Growing drop experiment

Even in mass-transfer-limiled processes, excursions in selectivity can be observed at finite contact times. This is predicted by rate models as simple as Eq. (8.4-1) for two metals with different equilibrium constant valoes, The phenomenon involves initially fast coextraction followed by crowding out of the less preferred metal during coijipetidon for extractant. This has been observed during simultaneous extraction of copper and zinc chlorides by TIOA in a growing-drop experiment"1 21 and in extraction or uranyl nitrate and nitric acid by TBP in a Lewis cell.2 as shown in Fig. 8.4-5. 

Fig. 5.18 Principle of a growing drop experiment according to Passerone et al. (1991) S - motor driven syringe, C - capillary, DPT - differential pressure transducer, LI and L2 - the two liquids...

FIG. 17 (a) Typical current (/)-time (t) characteristics for bromine transfer from an aqueous phase to an expanding DCE drop measured at a 1 qm diameter Pt UME positioned beneath the growing drop. The images (l)-(4) correspond to the points indicated on the transient. The final drop size in (4) is 1.00 mm. Data are analyzed to produce (normalized) concentration vs. distance profiles, such as that in (b), showing experiment (O) and theory for a transport-limited process (—). 

The kinetics of the adsorption process taking place at the surface of a growing drop or bubble is important for the interpretation of data from drop volume or maximum bubble pressure experiments. The same problem has to be solved in any other experiment based on growing drops or bubbles, such as bubble and drop pressure measurements with continuous, harmonic or transient area changes (for example Passerone et al. 1991, Liggieri et al. 1991, Horozov et al. 1993, Miller at al. 1993, MacLeod Radke 1993, Ravera et al. 1993, Nagarajan Wasan 1993). 

Eq. (4.45) can be used to describe the adsorption process at the surface of growing drops. The analysis of this rather complex equation showed that the rate of adsorption at the surface of a growing drop with linear volume increase, as it is arranged in a usual drop volume experiment, is about 1/3 of that at a surface with constant area. This result is supported by experimental findings (Davies et al. 1957, Kloubek 1972, Miller Schano 1986, 1990) and also by an approximate solution first discussed by Delahay Trachtenberg (1957) and Delahay Pike (1958) ... 

Although this is a very complex equation, it allows to take into consideration any function of R(t), and consequently A(t), resulting from experiments with growing drops or bubbles. In combination with an adsorption isotherm (diffusion-controlled case) or a transfer mechanism (mixed diffusion-kinetic-controlled model) it describes the adsorption process at a growing or even receding drop. Eq. (4.48) can be applied in its present form only via numerical calculations and an algorithm is given by MacLeod Radke (1994). 

The following so-called dynamic capillary method was developed by Van Hunsel Joos (1987b) and complements the area of application with respect to other methods. This method allows measurements from 50 ms up about 1 s, similar to the inclined plate and growing drop techniques described above, and can be used at liquid/liquid and liquid/gas interfaces without modification. The principle of the experiment is schematically given in Fig. 5.23. Two fluids are contained in a tube of diameter R. The interface (or surface in case of studies at the water/air interface) is located in such a way that its interfacial tension can be measured by the capillary rise of the lower liquid in a narrow capillary c, which connects the both fluids. The height of the capillary rise h is determined via a cathetometer Cat. 

The use of an equation as complex as Eq. (67) requires a lot of numerical calculations so that approximate solutions are very favorable. The first model to describe the adsorption at the surface of a growing drop was derived by Ilkovic in 1938 (107). The boundary conditions were chosen such that the model corresponded to a mercury drop in a polarography experiment. These conditions, however, are not suitable for describing the adsorption of surfactants at a liquid-drop surface. Delahay and coworkers (108, 109) used the theory of Ilkovic and derived an approximation suitable for the description of adsorption kinetics at a growing drop. The relationship was derived only for the initial period of the adsorption process ... 

E is found by bisecting the vertical line drawn from the limiting current to the residual current line, FG in figure P.3. FG is the wave height, and a horizontal line from K gives C and thus the half-wave potential, E. E has a characteristic value for an electrode reaction, and can be used for qualitative analysis. It is related to the standard electrode potential, E, by equation (P.12), which involves the activity coefficients and the diffusion characteristics in the solution and in the growing drop. Activation overpotential may also contribute to E , and it is best regarded as an independent constant for the reaction, which can be determined in separate calibration experiments. 

In order to define the conditions of the growing cultures, buffered medium (VL) inoculated with E, coli ATCC 11775 and supplemented with nitrate, glucose and DMA was incubated at 37 C, and pH, nitrite concentration, nitrate concentration, cell growth and nitrosamine formation were followed (Fig. 1). Within 2 hrs, >90% of the nitrate is converted to nitrite (some of the nitrite is further reduced) and over 8 hrs the pH drops from 7.3 to 6.0. This would indicate that in experiments carried out for 20 hrs or more the control medium should be adjusted to pH 6.0 to 6.5 and nitrite should be added rather than nitrate. Such a control medium (VL) was supplemented with nitrite and DMA and NDMA formation was followed (Fig. 2). It can be seen that even without the addition of cells the rate of nitrosation is 4 fold greater than... 

In a polarographic experiment, a potential difference E is applied across the cell consisting of the dropping-mercury electrode and a nonpolarizable interface (e.g., a calomel electrode). In response to this potential difference, a current density i flows across the drop/solution interface. As each drop grows and falls, however, the surface area of the drop also grows, and then becomes effectively zero when the drop falls. Thus, the instantaneous current (current density times surface area) shows fluctuations, but the mean current is a unique function of the potential difference across the drop/solution interface, and therefore of that across the cell. 

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