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2.1 Gas Kinetics 43

2
Then, the net flux of molecules in the positive x direction (#/s m )is
1 dC N
J x ¼ J !x J x ¼ k c ð2:62Þ
3 dx
Comparing this equation with the Fick’s law of diffusion

dC N
J x ¼ D ð2:63Þ
dx
2
gives the diffusivity or diffusion coefficient of gas in m /s:
1
D ¼ k c ð2:64Þ
3
Combining with Eqs. (2.7) and (2.51), we can get leads to

r ffiffiffiffiffiffiffiffi r ffiffiffiffiffiffi
1 RT 8kT 2 RT RT
D ¼ p ffiffiffi ¼ : ð2:65Þ
1:5 2
3 2pN a d P pm 3p d PN a M
2
2.1.10 Viscosity of a Gas

Viscosity is a measure of the resistance of a fluid being deformed by either shear or
extensional stress. Viscosity in gases arises principally from the molecular diffusion
that transports momentum between layers of flow. The kinetic theory of gases
allows accurate prediction of the viscosity of a gas.
Similar to the analysis for diffusivity, consider a laminar flow of gas above a
horizontal plate. We can apply finite element analysis from x kÞ to x þ kÞ. The
ð
ð
concentration at x is C N . Assuming a constant gas velocity gradient of du from
dx

ð
ð x kÞ to x þ kÞ; the velocities at x þ kÞ and x kÞ are u þ du k and
ð
ð
dx

du
u k , respectively. The gas may be treated as layers perpendicular to the
dx
moving direction (say x axis). Also assume a constant gas molecule concentration
C N . In each layer, the steady flow gas velocity is also constant. Then, the rate of
transport of momentum per unit area in the þx and x directions, respectively, are

1 ou
M !x ¼ C N m cu k
6 ox
1 ou
M x ¼ C N m cu þ k
6 ox