Small particle dynamics are NOT intuitive
10/01/2000
by Robert P. Donovan
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The behavior of aerosol particles in cleanrooms is quite different from that of the macroscopic solid objects encountered in everyday life. Over the next three months, my column will illustrate some of these differences by comparing the behavior of a familiar spherical object—a regulation baseball—with that of a hypothetical object similar in composition, density, color and every other property to the baseball except for its diameter, which will be assumed to be 1 micron.
This hypothetical sphere will be called a "1-micron baseball" and is intended to be representative of a typical aerosol particle in a cleanroom.
One obvious difference between these two baseballs is that the human eye can detect the regulation baseball but not the 1-micron baseball. This is just the beginning. A baseball released from one's grip falls to the ground; the 1-micron baseball does not —it stays suspended in the air more or less right where it was released. Such non-intuitive behaviors, dependent only on particle diameter, abound and will be explored.
The goal of these columns is to help cleanroom workers think in terms of aerosol particles rather than baseballs and to provide some concepts from classical particle dynamics that assist in making this transition.
When throwing a baseball, one has a pretty good idea of where it's going and how to control/adjust its trajectory. How about throwing a baseball that is 1 micron in diameter? Even the strikeout king (my hero, Pedro Martinez of the Red Sox) would have trouble getting an object of this size past a batter (or even to reach the batter).
It's not that the type of physical forces acting on a regulation-sized baseball and a 1-micron baseball differ. Air resistance (drag) slows both of them. It's primarily that the magnitudes of some of these drag forces vary dramatically with size and thus the type of drag dominating the air resistance changes with size.
Air resistance
Consider the motion of a sphere, such as a baseball, that is thrown parallel to the earth's surface and hence perpendicular to the gravitational force (which will be ignored). The motion of that sphere in the horizontal direction depends upon both the initial velocity with which the pitcher launches the baseball and the air resistance opposing the horizontal component of its motion.
Let's assume that the initial velocity is the same for both the regulation and the 1-micron baseballs as they leave the pitcher's hand. Once clear of the pitcher, the only force acting horizontally on these thrown objects is the drag force. Because this force opposes the initial motion, the thrown objects are continuously slowing down and eventually the horizontal velocity component reaches zero. The rates at which the differently sized baseballs slow down and the distances traveled before the horizontal components of their velocities become zero differ dramatically.
The regulation baseball thumps into the catchers mitt some 60 feet away with a resounding crack (when Pedro throws it); neglecting any air motion, the 1-micron baseball remains more or less right where it is released. The only difference between these thrown baseballs is their diameter.
Drag force
Drag forces, when air compressibility is negligible as it is in this illustration, are of two types: inertial (due to pressure differences between the front and the back of the baseball) and viscous (due to skin friction). Total drag is the sum of the pressure drag and the skin friction drag. A convenient parameter for predicting which of these drag forces dominate is provided by the particle Reynolds number, Re, a dimensionless ratio of inertial forces to viscous forces defined as:1
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All the variables appearing in Equation (1) are the same for both the regulation and the 1-micron baseball except for the diameter (say 10 cm for the regulation baseball and
10-4 cm for the 1-micron baseball). This equation thus shows that the particle Re of the 1-micron baseball is on the order of 1 and that the particle Re of the regulation baseballis 105 times larger. And therein lies the story. For particle Re < 1, viscous forces—the skin friction component of air resistance as described by Stokes law—dominate drag. For particle Re > 1000, inertial forces—the pressure drop component of air resistance as described by Newton's laws—dominate drag. A dimensionless drag coefficient, CD, relates the net drag force on a sphere to Re. Skin friction drag on the 1-micron baseball creates a larger value of drag coefficient (CD ~ 26) than does the pressure gradient drag on the regulation baseball (CD ~ 0.4). Thus the 1-micron baseball slows down more rapidly than the regulation baseball. Reference 1 presents a plot of CD versus Re over the entire viscous/inertial force spectrum.
A simple calculation of particle Re from Equation 1 can immediately alert one to the regime appropriate for predicting particle behavior in a given situation. The motion of cleanroom particles will almost always be at low values of particle Re, so that Stokes law applies to them like the 1-micron baseball, which makes their behavior far less intuitive than that of larger spheres like the regulation baseball.
Robert P. Donovan is a process engineer assigned to the Sandia National Laboratories as a contract employee by L & M Technologies Inc., Albuquerque, NM. His Sandia project work is developing technology for recycling spent rinse waters from semiconductor wet benches.
Reference
- Hinds, W. C., Aerosol Technology, John Wiley & Sons, (1982).