(C-C2 ) / (C 1 -C 2 ) Distance (mm) 0 2 4 6 8 10 -10 -8 -6 -4 -2 0.2 0.4 0.6 0.8 1.0

Data Input Choice
log D
Arrhenius Data

log D (m2/s)
Time (years)
D = 1.00e-16 (m2/s)
Time = 0 (s)
Time = 0 (years)
(4Dt)½ = 0.000 mm
X Scale 1mm 10mm 10cm 1m

Figure 2.20. Diffusion Infinite Extent Couple. This diagram shows an exact solution to the diffusion equation given by Crank (1975, equation 2.14) for diffusion across a boundary between two phases of infinite extent. Phase 1 on the left initially has a uniform high concentration (C1) of the diffusing component. Phase 2 on the right initially has a low concentration (C2) of the diffusing component. The red line shows normalized concentrations (C-C2)/(C1-C2). The same diffusion coefficient D (m2/s) is used for both phases.

Move the Time Slider to show changes of the normalized concentrations with time. Use the radio buttons to change the scale if you wish. To see the effect of the diffusion coefficient, use the slider to change log D. Alternatively, you may specify D by entering the parameters for the Arrhenius equation D = Do Exp(-Ea/(R*T)). Then you may use the sliders to see how the parameters Ea (activation energy), Do (constant), and temperature (T) affect the results.

Notice that the parameter (4DT)½ gives a reasonable estimate of the distance on either side of the phase boundary over which there is significant diffusion in time t. Notice that the Time Slider is in logarthmic units.