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Engineering Mathematics
Review of Viscous Flows
Review of Computational Fluid Mechanics

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ME 437 The National Science Foundation
 Aerosols
Introduction to Aerosols | Drag, Lift Forces | Aerosol Kinetics | Virtual Mass, Basset Forces & BBO Equation | Nonspherical Particles | Brownian Motions | Particle Deposition Mechanisms | Electrodynamics | Aerosol Coagulation |

Drag Force

Drag Force Calculation Models

Parallel Wall Effects

Parallel Wall Effects


Vertical Wall Effects

Vertical Wall Effects


Cunningham Correction Factor

Cunningham Correction Factor


Cunningham Correction Factor

For very small particles, when the particle size becomes comparable with the gas mean free path, slip occurs and the expression for drag must be modified accordingly. Cunningham obtained the needed correction to the Stokes drag force:

(9)
where the Cunningham correction factor C is given by

(10)

Here, λ denotes the molecular mean free path in the gas. Note that Cc > 1 for all values of d and λ. Figure 5 shows the variation of Cunningham correction factor with Knundsen number.

It is seen that Cc is about 1 for Kn < 0.1 and increases sharply as Kn increases beyond 0.5. Table 4 illustrates the variation of the Cunningham correction factor with particle diameter in air under normal pressure and temperature conditions with λ = 0.07 µm. Equation 10 is applicable to a wide range of

that covers slip, transition, and part of free molecular flows. However, the particle Reynolds number Mach (based on relative velocity) should be small.

Table 4: Variations of Cc with d for λ = 0.07 µm
Diameter, µmCc
10 µm 1.018
1 µm 1.17
0.1 µm 3.01
0.01 µm 23.77
0.001 µm 232.5


Dr. Goodarz Ahmadi | Turbulence & Multiphase Fluid Flow Laboratory | Department of Mechanical & Aeronautical Engineering
Copyright © 2002-2005 Dr. Goodarz Ahmadi. All rights reserved.
Potsdam, New York, 13699
ahmadi@clarkson.edu