Colloquium: spontaneous symmetry breaking of active particles in viscous environments
File(s)
Accepted version
Author(s)
Schnitzer, Ory
Yariv, Ehud
Type
Journal Article
Abstract
Active particles typically exploit built-in asymmetries to convert available energy into directed motion. A distinct paradigm emerges when directed motion arises instead from spontaneous symmetry breaking (SSB), enabled by nonlinearity and triggered by instability. This Colloquium examines the onset of SSB in continuum models of isotropic active particles in viscous fluids, motivated by recent experiments and theoretical advances across diverse systems. We focus on the zero-Reynolds-number regime, where the linearity and instantaneity of Stokes flows demand that SSB involves coupling of the hydrodynamics to auxiliary physics, such as solute transport and kinetics, electromagnetism or elasticity. We begin by reviewing the motion of passive particles and conventional swimmers in Stokes flow. This is followed by a phenomenological description of a symmetry-breaking active particle, where the near-onset dynamics is captured by a canonical amplitude equation corresponding to the normal form of a degenerate pitchfork bifurcation. Subsequently, we analyze SSB onset from first principles in two setups: (i) the Quincke effect, where an isotropic particle rotates in the plane perpendicular to a sufficiently strong external electric field, and (ii) several fundamental models of chemically active isotropic colloids that self-propel when diffusion is sufficiently weak. In all these systems, instability stems from the same positive-feedback loop - polarization drives flow, flow amplifies polarization via advection. We demonstrate that, in those problems where advection is confined to the particle surface, steady translation or rotation emerges from a symmetric state via a pitchfork bifurcation - supercritical or subcritical - that is degenerate due to rotational invariance. In these scenarios, which fit the phenomenological description, a weakly nonlinear analysis of the multiphysics problem reproduces the canonical amplitude equation with the phenomenological coefficients determined. In contrast, when advection takes place in the bulk fluid, the phenomenological SSB picture collapses due to persistent leading-order advective effects far from the particle. Asymptotic analyses accounting for these far-field effects yield non-canonical reduced-order models revealing anomalous onset scenarios, including singular bifurcations departing from the conventional square-root form, onset without bifurcation, and history-dependent dynamics. Finally, we analyze the alignment of spontaneous motion under weak imposed asymmetry (external fields and ambient flows), demonstrating the counterintuitive response of symmetry-breaking particles to perturbations.
Date Acceptance
2026-09-16
Citation
Reviews of Modern Physics
ISSN
0034-6861
Publisher
American Physical Society (APS)
Journal / Book Title
Reviews of Modern Physics
Copyright Statement
Copyright This paper is embargoed until publication. Once published the author’s accepted manuscript will be made available under a CC-BY License in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy).
License URL
Publication Status
Accepted
Date Publish Online
2026-09-16