The drag on needles moving in a Langmuir monolayer

Abstract

The motion of membrane-bound objects is important in many aspects of biology and surface chemistry. Here we derive some general relations for objects moving in a surface film overlying a fluid of depth H. A solution to the problem of the drag can be obtained from a two-dimensional system of integral equations. Here we focus on the problem of an ideal needle moving edge-on (in the direction of its tip) or broadside-on (perpendicular to the direction of the tip). It is shown that in comparison to the drag on a circular disk a new scaling regime of the drag on a needle arises when the ratio between surface shear viscosity and subphase viscosity $\eta_s/\eta$ is smaller than the length of the needle.