Stokes Drag on a Thin Circular Disk Moving Edgewise Midway Between Parallel Plane Boundaries

Abstract

This technical brief presents experimental results for the drag on a circular disk moving at terminal velocity through a viscous fluid midway between parallel plane walls. The axis of the disk is oriented perpendicularly to these walls. The notation is shown in Fig. 1. A circular disk of diameter d and thickness t moves edgewise with a velocity U through a viscous fluid of density ρ and viscosity μ midway between two plane walls that are parallel to the plane of the disk. The distance between the parallel walls is D. Define the aspect ratio of the disk as A=t∕d and the Reynolds number as Re=dρU∕μ. I will assume that the flow is a Stokes flow (Re⪡1) and that the disks are thin (A⪡1).