Erratum to: Can ligand addition to soil enhance Cd phytoextraction? A mechanistic model study
Erratum
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Erratum to: Environ Sci Pollut Res (2014) 21:12811–12826
DOI 10.1007/s11356-014-3218-8
In the paper “Can ligand addition to soil enhance Cd phytoextraction? A mechanistic model study” by Zhongbing Lin, André Schneider, Christophe Nguyen, and Thibault Sterckeman published in the Environmental Science and Pollution Research (November 2014, Volume 21, Issue 22, pp 12811-12826; http://dx.doi.org/10.1007/s11356-014-3218-8), there were nine typesetting mistakes and two other errors which must be corrected as follows.
Page 12813, Eq. (1) must be replaced by
$$ \mathrm{M}+\mathrm{L}\underset{k_{\mathrm{d}}^{\mathrm{M}\mathrm{L}}}{\overset{k_{\mathrm{a}}^{\mathrm{M},\mathrm{L}}}{\rightleftarrows }}\mathrm{ML} $$
(1)
Page 12813, Column 2, comas should be added to Line 1 so the beginning of the sentence reads
“In Eq. (2), [Cd], [Ca], [L], [CdL] and [CaL] represent the concentrations…”
Page 12813, Eq. (5) must be replaced by
$$ \left\{\begin{array}{c}\hfill \theta \frac{\partial }{\partial t}\left[Cd\right]=\frac{1}{r}\frac{\partial }{\partial r}\left(rf\theta {D}_{\mathrm{Cd}}\frac{\partial }{\partial r}\left[Cd\right]+{r}_0{v}_0\left[Cd\right]\right)+\theta \left({k}_{\mathrm{d}}^{\mathrm{Cd}\mathrm{L}}\left[CdL\right]-{k}_{\mathrm{a}}^{\mathrm{Cd},\mathrm{L}}\left[Cd\right]\left[L\right]\right)+\left({k}_{\mathrm{d}\mathrm{es}}\left\{CdS\right\}-\theta {k}_{\mathrm{a}\mathrm{ds}}\left[Cd\right]\right)\hfill \\ {}\hfill \left(\theta +{b}_{\mathrm{L}}\right)\frac{\partial }{\partial t}\left[CdL\right]=\frac{1}{r}\frac{\partial }{\partial r}\left(rf\theta {D}_{\mathrm{L}}\frac{\partial }{\partial r}\left[CdL\right]+{r}_0{v}_0\left[CdL\right]\right)+\theta \left({k}_{\mathrm{a}}^{\mathrm{Cd},\mathrm{L}}\left[Cd\right]\left[L\right]-{k}_{\mathrm{d}}^{\mathrm{Cd}\mathrm{L}}\left[CdL\right]\right)\hfill \\ {}\hfill \left(\theta +{b}_{\mathrm{Ca}}\right)\frac{\partial }{\partial t}\left[Ca\right]=\frac{1}{r}\frac{\partial }{\partial r}\left(rf\theta {D}_{\mathrm{Ca}}\frac{\partial }{\partial r}\left[Ca\right]+{r}_0{v}_0\left[Ca\right]\right)+\theta \left({k}_{\mathrm{d}}^{\mathrm{Ca}\mathrm{L}}\left[CaL\right]-{k}_{\mathrm{a}}^{\mathrm{Ca},\mathrm{L}}\left[Ca\right]\left[L\right]\right)\hfill \\ {}\hfill \left(\theta +{b}_{\mathrm{L}}\right)\frac{\partial }{\partial t}\left[CaL\right]=\frac{1}{r}\frac{\partial }{\partial r}\left(rf\theta {D}_{\mathrm{L}}\frac{\partial }{\partial r}\left[CaL\right]+{r}_0{v}_0\left[CaL\right]\right)+\theta \left({k}_{\mathrm{a}}^{\mathrm{Ca},\mathrm{L}}\left[Ca\right]\left[L\right]-{k}_{\mathrm{d}}^{\mathrm{Ca}\mathrm{L}}\left[CaL\right]\right)\hfill \\ {}\hfill \left(\theta +{b}_{\mathrm{L}}\right)\frac{\partial }{\partial t}\left[L\right]=\frac{1}{r}\frac{\partial }{\partial r}\left(rf\theta {D}_{\mathrm{L}}\frac{\partial }{\partial r}\left[L\right]+{r}_0{v}_0\left[L\right]\right)+\theta \left({k}_{\mathrm{d}}^{\mathrm{Cd}\mathrm{L}}\left[CdL\right]-{k}_{\mathrm{a}}^{\mathrm{Cd},\mathrm{L}}\left[Cd\right]\left[L\right]\right)+\theta \left({k}_{\mathrm{d}}^{\mathrm{Ca}\mathrm{L}}\left[CaL\right]-{k}_{\mathrm{a}}^{\mathrm{Ca},\mathrm{L}}\left[Ca\right]\left[L\right]\right)\hfill \\ {}\hfill \frac{\partial }{\partial t}\left\{CdS\right\}=\theta {k}_{\mathrm{a}\mathrm{ds}}\left[Cd\right]-{k}_{\mathrm{d}\mathrm{es}}\left\{CdS\right\}\hfill \end{array}\right\} $$
