Hydrodynamic interactions between a point force and a slender filament

TL;DR

This paper analyzes the flow interactions between a point force and a nearby slender filament in a viscous fluid, revealing a resistive-force theory-like behavior with logarithmic drag dependence, relevant for biological transport processes.

Contribution

It introduces an asymptotic analysis of hydrodynamic interactions between a point force and a slender filament, extending resistive-force theory with new drag coefficient insights.

Findings

The leading-order force distribution resembles resistive-force theory.

Drag coefficients depend logarithmically on the distance to the filament.

Theoretical predictions agree well with boundary element computations.

Abstract

The Green's function of the incompressible Stokes equations, the stokeslet, represents the singular flow due to a point force. Its classical value in an unbounded fluid has been extended near surfaces of various shapes, including flat walls and spheres, and in most cases the presence of a surface leads to an advection flow induced at the location of the point force. In this paper, motivated by the biological transport of cargo along polymeric filaments inside eukaryotic cells, we investigate the reaction flow at the location of the point force due to a rigid slender filament located at a separation distance intermediate between the filament radius and its length (i.e. we compute the advection of the point force induced by the presence of the filament). An asymptotic analysis of the problem reveals that the leading-order approximation for the force distribution along the axis of the filament takes a form analogous to resistive-force theory but with drag coefficients that depend logarithmically on the distance between the point force and the filament. A comparison of our theoretical prediction with boundary element computations show good agreement. We finally briefly extend the model to the case of curved filaments.