MTWCR model

The more popular version of the MTWCR model seems to have been that of Rod [57]. It has been used to describe the case of divalent metal extraction by an acidic extractant [38, 58, 59, 60, 61]. Its basic ingredients are the following. 

Let HR denote the acid extractant, the metal ion and MR2 the extracted complex. Then the extraction reaction is considered to proceed according to the following steps 

In the above reactions the first step describes the fast partitioning of the extractant in the aqueous phase followed by fast dissociation of the extractant in step two the third and fourth steps describe the formation of the metal complexes the last step involves the rapid partitioning of the metal complex into the organic phase. 

Some acid extractants, such as D2EHPA, are strongly dimerized in the organic phase and consequently step 1 should be replaced by HR2 2 HR [62] in that case it has been also assumed sometimes [61] that in this case the complexation reaction in the aqueous phase involved the species HR  

We now present the main equations and results given in ref. [57]. The ingredients of this MTWCR model do not seem to have been reviewed so far. 

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The MTWCR model presented below was first proposed by Rod [57]. Due to the complexity of the problem, the following assumptions were adopted... 

Typical concentration profiles [59] for the MTWCR model are shown in Figure... 

Figure 3.9 Concentration profiles in the MTWCR model (quiescent films in both phases and reaction zone denoted by dashed lines and dotted line, respectively).

Let us notice lastly that, in refs. [59, 68], it was stated that eq 3.53 could be obtained by Astarita s method [66], used previously in a pioneering MTWCR model [51]. The use of Astarita s method within the MTWCR model of Rod has been explained in a PhD thesis [67],... 

First, in at least two studies [38, 58] various interfacial mechanisms have been found inadequate for describing the experimental data, which led the authors to use the MTWCR model. 

The MTWCR model introduced by Rod has been used to interpret mainly experiments performed with the RDC of Albery because this technique allows an estimation of the diffusion layer thickness. However, since the latter depends on the species considered through its diffusion coefficient (cf. eq 3.22), it is not clear which value was taken for the film thickness, which is supposed to be unique for a given phase in the film model, for all the species involved (cf. Figure 9). 

However, in some cases (e.g. [38]) the model was not successful. This happened in the case of the extraction of zinc and nickel with HDEHP using the RDC technique, and this was interpreted as follows in the case of zinc the transfer was found to be controlled by mass transfer alone because the chemical reaction was too fast to limit the kinetics in the case of nickel the reaction was too slow and much extractant was partitioning to the aqueous phase without complexing the metal cation, thus making it impossible to use the MTWCR model of Rod [57] presented above. 

Concentration profiles in the MTWCR model (quiescent films in both... 

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