Rotating disk diffusion

This paper describes a development effort made in the small demineralizer area (less than 500 gallons per day). The concept discussed is a rotating disk diffusion still capable of being multistaged yet remaining fundamentally simple. 

Volt mmetiy. Diffusional effects, as embodied in equation 1, can be avoided by simply stirring the solution or rotating the electrode, eg, using the rotating disk electrode (RDE) at high rpm (3,7). The resultant concentration profiles then appear as shown in Figure 5. A time-independent Nernst diffusion layer having a thickness dictated by the laws of hydrodynamics is estabUshed. For the RDE,... 

Fig. 3. Steady state concentration profiles of catalyst and substrate species in the film and diffusion layer for for various cases of redox catalysis at polymer-modified electrodes. Explanation of layers see bottom case (S + E) f film d diffusion layer b bulk solution i, limiting current at the rotating disk electrode other symbols have the same meaning as in Fig. 2 (from ref.

Pollard and Newman" have also studied CVD near an infinite rotating disk, and the equations we solve are essentially the ones stated in their paper. Since predicting details of the chemical kinetic behavior is a main objective here, the system now includes a species conservation equation for each species that occurs in the gas phase. These equations account for convective and diffusive transport of species as well as their production and consumption by chemical reaction. The equations stated below are given in dimensional form since there is little generalization that can be achieved once large chemical reaction mechanisms are incorporated. 

In such systems the researcher can electrochemically clean and precondition the metal electrode before each run to provide an identical surface for the anodic and the cathodic half-reactions as well as for the catalytic reaction between them. Use of a rotating disk electrode/ckatalyst also allows surface- and diffusion-controlled processes to be easily distin-guished. ... 

The constancy of the diffusion layer over the entire surface and thus the uniform current-density distribution are important features of rotating-disk electrodes. Electrodes of this kind are called electrodes with uniformly accessible surface. It is seen from the quantitative solution of the hydrodynamic problem (Levich, 1944) that for RDE to a first approximation... 

Thin catalyst layers on a GC rotating disk electrode (RDE) or a rotating ring-disk electrode (RRDE) serve for studies of ORR kinetics. In order to separate the kinetic current from the measured current j, Schmidt and co-workers [Schmidt et al., 1998b] corrected the latter for the influence of oxygen diffusion in the aqueous electrolyte and in the polymer film using the foUowing equation ... 

Two examples will now be given of solution of the convective diffusion problem, transport to a rotating disk as a stationary case and transport to a growing sphere as a transient case. Finally, an engineering approach will be mentioned in which the solution is expressed as a function of dimensionless quantities characterizing the properties of the system. 

As a rotating disk is a very useful device for many types of electrochemical research, convective diffusion to a rotating disk, treated theoretically by V. G. Levich, will be used here as an example of this type of transport process. Consider a disk in the xz plane, rotating around the y axis with radial velocity a) (see Fig. 2.22). If the radius of the disk is sufficiently larger... 

In convective diffusion to a rotating disk, the characteristic velocity V0 is given by the product of the disk radius r, as a characteristic dimension of the system, and the radial velocity co, so that the Reynolds number is given by the equation... 

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 ... 

This chapter provides analytical solutions to mass transfer problems in situations commonly encountered in the pharmaceutical sciences. It deals with diffusion, convection, and generalized mass balance equations that are presented in typical coordinate systems to permit a wide range of problems to be formulated and solved. Typical pharmaceutical problems such as membrane diffusion, drug particle dissolution, and intrinsic dissolution evaluation by rotating disks are used as examples to illustrate the uses of mass transfer equations. 

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

DP McNamara, GL Amidon. Dissolution of acidic and basic compounds from the rotating disk Influence of convective diffusion and reaction. J Pharm Sci 75 858-868, 1986. 

Fig. 4. Migration contribution to the limiting current in acidified CuS04 solutions, expressed as the ratio of limiting current (iL) to limiting diffusion current (i ) r = h,so4/(( h,so, + cCuS(>4). "Sulfate refers to complete dissociation of HS04 ions. "bisulfate" to undissociated HS04 ions. Forced convection" refers to steady-state laminar boundary layers, as at a rotating disk or flat plate free convection refers to laminar free convection at a vertical electrode penetration to unsteady-state diffusion in a stagnant solution. [F rom Selman (S8).]...

Mass-transfer rates from limiting-current measurements in well-supported solutions should invariably be correlated with ionic and not with molecular diffusivities. The former can be calculated from limiting-current measurements, for example, at a rotating-disk electrode. 

The diffusivities thus obtained are necessarily effective diffusivities since (1) they reflect a migration contribution that is not always negligible and (2) they contain the effect of variable properties in the diffusion layer that are neglected in the well-known solutions to constant-property equations. It has been shown, however, that the limiting current at a rotating disk in the laminar range is still proportional to the square root of the rotation rate if the variation of physical properties in the diffusion layer is accounted for (D3e, H8). Similar invariant relationships hold for the laminar diffusion layer at a flat plate in forced convection (D4), in which case the mass-transfer rate is proportional to the square root of velocity, and in free convection at a vertical plate (Dl), where it is proportional to the three-fourths power of plate height. 

The effective diffusivities determined from limiting-current measurements appear at first applicable only to the particular flow cell in which they were measured. However, it can be argued plausibly that, for example, rotating-disk effective diffusivities are also applicable to laminar forced-convection mass transfer in general, provided the same bulk electrolyte composition is used (H8). Furthermore, the effective diffusivities characteristic for laminar free convection at vertical or inclined electrodes are presumably not significantly different from the forced-convection diffusivities. 

Effective ionic diffusivities at a rotating-disk electrode are calculated from the Levich equation as derived for constant physical properties, used here in inverted form ... 

This value is based on Cu2+ diffusivities calculated Arvia et al. (A5) from limiting-current measurements at a rotating-disk electrode by, with CuS04 concentrations below 0.1 M. In practical applications (e.g., copper refining or electrowinning) higher Cu2+ concentrations are often required, as is also the case in free-convection limiting-current measurements. 

Recently, effective diffusivities at a rotating-disk electrode were determined for a wide range of CuS04 and H2S04 concentrations (H7, S8, Lla). These data, together with the data of Arvia et al. (A5), yield for the mobility product, at or near 25°C ... 

Effective diffusivities for these ions in equimolar concentration ratio and with various inert electrolytes, have been determined by several methods (see Table III). The mobility products obtained from capillary cell (stagnant diffusion) and rotating-disk measurements are in fairly good agreement. 

CC, Capillary cell (stagnant diffusion) DS, diffusion to spherical electrode ICT. from mobility measurements (International Critical Tables) LFA. laminar-flow annular cell (Leveque relation) LM, from limiting mobility at infinite dilution POL. polarographic cell RDE, rotating-disk electrode. 

Measurements of rotating-disk effective diffusivities (H7, S8)forCu2+ ion (see Section I V,C) indicate that a greater increase in surface area takes place when the limiting current is generated by linear potential decrease than... 

In this connection it should be noted that the most careful studies (N9a, D2) undertaken to confirm the rotating-disk correlation, Eq. (la) in Table VII, used the iodine reduction reaction with very small reactant concentrations, and employed diaphragm cell diffusivities of KI j in KI. 

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