Trading particle shape with fluid symmetry: on the mobility matrix in 3D chiral fluids (2310.17528v2)

Abstract: Chiral fluids - such as fluids under rotation or a magnetic field as well as synthetic and biological active fluids - flow in a different way than ordinary ones. Due to symmetries broken at the microscopic level, chiral fluids may have asymmetric stress and viscosity tensors, for example giving rise to a hydrostatic torque or non-dissipative (odd) and parity-violating viscosities. In this article, we investigate the motion of rigid bodies in such an anisotropic fluid in the incompressible Stokes regime through the mobility matrix, which encodes the response of a solid body to forces and torques. We demonstrate how the form of the mobility matrix, which is usually determined by particle geometry, can be analogously controlled by the symmetries of the fluid. By computing the mobility matrix for simple shapes in a three-dimensional anisotropic chiral fluid, we predict counter-intuitive phenomena such as motion perpendicular to applied forces and spinning under the force of gravity.

• The paper demonstrates that fluid chiral symmetry can dictate the mobility matrix, enabling propulsion under ambient torque without external forces.
• It employs theoretical formulations to show that odd viscosity in chiral fluids generates lift forces, resulting in unexpected particle trajectories.
• The study highlights how rotation-translation coupling in chiral fluids induces spin in non-chiral objects, suggesting novel microfluidic control strategies.

Insights on the Mobility Matrix in Chiral Fluids

The study of rigid body motion in fluids is a fundamental aspect of fluid dynamics, with significant implications across various scales and applications. Conventionally, the mobility of a particle immersed in a fluid is predominantly influenced by its geometry. However, the paper titled "Trading particle shape with fluid symmetry: on the mobility matrix in 3D chiral fluids" introduces an intriguing paradigm wherein the fluid's inherent chiral properties profoundly alter this relationship by influencing the mobility matrix, which determines how particles respond to forces and torques in a fluid.

Chiral Fluids: An Overview

Chiral fluids are characterized by broken symmetries at the molecular level, manifesting in unique macroscopic properties such as asymmetric stress and non-dissipative viscosities. These features are not present in standard isotropic fluids. Examples of such fluids include those under rotation or subjected to magnetic fields, as well as certain biological and synthetic active fluids. The paper explores these phenomena by examining how the inherent chiral nature of a fluid can dictate the motion of simple geometric particles beyond what particle shape alone would normally permit.

The Mobility Matrix and Anisotropic Fluid Interactions

The core investigation within the study revolves around the mobility matrix, a construct that encapsulates the response of a solid body to applied forces and torques. Traditionally, this matrix is determined solely by the particle geometry in isotropic fluids. In this paper, however, it is demonstrated through theoretical formulation and computation that the symmetries of the fluid itself can dictate the form of the mobility matrix.

This dependency leads to several counter-intuitive and fascinating dynamics in chiral fluids:

1. Propulsion Under Ambient Torque: A chiral fluid can exert an ambient torque on an immersed particle, propelling it even without any external force. This propulsion depends on the torque density and the coupling between rotation and translation, illustrated through the motion of a helical structure.
2. Lift Force and Trajectories: The presence of odd viscosity in such fluids is shown to generate lift forces on particles, causing motion at an angle to applied forces. This effect is akin to a sphere spiraling under optical tweezers, where traditional isotropic fluid dynamics would predict a straightforward path.
3. Rotation-Translation Coupling: In a chiral fluid, non-chiral objects, such as an upright triangle, may spin when subjected to simple translational forces such as gravity. This phenomenon is facilitated by the fluid's parity-violating properties rather than the object's intrinsic chirality.

Implications and Future Directions

The implications of these findings are profound, suggesting that by manipulating the properties of a fluid, rather than the particles themselves, it is possible to precisely control motion in a manner previously attributed solely to particle shape and design. This can pave the way for new technologies in microfluidics and synthetic bio-systems, where control over minute scales is crucial.

The theoretical advancements outlined in the paper provide a robust framework for leveraging chiral fluid properties in practical applications, enabling new avenues of research in active matter and soft robotics. Moreover, these results highlight the necessity of a deeper investigation into the role of fluid symmetry in dynamic systems traditionally dominated by particle-centric views.

As the field progresses, one can anticipate significant interdisciplinary collaborations to harness the potential of chiral fluids in diverse technological landscapes. The insights from this study could be further expanded by experimental validations and by exploring other unexplored chiral fluid systems, enriching our understanding of fluid dynamics in the quantum regime and beyond.