Rotational dynamics of a disk in a thin film of weakly nematic fluid subject to linear friction

TL;DR

This paper analytically investigates the rotational behavior of a disk in a weakly nematic fluid film, revealing how anisotropy and confinement influence hydrodynamic properties, with validation through finite-element simulations.

Contribution

It provides the first analytical expressions for the flow and resistance of a rotating disk in anisotropic, confined thin films, incorporating linear friction effects.

Findings

Analytical solutions match finite-element simulations well.

Rotation behavior differs from translation, especially without linear friction.

Results applicable to microfluidics and nematic liquid crystal films.

Abstract

Dynamics at low Reynolds numbers experiences recent revival in the fields of biophysics and active matter. While in bulk isotropic fluids it is exhaustively studied, this is less so in anisotropic fluids and in confined situations. Here, we combine the latter two by studying the rotation of a disk-like inclusion in a uniaxially anisotropic, globally oriented, incompressible two-dimensional fluid film. In terms of a perturbative expansion in parameters that quantify anisotropies in viscosity and in additional linear friction with a supporting substrate or other type of confinement, we derive analytical expressions for the resulting hydrodynamic flow and pressure fields as well as for the resistance and mobility coefficients of the rotating disk. It turns out that, in contrast to translational motion, the solutions remain well-behaved also in the absence of the additional linear friction. Comparison with results from finite-element simulations show very good agreement with those from our analytical calculations. Besides applications to describe technological systems, for instance, in the area of microfluidics and thin cells of aligned nematic liquid crystals, our solutions are important for quantitative theoretical approaches to fluid membranes and thin films in general featuring a preferred direction.