(5)
Page 12813, the equation number of Eq. (9) must be added
$$ J\left[Cd,CdL,Ca,CaL,L,CdS\right]=\left\{\begin{array}{ccc}\hfill \left[-\frac{I_{\max}\left[Cd\right]}{K_m+\left[Cd\right]},- TSCF{v}_0\left[CdL\right],0,0,- TSCF{v}_0\left[L\right],0\right]\hfill & \hfill r={r}_0\hfill & \hfill t\ge 0\hfill \\ {}\hfill \left[0,0,0,0,0,0\right]\hfill & \hfill r={r}_1\hfill & \hfill t\ge 0\hfill \end{array}\right\} $$
(9)
Page 12817, Eq. (27) must be replaced by
$$ \max \left(0.01,\kern0.5em 0.9943\theta -0.1722\right)<f<1.3268\theta +0.0022 $$
(27)
Page 12818, Eq. (28) must be replaced by
$$ \left\{\begin{array}{c}\hfill {\beta}_1=\frac{{\left[Cd\right]}_0}{{\left[Cd\right]}_{0\_C}}=\frac{\theta +{b}_{\mathrm{Cd}}}{\left(\theta +{b}_{\mathrm{Cd}}\right)+\left(\theta +{b}_{\mathrm{L}}\right){K}_{\mathrm{S}}^{\mathrm{Cd}\mathrm{L}}{\left[L\right]}_0}\hfill \\ {}\hfill {\beta}_2=\frac{{\left[Cd\right]}_0+{\left[CdL\right]}_0}{{\left[Cd\right]}_{0\_C}}=\frac{\left(\theta +{b}_{\mathrm{Cd}}\right)\left(1+{K}_{\mathrm{S}}^{\mathrm{Cd}\mathrm{L}}{\left[L\right]}_0\right)}{\left(\theta +{b}_{\mathrm{Cd}}\right)+\left(\theta +{b}_{\mathrm{L}}\right){K}_{\mathrm{S}}^{\mathrm{Cd}\mathrm{L}}{\left[L\right]}_0}\hfill \\ {}\hfill {\beta}_3=\frac{\left(\theta +{b}_{\mathrm{L}}\right){\left[CdL\right]}_0}{{\left\{CdS\right\}}_0}\hfill \end{array}\right\} $$
(28)
Page 12818, Column 2, the beginning of the sentence in Line 1 must be replaced by
“The mean concentrations of Cd2+ (\( \overline{{\left[Cd\right]}_{\mathrm{r}0}} \)) and CdL (\( \overline{{\left[CdL\right]}_{\mathrm{r}0}} \)) in solution…”
Page 12818, Eq. (29) must be replaced by
$$ \left\{\begin{array}{cc}\hfill \begin{array}{c}\hfill \overline{{\left[Cd\right]}_{\mathrm{r}0}}=\frac{1}{T}{\displaystyle \underset{0}{\overset{T}{\int }}\left[Cd\right]dt}\hfill \\ {}\hfill \overline{{\left[CdL\right]}_{\mathrm{r}0}}=\frac{1}{T}{\displaystyle \underset{0}{\overset{T}{\int }}\left[CdL\right]dt}\hfill \end{array}\hfill & \hfill r={r}_0\hfill \end{array}\right\} $$
(29)
Page 12818, Eq. (30) must be replaced by
$$ {\Delta}_{\mathrm{CdL}}={k}_{\mathrm{d}}^{\mathrm{CdL}}\overline{{\left[CdL\right]}_{\mathrm{r}0}} $$
(30)
Page 12818, Eq. (31) must be replaced by
$$ \left\{\begin{array}{cc}\hfill \begin{array}{c}\hfill {E}_{\mathrm{Cd}\mathrm{L}}=\frac{1}{K_{\mathrm{S}}^{\mathrm{Cd}\mathrm{L}}}\frac{1}{T}{\displaystyle \underset{0}{\overset{T}{\int }}\frac{\left[CdL\right]}{\left[Cd\right]\left[L\right]}dt}\hfill \\ {}\hfill {E}_{\mathrm{Cd}\mathrm{S}}=\frac{1}{b_{\mathrm{Cd}}}\frac{1}{T}{\displaystyle \underset{0}{\overset{T}{\int }}\frac{\left\{CdS\right\}}{\left[Cd\right]}dt}\hfill \end{array}\hfill & \hfill r={r}_0\hfill \end{array}\right\} $$
(31)
Page 12, the caption of Fig. 5 must be replaced by
“Fig. 5 Empirical cumulative distribution function (ECDF) of log10-equilibrium indicators of complexation (log10(E CdL)) and sorption kinetics (log10(E CdS)) at root surface in scenarios S + H and S + L”
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