Biomedical Engineering Reference
In-Depth Information
TABLE E9-3.4 General Multilayer Isotherm. The Parameters in Eqn (E9-3.3) Were Evaluated by Minimizing
the Variance between Calculated Values ( Eqn E9-3.3 ) and the Experimental Data. The
Parameters Obtained Are: N
6.947093; a 0 ¼
¼
3.158229; c
¼
11.119;
C As1 N ¼
5.45012dCont'd
Error 2
(C 0 As LC As ) 2
Relative humidity,
N p/p
Loading,
C 0 As , mol/L
Multilayer isotherm,
Eqn (E9-3.3) , C As , mol/L
0.2780
17.4
18.51244
1.237517
0.2790
17.94
18.5897
0.422111
0.2920
20.03
19.58186
0.20083
0.3070
20.43
20.69135
0.068302
0.3500
23.45
23.5883
0.019127
0.3690
25.28
24.71373
0.320664
0.5260
30.97
30.73444
0.055487
0.5390
32.04
31.03673
1.00655
0.6490
33.03
32.92047
0.011997
0.6970
33.32
33.477
0.024648
0.7580
33.87
34.03667
0.027779
0.8250
34.11
34.51437
0.163514
0.8250
34.15
34.51437
0.132765
s
P 24
i ¼
ðC As;i C 0 As;i Þ
2
1
s L ¼
¼
0.451883
24
1
a 0 ¼
0.451883. Since
the number of layers N is close to 7, we next fixed the value of N at 7 and re-evaluated
the parameters. Table E9-3.5 shows the final results after fixing the number of layers
at 7. The variance change is very minimum and at 0.452307. Therefore, there is no sacrifice
with the quality of fit by fixing N
3.158229; c
¼
11.119; C As1 N ¼
5.45012 and the variance is small, s L ¼¼
7.
Fig. E9-3.3 shows the experimental data (as circles) and the general multilayer isotherm
model fit (as solid line). One can observe that the fit is very well. The quality of fit showed
improvement over the bilayer model fit as the final variance is smaller and the curve follows
the data right on capturing the details of the change.
¼
9.1.4.4. Multispecies Multilayer Adsorption Isotherms
We have so far been focused on the multilayer adsorption of single species. We have
seen that they can be treated elegantly and predicting the trends of the adsorption
isotherms observed experimentally. In this section, we give the corresponding isotherms
for multispecies adsorptions. They can be derived very much the same as for single
species.
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