Suspension Acoustics: An Introduction to the Physics of Suspensions
Written by a leading expert in the field, this book is an introduction to the physics of suspensions of bubbles, droplets, and solid particles in both gases and fluids.
TABLE OF CONTENTS Suspension Acoustics: An Introduction to the Physics of Suspensions
4.5: Extensions to Stokes Law
4.5 Extensions to Stokes Law
As the previous examples show, there may be situations in which small particles move in fluids at small Reynolds, but in conditions that do not exactly match those used in deriving Stokes law. Consequently, a considerable amount of work has been done to remove some of the restrictions implied by its derivation. The following list gives some of those extensions. In most of these, the fluid force is entirely due to viscous effects and acts along the direction of the relative velocity. To avoid confusion with the force F p, which may include other effects, we shall use the symbol F D for the viscous drag.
Very Small Particles
As the size of the sphere is decreased, the molecular nature of the fluid around it starts to play a role, particularly in gases, where the molecules are normally widely separated. A measure of the importance of molecular effects in gases is usually given in terms of a nondimensional parameter known as the Knudsen number. This defined as the ratio of the molecular mean free path to the size of the particle. Thus, Kn= ?/a, where ? is the mean free path. In air at 20 C and 1 atm, this distance is of the order of 0.1 ?m. Hence, sub-micron particles can be significantly affected by molecular collisions.
A correction factor for Stokes law that takes into account this effect was proposed, independently, by Millikan and by...
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