# Harnessing elasticity to generate self-oscillation via an electrohydrodynamic instability

## TL;DR

This paper demonstrates how elastic structures in dielectric fluids can induce self-oscillations through electrohydrodynamic instabilities, offering new insights for designing adaptive soft machines.

## Contribution

It introduces a novel elasto-electro-hydrodynamic model showing how elasticity transforms bifurcations into self-oscillations, supported by numerical and theoretical analysis.

## Key findings

- Elastic structures can induce self-oscillations via EEH instability.
- The model predicts critical conditions matching numerical results.
- Elasticity transforms pitchfork bifurcation into Hopf bifurcation.

## Abstract

Under a steady DC electric field of sufficient strength, a weakly conducting dielectric sphere in a dielectric solvent with higher conductivity can undergo spontaneous spinning (Quincke rotation) through a pitchfork bifurcation. We design an object composed of a dielectric sphere and an elastic filament. By solving an elasto-electro-hydrodynamic (EEH) problem numerically, we uncover an EEH instability exhibiting diverse dynamic responses. Varying the bending stiffness of the filament, the composite object displays three behaviours: a stationary state, undulatory swimming and steady spinning, where the swimming results from a self-oscillatory instability through a Hopf bifurcation. By conducting a linear stability analysis incorporating an elastohydrodynamic model, we theoretically predict the growth rates and critical conditions, which agree well with the numerical counterparts. We also propose a reduced model system consisting of a minimal elastic structure which reproduces the EEH instability. The elasto-viscous response of the composite structure is able to transform the pitchfork bifurcation into a Hopf bifurcation, leading to self-oscillation. Our results imply a new way of harnessing elastic media to engineer self-oscillations, and more generally, to manipulate and diversify the bifurcations and the corresponding instabilities. These ideas will be useful in designing soft, environmentally adaptive machines.