Hydrodynamic flows induced by localized torques (rotlets) in wedge-shaped geometries

TL;DR

This paper derives analytical solutions for flow fields induced by localized torques in wedge-shaped microfluidic geometries, revealing how confinement influences particle motion and enabling better control in microfluidic device design.

Contribution

It introduces a novel analytical derivation of flow responses to torques in wedge geometries, expanding understanding beyond force-induced flows in low-Reynolds-number hydrodynamics.

Findings

Flow fields depend on wedge geometry and torque orientation.

Particles experience coupled translational and rotational motion due to broken symmetry.

Provides hydrodynamic mobility tensors for torque-induced particle motion.

Abstract

Wedge-shaped geometries in low-Reynolds-number flows are of increasing importance, for instance, in the design of microfluidic devices. The corresponding Green's functions describing the induced flow in response to a locally applied force were derived some time ago. To achieve a complete characterization of particle motion at low Reynolds numbers, we derive the flow response to locally applied torques. This is accomplished through a direct calculation based on the Fourier-Kontorovich-Lebedev transform using the Papkovich-Neuber representation of the hydrodynamic fields. We then illustrate the resulting flow fields, highlighting their structure, key features, and dependence on the geometry and orientation of the applied torque. Based on these solutions, we compute the corresponding hydrodynamic mobility tensor that couples torque and motion. Owing to the broken spatial symmetry imposed by the wedge-shaped confinement, a particle subjected to a torque will experience not only rotational motion but also translational motion. These results provide analytical tools relevant for predicting and controlling particle behavior in confined microfluidic environments.