Biomedical Engineering Reference
In-Depth Information
2a vs. 2b
3a vs. 3b 2a vs. 3a 2a vs. 3b 3a vs. 2b 3b vs. 2b
T Native
0.955
0.471 0.607 0.710 0.830 0.784
F Native
0.105
0.384 0.345 0.247 0.183 0.264
T Modified
0.328
0.969 0.401 0.326 0.621 0.623
F Modified 0.268 0.196 0.416 0.148 0.207 0.060
Table 5a. Effect of column history on influent cadmium bound. T values are probability that
the two compared means are statistically equivalent. F values are statistical probability that
their variances are equivalent. 2a NiCd, 2b ZnCd, 3a NiZnCd, 3b ZnNiCd.
2a vs. 2b
3a vs. 3b 2a vs. 3a 2a vs. 3b 3a vs. 2b 3b vs. 2b
T Native
0.483
0.104 0.326 0.557 0.345 0.665
F Native
0.093
0.454 0.036 0.043 0.267 0.304
T Modified
0.760
0.183 0.310 0.536 0.427 0.377
F Modified 0.459 0.034 0.047 0.413 0.055 0.374
Table 5b. Effect of column history on influent nickel bound. T values are probability that the
two compared means are statistically equivalent. F values are statistical probability that
their variances are equivalent. 2a CdNi, 2b ZnNi, 3a CdZnNi, 3b ZnCdNi.
2a vs. 2b
3a vs. 3b 2a vs. 3a 2a vs. 3b 3a vs. 2b 3b vs. 2b
T Native
0.214
0.515 0.193 0.542 0.959 0.274
F Native
0.939
0.953 0.736 0.691 0.553 0.221
T Modified
0.412
0.327 0.383 0.440 0.470 0.354
F Modified 0.094 0.392 0.357 0.264 0.157 0.224
Table 5c. Effect of column history on influent zinc bound. T values are probability that the
two compared means are statistically equivalent. F values are statistical probability that
their variances are equivalent. 2a CdZn, 2b NiZn, 3a CdNiZn, 3b NiCdZn.
Three assumptions were made in pursuing this avenue of exploration. 1) There exist
common binding sites shared between all three of the metal ions (δ
0
). 2) For each metal ion,
there exist ion-specific binding sites available only to that particular ion (α, β, γ). 3) For each
stage in the influent solution exposure sequence, there may be enhancement or inhibition of
binding due to the history of metal exposure, i.e., some level of cooperativity between sites.
Making these assumptions allows for the construction of an overall binding equation for the
three-metal system:
M
Bound
= [ α
Cd
X
Cd
+ α
Ni
X
Ni
+ α
Zn
X
Zn
] + { β
CdNi
X
CdNi
+ β
CdZn
X
CdZn
+ β
NiCd
X
NiCd
+ β
NiZn
X
NiZn
+ β
ZnCd
X
ZnCd
+ β
ZnNi
X
ZnNi
} + ( γ
CdNiZn
X
CdNiZn
+
(1)
γ
CdZnNi
X
CdZnNi
+ γ
NiCdZn
X
NiCdZn
+ γ
NiZnCd
X
NiZnCd
+ γ
ZnCdNi
X
ZnCdNi
+ γ
ZnNiCd
X
ZnNiCd
)
+ δ
0
X
common
From the sequential experiments, the amount of total metal bound is known for each of the
above situations except for metal binding to the common binding sites, X
Common
. While the
site-type X
Common
is available for each condition, the degree to which it is available may be
limited by the metal exposure history on the column and the comparative affinities of each
metal for those sites. To account for this, a secondary set of data was incorporated into the
