Fundamentals of mass transport in the microscale - Micromixers Fundamentals Design and Fabrication - page 12

FIGURE 2.1

Collision integral U as a function of dimensionless temperature k B T/3.

The most important characteristic length scale in gas dynamics is the mean free path , which is the
average distance traveled by a molecule between successive collisions:

1
p ps 2 n l ¼ (2.5)

where n is the number density (number of molecules per unit volume):

p
k B T :

n ¼ (2.6)

The ratio between the mean free path and the characteristic length of the device, for instance, the
channel diameter, is called the Knudsen number:

l
L :

Kn ¼ (2.7)

Because the Knudsen number represents a link between the length scale of a device and the
interaction between fluid molecules, it can be used to estimate the right model for describing the