Rotating mass transport

If a fluid is placed between two concentric cylinders, and the inner cylinder rotated, a complex fluid dynamical motion known as Taylor-Couette flow is established. Mass transport is then by exchange between eddy vortices which can, under some conditions, be imagmed as a substantially enlranced diflfiisivity (typically with effective diflfiision coefficients several orders of magnitude above molecular difhision coefficients) that can be altered by varying the rotation rate, and with all species having the same diffusivity. Studies of the BZ and CIMA/CDIMA systems in such a Couette reactor [45] have revealed bifiircation tlirough a complex sequence of front patterns, see figure A3.14.16. 

Overall, the RDE provides an efficient and reproducible mass transport and hence the analytical measurement can be made with high sensitivity and precision. Such well-defined behavior greatly simplifies the interpretation of the measurement. The convective nature of the electrode results also in very short response tunes. The detection limits can be lowered via periodic changes in the rotation speed and isolation of small mass transport-dependent currents from simultaneously flowing surface-controlled background currents. Sinusoidal or square-wave modulations of the rotation speed are particularly attractive for this task. The rotation-speed dependence of the limiting current (equation 4-5) can also be used for calculating the diffusion coefficient or the surface area. Further details on the RDE can be found in Adam s book (17). 

Appropriate electroanalytical procedures to verify the one or other case have been given in the references of this section. The main techniques are cyclic voltammetry, chronoamperometry, chronocoulometry, and rotating disk voltammetry. The last one appears to be best suited since constant mass transport in the film is a very important feature as outlined aixive Table 2 gives examples for... 

The devolatilization of a component in an internal mixer can be described by a model based on the penetration theory [27,28]. The main characteristic of this model is the separation of the bulk of material into two parts A layer periodically wiped onto the wall of the mixing chamber, and a pool of material rotating in front of the rotor flights, as shown in Figure 29.15. This flow pattern results in a constant exposure time of the interface between the material and the vapor phase in the void space of the internal mixer. Devolatilization occurs according to two different mechanisms Molecular diffusion between the fluid elements in the surface layer of the wall film and the pool, and mass transport between the rubber phase and the vapor phase due to evaporation of the volatile component. As the diffusion rate of a liquid or a gas in a polymeric matrix is rather low, the main contribution to devolatilization is based on the mass transport between the surface layer of the polymeric material and the vapor phase. 

Eqs. (40)-(45) describe the behavior of a mass transport process occurring at very large Schmidt numbers. For finite values of Sc, Chin [16] extended the 0-series expansion analysis and obtained the following asymptotic series for Sfiav on a rotating hemisphere ... 

The RHSE has the same limitation as the rotating disk that it cannot be used to study very fast electrochemical reactions. Since the evaluation of kinetic data with a RHSE requires a potential sweep to gradually change the reaction rate from the state of charge-transfer control to the state of mass transport control, the reaction rate constant thus determined can never exceed the rate of mass transfer to the electrode surface. An upper limit can be estimated by using Eq. (44). If one uses a typical Schmidt number of Sc 1000, a diffusivity D 10 5 cm/s, a nominal hemisphere radius a 0.3 cm, and a practically achievable rotational speed of 10000 rpm (Re 104), the mass transfer coefficient in laminar flow may be estimated to be ... 

An alternative to the rotating disk method in a quiescent fluid is a stationary disk placed in a rotating fluid. This method, like the rotating disk, is based on fluid mechanics principles and has been studied using benzoic acid dissolving into water [30], Khoury et al. [31] applied the stationary disk method to the study of the mass transport of steroids into dilute polymer solutions. Since this method assumes that the rotating fluid near the disk obeys solid body rotation, the stirring device and the distance of the stirrer from the disk become important considerations when it is used. A similar device was developed by Braun and Parrott [32], who used stationary spherical tablets in a stirred liquid to study the effect of various parameters on the mass transport of benzoic acid. 

Mauger et al. [35] used the rotating filter assembly to assess the mass transport kinetics of particle populations of a steroid and demonstrated the applicability of a proposed diffusion model used to interpret the data. 

Rotating disk method (free boundary method) Diffusion coefficient determination from solids mass transport studies 25-29... 

Rotating filter assembly (free boundary method) Mass transport studies from finely divided drug powders 34,35... 

G Hansford, M Litt. Mass transport from a rotating disk into power-law liquids. Chem Eng Sci 23 849, 1968. 

MZ Southard, DW Green, VJ Stella, KJ Himmelstein. Dissolution of ionizable drugs into unbuffered solution A comprehensive model for mass transport and reaction in the rotating disk geometry. Pharm Res 9 58-69, 1992. 

In contrast to the rotating disc electrode, mass transport to the ring is nonuniform. Nevertheless, the thickness of the diffusion layer Spj, which depends on the coordinate x in the direction of flow, and the rate of mass transport can be calculated. We consider a simple redox reaction, and rewrite Eq. (14.5) in the form ... 

We note in passing that the same equation holds for the rotating disc electrode. Though the mass transport on the ring is nonuniform, the ratio ared/a0x) and hence also, turns out to be constant, so Eq. 

Robinson and Walsh have reviewed earlier cell designs. The performance of a 500 A pilot plant reactor for copper ion removal is described. Simplified expressions were derived for mass transport both in single pass [243] and batch recirculation [244]. For a detailed discussion of the principle and the role of the rotating cylinder electrode reactor in metal ion removal the reader is referred to Refs. [13] and [241] (46 references). 

There are a few electrochemical techniques in which the working electrode is moved with respect to the solution (i.e. either the solution is agitated or the electrode is vibrated or rotated). Under these conditions, the thickness of the diffusion layer decreases so that the concentration gradient increases. Since the rate of the mass transport to an electrode is proportional to the concentration gradient (Chapter 1, Section 4.2.2), the thinning of the diffusion layer leads to an increase of the mass transport, and hence to an increase of the faradaic currents. 

Figure 5.12 Typical cyclic voltammogram at 0.3mV/s of a hydrogenase film adsorbed at a pyrolytic graphite edge electrode immersed in a pH 9.00 hydrogen saturated solution at 45°C (active-inactive interconversion is too slow to be reasonably studied at lower temperatures) and rotating at ISOOrpm. Under these conditions mass transport of hydrogen is not rate limiting.

In Section 7.2, we looked at electroanalytical systems where the electrode rotates while the bulk of the solution remained still. In this present section, we will reverse this experimental concept by considering the case where it is the solution which flows - this time past a stationary electrode. Here, we shall be looking at flow ceils and channel electrodes. The principal mode of mass transport in both cases is convection, since the solution moves relative to the electrode. 

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