-dimensional motions, through a secondary bifurcation. Although the study represents a first step towards extending state-of-the-art models for polyelectrolyte hydrogel filaments to three dimensions, the richness of the resulting dynamics achievable under time-independent forcing underscores the potential of the proposed actuation mechanism for the design of biomimetic cilia and soft robotic systems.