Odd Viscosity and Odd Elasticity

Abstract

Elasticity typically refers to a material's ability to store energy, whereas viscosity refers to a material's tendency to dissipate it. In this review, we discuss fluids and solids for which this is not the case. These materials display additional linear response coefficients known as odd viscosity and odd elasticity. We first introduce odd viscosity and odd elasticity from a continuum perspective, with an emphasis on their rich phenomenology, including transverse responses, modified dislocation dynamics, and topological waves. We then provide an overview of systems that display odd viscosity and odd elasticity. These systems range from quantum fluids and astrophysical gases to active and driven matter. Finally, we comment on microscopic mechanisms by which odd viscosity and odd elasticity arise.

Generic stress rectification in nonlinear elastic media

“…Our choice of deriving the elastic stress from an energy density implicitly rules out odd elastic materials, where a more general stress dependence emerges from e.g., the presence of active, energy-consuming elements within the elastic material. 23 By contrast, here we explicitly model any active elements through the force density f, which we embed in an otherwise passive material.…”

“…, the presence of active, energy-consuming elements within the elastic material. 23 By contrast, here we explicitly model any active elements through the force density f , which we embed in an otherwise passive material.…”

Hydrodynamics of an odd active surfer in a chiral fluid

“…However, in this work, our aim was to analyze active swimming behavior using a minimal model for analytical tractability, and therefore we did not employ these numerical techniques. Furthermore, extensions of existing numerical simulation methods to a system of swimming bodies in a fluid with odd viscosity have rarely been performed [66]. Although such numerical methods are beyond the scope of this work, their application could provide new insights into the effect of odd viscosity on the active dynamics of microswimmers, and as such, they represent an area for future investigation.…”

“…Chiral fluids show several peculiar features such as dissipationless transport [58,59], non-reciprocal response [60][61][62][63][64], and topological edge flows [52,65]. Odd viscosity is a rheological property that describes chiral fluids [66,67] and represents a transport coefficient that does not contribute to dissipation of mechanical energy of the fluid [68]. The effect of odd viscosity on various types of flows has been examined extensively in the context of microparticle transport [59,60,62,69] or Langevin dynamics in fluctuating active systems [70].…”

Chiral active matter in external potentials

“…29 Chiral active particles exhibit fascinating phenomena also in the presence of alignment interactions giving rise to pattern formation 30,31 consisting of rotating macro-droplets, 32 chiral self-recognition, 33 dynamical frustration, 34 and chimera states. 35 In addition, chirality appears as a fundamental ingredient to observe the hyperuniform phase 36,37 in active matter as well as emerging odd properties 38,39 for instance in the viscosity, [40][41][42] elasticity, 43 and mobility. 44 Recently, the circular motion has been also investigated in the framework of active glasses where it gives rise to a novel oscillatory caging effect entirely due to the chirality.…”