Motion of a sphero-cylindrical particle in a viscous fluid in confined geometry

Abstract

The motion of a millimeter size spherocylinder particle settling in a very viscous oil in a closed container is measured by laser interferometry, with the goal to model the motion of a particle of this shape in a fluid at microscales. The container is a cylinder with vertical axis and closed at both ends by horizontal plates. The displacement of the particle along the container axis is recorded with a resolution of the order of 100 nm, that is much smaller than the particle–wall separation when in the lubrication regime. The particle friction coefficient, measured as a function of the particle–wall distance, is then used to test the theoretical predictions of an accurate hydrodynamic analysis. The Stokes flow problem is solved by using the hydromultipole method, that is in general appropriate for spheres but is extended here to a non-spherical particle by using a compound of overlapping spheres. The lateral wall effect is negligible but the two parallel horizontal end plane walls are accurately taken into account. The result of the theoretical model is in good quantitative agreement with experiment for the whole settling motion of the spherocylinder, that is for any position between the walls.