Spiral step separation

Figure 5.4. Relationship between normal growth rate R of a crystal lace and the step height h, the advancing rate v, and the step separation A, of a growth spiral.

Figure 5.7. Phase contrast photomicrographs depicting interlaced spiral steps observed on (0001) faces of (a) magnetoplumbite and (b) SiC 6H polytype, (c) Schematic figure. The very narrow step separations observed at the center of the spiral in (b) are due to a sharp increment of supersaturation at the final stage due to the discontinued electrical supply.

Elemental growth spiral layers originating from an isolated dislocation can advance, keeping the step separation constant, unless factors which affect the advancing rate of the spiral steps, such as a local fluctuation in driving force or impurity adsorption, takes place. The step separation of a spiral, A, is related to the critical radius of two-dimensional nuclei, r, in the following manner (see ref. [11], Chapter 3) ... 

When the step separation is wide enough, typical spiral step patterns observable by optical microscopy may appear, but if the separation becomes narrower than the resolution power of the optical microscope, the spirals appear in the forms of polygonal pyramids or conical growth hillocks. Even if spiral patterns are not directly observable, we may assume that these growth hillocks are formed by the spiral growth mechanism. Examples representing the two cases are compared in Fig. 5.8. 

Figure 5.8. (a) Typical spiral pattern (phase contrast photomicrograph of (0001) face of Sic grown from the vapor phase), and spiral growth hillocks which appear as (b) polygonal and (c) conical pyramids due to narrow step separation. Part (b) is a differential interference photomicrograph, (1010), and part (c) is a reflection photomicrograph, (1011), of hydrothermally synthesized quartz. 

Step patterns due to elemental spiral growth steps, with a step height of 1 nm and a step separation of 10 10 nm order, are universally observed on the surface of the 001 faces ofkaolinite, dickite, and nacrite. 

Another aspect of the growth morphology in electrodeposition of metals is the formation of macrospirals characterized by spiral steps with a height of more than 10 nm and a step separation of more than 1 pm. Such macrospirals have been observed in various studies [5.15, 5.73). Fig. 5.37 shows an example of macrospiral growth observed during electrodeposition of copper [5.73]. 

When spiral steps from two dislocations are separated by a distance larger than 9pJ2, two-dimensional re-entrant comers may appear and preferential growth will start after that, i.e. the steps will advance faster at the re-entry comers in comparison with other directions. When the step separation is much wider than a critical value, it becomes possible that the supersaturation between neighboring steps can achieve a level sufficient to overcome the barrier of 2D nucleation and to permit nucleation on the surface of spiral layers. 

Cyclone Separators Cyclone separators are described in Chapter 7. Typically used to remove particulate from a gas stream, the gas enters tangentially at the top of a cylinder and is forced downward into a spiral motion. The particles exit the bottom while the gas turns upward into the vortex and leaves through the top of the unit. Pressure drops through cyclones are usually from 13 to 17 mm water gauge. Although seldom adequate by themselves, cyclone separators are often an effective first step in pollution control. 

If spiral growth occurs due to the existence of screw dislocations, the results depend upon whether the diffusion length ijy is smaller or larger than the typical separation of the spiral arms i. In the first case the situation hardly changes from the purely kinetic situation without diffusion, but in the second case interaction between steps comes into effect [90] and phenomena such as step bunching [91] take place. We can estimate qualitatively the... 

Once wound, the separator is cut and the loose end taped to the spiral. The spiral is pushed off the winding pin and inserted into a can. The can is filled with electrolyte and the separator must be wetted quickly by the electrolyte so that the header (or cover) can be installed in the next processing step. 

Particles with the lowest specific gravity are carried with the water towards the outside wall of the spiral. The spiral separates at its greatest efficiency when used in the size range of 10 to 200 mesh. Some particles will be recovered both above and below these size ranges, but occasionally, ultrafine and very coarse heavies will be lost in the tailings, as will be middlings or unliberated ore particles. The spiral will benefit, therefore, from the use of hydraulic classification as a feed preparation step. 

A hyperfiltration process developed by Mobil Oil, now ExxonMobil, for this separation is illustrated in Figure 5.28(b). Polyimide membranes formed into spiral-wound modules are used to separate up to 50 % of the solvent from the dewaxed oil. The membranes have a flux of 10-20 gal/ft2 day at a pressure of 450-650 psi. The solvent filtrate bypasses the distillation step and is recycled directly to the incoming oil feed. The net result is a significant reduction in the refrigeration load required to cool the oil and in the size and energy consumption of the solvent recovery vacuum distillation section. 

The combined solutions containing the enzyme from the cell separation step (approximately 160 liters) were then concentrated using a 40 square foot, 10,000 MWCO regenerated cellulose S40Y10 Diaflo spiral membrane (Amicon Division of W. R. Grace Co.- Conn., Danvers, MA). A roughly ten fold concentration of the enzyme was achieved in this step. Further concentration and diafiltration of the protein product solution were carried out at the lab scale. 

As indicated in Figure 10b, this membrane proved quite easy to clean. In contrast to the polysulfone membranes used in the cell separation step, the spiral ultrafilter showed 100% recovery of hydraulic permeability with a minimum effort to clean (i.e., no extra cleaning steps were ever used). Again, the ease of cleaning is related to both the nature of the process stream to which the unit was exposed, and the properties of the membrane itself. In the enzyme concentration step, solids load was very low (compared to the original cell broth). The membrane itself, on the other hand, exhibits much less tendency to adsorb protein than polysulfone because of the hydrophilic nature of regenerated cellulose. 

The spiral-wound membrane is essentiaUy a flat membrane wrapped around a perforated tube, through which the effluent streams out of the membrane. As can be seen (Fig. 3.13C) that sandwich is actuaUy four layers a membrane, a feed channel, another membrane, and a permeate channel, which forces aU the separated material toward that perforated tube in the center. This type of membrane is an intermediate step between the flat, laboratory membrane and the hoUow-fiber membrane, at least in terms ot surface area per unit volume and stability. 

Some applications require flexibility to bend and curl the hoses. To accomplish this, the extmded and sintered tubes can be convoluted in a separate step. The tube is passed through a heated die, which melts the PTFE and creates a spiral peak and valley pattern into the tube. A key requirement of the convolution process is to assure that the wall thickness remains uniform, in other words, the tube is not stretched. Any thinning of the wall will weaken and reduce the burst pressure of the hose. Figure 5.31c shows an example of convoluted tube, which is partly braided with stainless steel. 

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