Module 3: Characteristics of Particles - Surface Area and Volume

Features

Lesson Material
Practice Problems

Objective

Calculate the surface area and volume of spherical particles.

The size range of particles of concern in air pollution studies is remarkably broad. Some of the droplets collected in the mist eliminators of wet scrubbers and the solid particles collected in large-diameter cyclones are as large as raindrops. Some of the small particles created in high temperature incinerators and metallurgical processes can consist of less than 50 molecules clustered together. The EPA has defined categories within this large size range of particles (discussed later). It is important to recognize the categories since particles behave differently depending on their size. Most particles of primary interest in air pollution emission testing and control have diameters that range from 0.1 to 1000 micrometers (microns).

Here are some useful conversions for particle sizes:

To appreciate the difference in particle sizes commonly found in emission testing and air pollution control, compare the diameters, volumes and surfaces areas of particles in Table 1.

The data in Table 1 indicates that particles of 1000 micrometers are 1,000,000,000,000 (one trillion) times larger in volume than 0.1 micrometer particles.

As an analogy, assume that the 1000-micrometer particle is a large domed sports stadium. A basketball in this "stadium" would be equivalent to a 5-micrometer particle. Approximately 100,000 spherical particles of 0.1-micrometer diameter would fit into this 5-micrometer "basketball." The entire 1000-micrometer "stadium" is the size of a small raindrop. As previously stated, particles over this entire size range of 0.1 to 1000 micrometers are of interest in air pollution control.

Assume that all of the particles are simple spheres. The small raindrop shown in Figure 1 has a diameter of 1000 micrometers. The 100-micrometer particle, which is shown next to the raindrop, looks like a small speck compared to the office pushpin in the background. However, both the raindrop and the 100-micrometer particle are on the large end of the particle size range of interest in the air pollution field.

Particles in the size range of 10 to 100 micrometers are also on the large end of the particle size scale of interest in the field of air pollution. A 10-micrometer particle could not be seen if it had been included in Figure 1; it is simply too small to see.

Equations for calculating the volume and surface area of spheres are provided below. For more information and practice problems on spherical geometry, see the lesson on Plane Geometry in Module 1.