Rotating disks

Care must be taken with the convective terms in the transport equations to account for the axial flow direction. In the stagnation-flow problems for flow against a surface, the axial velocity is always negative (i.e., flowing toward the surface). The convective term in the radial-momentum equation uses the following upwind difference approximation  

Because the role of convection is to transfer information in the direction of the flow, the derivative dV/dz must be approximated by a difference formula that uses information that is upstream of the flow. If the derivative is approximated as (Vj - Vj- )/dz when the velocity is negative, then the derivative communicates information ahead of the flow, which is physically unrealistic. Moreover, and importantly, such a downwind difference formula can cause severe numerical instabilities. From the point of view of a control volume, recall the origin of the convective terms in the substantial derivative. They represent the mass, momentum, or energy that is carried into or out of the control volume from the surrounding regions with the fluid flow. Thus the term must have a directional behavior that depends on the local fluid velocity. 

While the direction of the axial velocity does not change in many of the stagnation flows, in some it does. Certainly the opposed flows Section 6.10) have both positive and negative velocities. So the convective difference formulas must change depending on the velocity direction. A sigmoid function can be used to switch the difference formula in a smoothly varying way as 

The rotating disk is a configuration that was first identified and analyzed by Von Karman [418], and studied extensively for its similarity reduction of the Navier-Stokes equations [65,374], It was later recognized for its value in chemical vapor deposition processes 

The governing equations for the rotating disk must include a circumferential momentum equation, and the circumferential velocity becomes a dependent variable. Also the circumferential velocity contributes to the radial-momentum equation. As simplified by the general equations of Section 6.2, the nonreacting, constant-property equations are summarized 

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Town, J. L. MacLaren, F. Dewald, H. D. Rotating Disk Voltammetry Experiment, /. Chem. Educ. 1991, 68, 352-354. 

Fig. 15. Mechanically agitated columns (a) Scheibel column (b) rotating-disk contactor (RDC) (c) asymmetric rotating-disk (ARD) contactor (d) Oldshue-Rushton multiple-mixer column (e) Kuhni column and (f) reciprocating-plate column.

The rotating-disk contactor (RDC), developed in the Netherlands (158) in 1951, uses the shearing action of a rapidly rotating disk to interdisperse the phases (Eig. 15b). These contactors have been used widely throughout the world, particularly in the petrochemical industry for furfural [98-01-1] and SO2 extraction, propane deasphalting, sulfolane [126-33-0] extraction for separation of aromatics, and caprolactam (qv) [105-60-2] purification. Columns up to 4.27 m in diameter are in service. An extensive study (159) has provided an excellent theoretical framework for scale-up. A design manual has also been compiled (160). Detailed descriptions and design criteria for the RDC may also be found (161). 

Shell process. Universal Oil Pro-ducts sulfolane sulfolane selectivity and capacity insensitive to water content caused by steam-stripping during solvent recov-ery heavy paraffinic countersolvent use 120 rotating-disk contactor, up to 4 m in diameter the high selectivity and capacity of sulfolane leads to low solvent-feed ratios, and thus smaller equip-ment... 

As observed from Figure 27, the cake removal by fluid shear is also aided by centrifugal force. Other arrangements include stationary filtration media and rotating disks to create the shear effects, and rotating cylindrical elements it has also been shown how such filters can be used for cake washing. 

Fig. 4. Typical design elements foi wet deagglomeiation in low viscosity systems (a) a high, ipm lotoi (shown below its normal position within stator) produces turbulence and cavitation as blades pass each other (b) a rotating disk creates a deep vortex to rapidly refresh the surface, and up- and downtumed teeth at the edge cause impact, turbulence, and sometimes cavitation and (c) the clearance of a high rpm rotor can be reduced as the batch...

Fig. 22. Schematics of chemical vapor deposition epitaxial reactors (a) horizontal reactor, (b) vertical pedestal reactor, (c) multisubstrate rotating disk reactor, (d) barrel reactor, (e) pancake reactor, and multiple wafer-in-tube reactor (38).

Unvulcanized Latex and Latex Compounds. A prime consideration has to be the fluid-state stabihty of the raw latex concentrate and hquid compound made from it. For many years, the mechanical stabihty of latex has been the fundamental test of this aspect. In testing, the raw latex mbber content is adjusted to 55% and an 80 g sample placed in the test vessel. The sample is then mechanically stirred at ultrahigh speed (ca 14,000 rpm) by a rotating disk, causing shear and particle cohision. The time taken to cause creation of mbber particle agglomerates is measured, and expressed as the mechanical stabihty time (MST). 

Fig. 3. Schematic of three commonly used types of MOCVD reactors where the arrows indicate gas flow (a) vertical rotating disk where (— represents an inlet to promote a laterally uniform gas flow, (b) planetary rotation, and (c) hori2ontal.

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,... 

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). 

Rotating disks are often used in electrochemical research. 

Refer to Fig. 15-39. The tower is formed into compartments by horizontal doughnut-shaped or annular baffles, and within each compartment agitation is provided by a rotating, centrally located, horizontal disk. Somewhat similar devices have been known for some time. The features here are that the rotating disk is smooth and flat and of a diameter less than that of the opening in the stationaiy baffles, which facihtates fabrication and apparently improves extraction rates. The typical proportions of the internals of the RDC are as follows ... 

FIG. 15-39 Rotating-disk (RDC) extractor, (Couitesy of Glitsch Frocess Systems Inc.)... 

Foam can also be broken with a rotating perforated basket [Lem-lich, Principles of Foam Fractionation, in Periy (ed.), Progre.ss in Separation and Purification, vol. 1, Interscience, New York, 1968, chap. 1]. If the foamate is aqueous (as it usually is), the operation can be improved by discharging onto Teflon instead of glass [Haas and Johnson, Am. In.st. Chem. Fng. J., II, 319 (1965)]. A turbine can be used to break foam [Ng, Mueller, and Walden, Can. J. Chem. Fng., 55, 439 (1977)]. Foam which is not overly stable has been broken by running foamate onto it [Brunner and Stephan, Ind. Fng. Chem., 57(5), 40 (1965)]. Foam can also be broken by sound or ultrasound, a rotating disk, and other means [Ohkawa, Sakagama, Sakai, Futai, and Takahara,y. Ferment. Technol, 56,428, 532 (1978)]. 

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