Hydrodynamic Interactions in Two Dimensions

TL;DR

This study investigates how hydrodynamic interactions between colloidal particles are significantly altered in a two-dimensional fluid environment, revealing increased interaction range and unique mobility behaviors compared to bulk fluids.

Contribution

The paper introduces a two-dimensional hydrodynamic tensor that accurately describes particle interactions in confined fluids, highlighting the impact of dimensionality on colloidal dynamics.

Findings

Hydrodynamic interactions extend over much larger distances in 2D fluids.

Eigen-mobilities vary logarithmically with particle separation.

Mobility differences are significant at large separations, unlike in 3D fluids.

Abstract

We measure hydrodynamic interactions between colloidal particles confined in a thin sheet of fluid. The reduced dimensionality, compared to a bulk fluid, increases dramatically the range of couplings. Using optical tweezers we force a two body system along the eigenmodes of the mobility tensor and find that eigen-mobilities change logarithmically with particle separation. At a hundred radii distance, the mobilities for correlated and anti-correlated motions differ by a factor of two, whereas in bulk fluids, they would be practically indistinguishable. We derive the two dimensional counterpart of the Oseen hydrodynamic tensor which quantitatively reproduces the observed behavior. These results highlight the importance of dimensionality for transport and interactions in colloidal systems and proteins in biological membranes.