Thermoresponsive self-oscillating hydrogel: spatially lumped model, relaxation dynamics and mechanical output
Abstract
Thermoresponsive gels with a lower critical solution temperature (LCST) can undergo self-oscillation driven by a thermal flux through repeated cycles of positive feedback, driven by heating-induced collapse, and negative feedback, characterized by deformation recovery due to collapse-induced suppression of heating and heat dissipation to the environment. In order to explore the detailed bifurcation structure of a thermosensitive self-oscillating gel and understand its mechanical output of peristaltic motion and net displacement, we develop a minimal spatially lumped two-variable phenomenological model whose equilibrium parameters are constrained by poly(N-isopropylacrylamide) (PNIPAAm) swelling data. A supercritical Hopf bifurcation creates stable small-amplitude oscillations near a fold of the swollen manifold, and canard-mediated growth transforms this branch into relaxation oscillations. Singular analysis relates the amplitude to fast jumps and the period to drift along slow manifolds, while continuation separates the Hopf boundary from the maximal-canard locus. For the representative maximum-power relaxation cycle considered here, the loaded model predicts greater work than a harmonic volume trajectory with the same stroke, period, and viscous load, with output concentrated in the fast collapse and re-swelling transitions. The net displacement during peristaltic locomotion of the thermoresponsive self-oscillating gel results from the work difference between collapse and re-swelling. These results provide a theoretical basis for designing autonomous thermoresponsive self-oscillating gel actuators whose oscillatory waveform and power output can be controlled through thermal feedback and mechanical loading.
Related
- Spatially developing drag reduction across a finite oscillating wall
- Spin-Hall devices: spin relaxation spatially separates current injection from Joule dissipation
- Inertial effects on the mechanical efficiency of a semi-passive oscillating hydrofoil energy harvester
- Mechanical response of a simple DNA nanostar hydrogel: symptoms of disorder and glassy emergence of solidity
- Variational formulation of the constitutive relaxation at finite rate of the mechanical state in multiphase flows with the diffuse-interface method
BibTeX
@misc{wang2026thermoresponsive,
title = {{Thermoresponsive self-oscillating hydrogel: spatially lumped model, relaxation dynamics and mechanical output}},
author = {Yunjie Wang and Ling Yuan and Yang Li and Lin Ren and Yuhan Wang and Xiaol Lv and Irving R Epstein and Qingyu Gao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.21225},
eprint = {2606.21225},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.21225},
}
RIS
TY - UNPB
TI - Thermoresponsive self-oscillating hydrogel: spatially lumped model, relaxation dynamics and mechanical output
AU - Yunjie Wang
AU - Ling Yuan
AU - Yang Li
AU - Lin Ren
AU - Yuhan Wang
AU - Xiaol Lv
AU - Irving R Epstein
AU - Qingyu Gao
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2606.21225
UR - https://arxiv.org/abs/2606.21225
AB - Thermoresponsive gels with a lower critical solution temperature (LCST) can undergo self-oscillation driven by a thermal flux through repeated cycles of positive feedback, driven by heating-induced collapse, and negative feedback, characterized by deformation recovery due to collapse-induced suppression of heating and heat dissipation to the environment. In order to explore the detailed bifurcation structure of a thermosensitive self-oscillating gel and understand its mechanical output of peristaltic motion and net displacement, we develop a minimal spatially lumped two-variable phenomenological model whose equilibrium parameters are constrained by poly(N-isopropylacrylamide) (PNIPAAm) swelling data. A supercritical Hopf bifurcation creates stable small-amplitude oscillations near a fold of the swollen manifold, and canard-mediated growth transforms this branch into relaxation oscillations. Singular analysis relates the amplitude to fast jumps and the period to drift along slow manifolds, while continuation separates the Hopf boundary from the maximal-canard locus. For the representative maximum-power relaxation cycle considered here, the loaded model predicts greater work than a harmonic volume trajectory with the same stroke, period, and viscous load, with output concentrated in the fast collapse and re-swelling transitions. The net displacement during peristaltic locomotion of the thermoresponsive self-oscillating gel results from the work difference between collapse and re-swelling. These results provide a theoretical basis for designing autonomous thermoresponsive self-oscillating gel actuators whose oscillatory waveform and power output can be controlled through thermal feedback and mechanical loading.
ER -