The Drag on a Single Particle Stokes Law

Since the red molecules differ from the others only by a coat of paint, X and D apply to all molecules of the gas. Thus the diffusional mean free path X is defined as a function of the molecular diffusivity of the vapor and its mean speed by (9.19). 

Expressions (9.13), (9.15), (9.16), and (9.19) have different numerical constants and their use leads to mean free paths X.AB that differ by as much as a factor of 2 for typical atmospheric gases. The consequences of using these different expressions are discussed in Chapter 12. In the remaining sections of this chapter we focus on the interactions of particles with a single gas, air, with a mean free path given by (9.6) and (9.7). 

The velocity and pressure in an incompressible Newtonian fluid are governed by the equation of continuity (a mass balance) 

Let us nondimensionalize the Navier-Stokes equations by introducing a characteristic velocity u0 and characteristic length L and defining the dimensionless variables 

Then (9.20) and (9.21) can be rewritten using the definitions presented above 

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