Fall Rate of Sub-micron Particles and Bare Shear Viscosity: I. Diffusion Equation

TL;DR

This paper explains the experimental breakdown of Millikan's Law for sub-micron particles by introducing the concept of bare shear viscosity, which depends on an averaging length and affects fall rates contrary to traditional theory.

Contribution

It introduces the role of bare shear viscosity in particle fall rates, contrasting it with the renormalized viscosity, and explains pressure effects on sub-micron particle fall behavior.

Findings

Bare shear viscosity decreases with increasing gas pressure.

Fall rate increases with pressure, opposite to Millikan's Law.

Bare shear viscosity can be experimentally measured via fall rate.

Abstract

Kim and Fedele discovered experimental evidence for the breakdown of the Millikan's Law for the fall rate of oil droplets in Nitrogen gas and the discrepancy is most pronounced for the smallest, sub-micron size particles. Here we explain these results by showing that the particle's motion is determined in part by the bare shear viscosity which is defined by the averaging length lambda. This is in contrast to the usual theory which involves the renormalized shear viscosity. An increase in gas pressure produces a decrease in the bare shear viscosity and as a result the fall rate increases. This behavior is opposite the Millikan Law prediction that an increase in pressure produces a decrease in fall rate. As a result, the bare shear viscosity is experimentally measurable by the fallrate. The theory here uses a convective diffusion equation and a Langevin approach will be presented elsewhere.