Page 126 - Materials Chemistry, Second Edition

Plume Migration in Aquifer and Soil 109

Solution:
(a) For ϕ = 0.3 and ϕ = 0.45,
t
w
ϕ = 0.45 − 0.3 = 0.15
a
Use Equation (3.40) to find the air-phase tortuosity factor at ϕ
w
= 0.3:
(0.15) 10/3
a ς= 2 = 0.0088
(0.45)
(b) For ϕ = 0.05 and ϕ = 0.45,
t
w
ϕ = 0.45 − 0.05 = 0.40
a
Use Equation (3.40) to find the air-phase tortuosity factor at
ϕ = 0.05
w
(0.40) 10/3
a ς= 2 = 0.23
(0.45)
Discussion:
The volumetric water content here is the percentage of total soil volume
(not the void volume) occupied by water. For this case, the air-phase
tortuosity becomes approximately 25 times larger when the volu-
metric water content drops from 0.3 to 0.05.

Example 3.25: Estimate the Diffusion Coefficient
at Different Temperatures

The diffusion coefficient of benzene in dilute aqueous solution at 20°C is 1.02
× 10 cm /s (Table 3.6) and the free-air diffusion coefficient of benzene is
-5
2
0.092 cm /s at 25°C (Table 2.5). Use these reported values to estimate:
2
1. The ratio of the diffusion coefficients of benzene in free air and in a
dilute aqueous solution at 20°C
2. The free air diffusion coefficient of toluene at 20°C.

Solution:
(a) Use Equation (3.42) and m = 2 (assumed) to determine the free air
diffusion coefficient of benzene at 20°C:
0.092  298  2
D @ T 2 =   293  
0

So the free air diffusion coefficient of benzene at 20°C
= 0.089 cm /s.
2