Rotating cylinder mass transfer

Tank Cells. A direct extension of laboratory beaker cells is represented in the use of plate electrodes immersed into a lined, rectangular tank, which may be fitted with a cover for gas collection or vapor control. The tank cell, which is usually undivided, is used in batch or semibatch operations. The tank cell has the attraction of being both simple to design and usually inexpensive. However, it is not the most suitable for large-scale operation or where forced convection is needed. Rotating cylinders or rotating disks have been used to overcome mass-transfer problems in tank cells. An example for electroorganic synthesis is available (46). 

However, flow generated by a cylinder rotating at high speed was subsequently used by others, and in particular by King and co-workers (K3, K4a), to demonstrate that dissolution and electrochemical corrosion may both be transport limited. The dependence of the mass-transfer coefficient on the rotation rate and on the diffusivity of the dissolving species was established by correlation of experimental data (see Table VII, System 43). 

It was shown above that the limiting c.d. increases with velocity raised to the 0.8 power and the pipe diameter raised to the -0.2 power for piping corrosion rates that are controlled by mass transport. In contrast, it is evident that the shear stress increases with the fluid velocity raised to the 1.75 power and the pipe diameter raised to the -0.2 power. Thus equality of shear stress does not give equality of mass transfer rates. In both cases corrosion is enhanced in pipes of smaller diameter for the same solution velocity. Such a relationship can be rationalized based on the effect of pipe diameter on the thickness of the mass transport and hydrodynamic boundary layers for a given fixed geometry. Cameron and Chiu (19) have derived similar expressions for defining the rotating cylinder rotation rate required to match the shear stress in a pipe for the case of velocity-... 

Silverman has defined a number of useful expressions that allow one to utilize the rotating cylinder method with a variety of practical geometries (12,15). Both shear stresses and mass transfer coefficients are included in the derivations described (12). Table 1 in NACE standard TM-0270-72 summarized the various features of experimental systems for studying flow induced corrosion (22). 

J. Rotating cylinder in an infinite liquid, no forced flow ji> = — Ngf4 = 0.07911V j 30 V Results presented graphically to NRe = 241,000. A/jjg = where v = —= peripheral velocity P 2 [E] Used with arithmetic concentration difference. Useful geometry in electrochemical studies. 112 < NRe <, 100,000. 835 < NSc < 11490 k = mass-transfer coefficient, cm/s co = rotational speed, radian/s. [60] [138] p. 238... 

Heitz [22] employed the mass transfer-controlled reaction between zinc and iodine to explore the correlations between mass transport in a pipe, to a rotating disk, and to a rotating cylinder. The correlations were expressed in terms of the equivalent velocity through the tube as (quoted by Poulson [17])... 

Ellison and Schmeal [19] explored a similar approach by using the corrosion of carbon steel in concentrated sulfuric acid as the mass-transpoit/corrosion probe. A model was proposed to reconcile corrosion rate data from pipe and rotating cylinder geometries based on the premise that the corrosion rate is controlled by the transport of Fe + from the interface. The data were subsequently used by Silverman [21] to construct a more precise model for correlating mass-transfer effects between pipe flow and a rotating cylinder. 

Silverman [21] derived velocity correlations between a rotating cylinder (mO, pipe flow (m2), annulus flow (1/3), and an impinging jet (wall jet region only, 1/4), as listed in Table 2. These equations assume that the appropriate transformations are to be made on the basis of equal mass-transfer rates for the different geometries. Silverman [21] also explored the case where the equality of surface shear stress is the appropriate criterion, on the basis that the equality of the shear stress will ensure the same corrosion processes for the various geometries. We stress that the equations listed in Table 2 must be used with great caution because they are based on the... 

Table 2. Velocity of a rotating cylinder that yields the same mass-transfer coefficients for the indicated geometries (after Silverman [21]).

The problem of transferring corrosion rate data from one hydrodynamic system to another has also been considered in some depth by Chen et al. [18], by using the corrosion of 90 10 Cu Ni alloy in aerated 1 m NaCl solution at 25 °C in pipe-flow, annular-flow, and rotating-cylinder systems. The authors recognized that two mass-transfer processes should be distinguished transfer through the diffusion boundary layer in e solution (mass-transfer coefficient, h), and transfer through the corrosion product film ( f). The overall mass-transfer coefficient was defined as... 

Rotating cylinders, described in Section 11.8, are popular experimental systems because the system setup is relatively simple to use and, at moderate rotation speeds, the flow is turbulent and yields a uniform mass-transfer-controlled current density. Empirical correlations are available that relate the cylinder rotation speed to the mass-transfer coefficient. ... 

The rotating cylinder is a popular tool for electrochemical research because it is convenient to use and both the primary and mass-transfer-limited current distributions are uniform.A schematic representation of the rotating cylinder is presented in Figure 11.12. At very low rotation speeds, the fluid flows in concentric circles around the rotating cylinder, satisfying a no-slip condition at the rotating inner cylinder and at the stationary outer cylinder. Since there is no velocity component in the radial direction, there is no convective enhancement to mass transfer. 

Figure 11.12 Schematic representation of a rotating cylinder electrode a) entire cylinder used as working electrode. This geometry provides a uniform current and potential distribution at and below the mass-transfer-limited current, b) band-shape cylindrical coupon used as a working electrode. This geometry is useful for studies conducted at the open-circuit condition.

This simple flow pattern becomes unstable at higher rotation speeds, and a cellular flow pattern (termed Taylor vortices) is observed. Taylor vortices provide an irregular enhancement to mass transfer. At still higher rotation speeds, the flow becomes fully turbulent. Mass-transfer studies with rotating cylinders are conducted in the turbulent flow regime because the flow provides a uniform enhancement to mass transfer. 

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