Archimedian spirals

Burton, Cabrera, and Frank [56] and Bennema and Gilmer [57] have developed a theory to predict the crystal growth rate for screw dislocations. The growth rate will depend on the shape of the growth spiral. For an Archimedian spiral, shown in Figure 6.14 [58], the distance between the steps of the spiral yo is... 

The operation of scroll pumps, a new generation of backing pumps, is based on two Archimedian spirals, one fixed while the other moves with a slightly offset rotation. An Archimedian spiral is one where the distance (spacing) between each rotation of the spiral is constant. Similarly to rotary pumps, scroll pumps operate by capturing... 

Fig. 6. Fit of an Archimedian spiral (A) and an involute of a circle (B) to the pixels with the maximum grey levels in a spiral pattern observed in a 4.5 x 4.5 mm area (from [36]).

SpiralTlevator Materials are moved upward by the centrally located spiral-type conveyor in a cylindrical or cone-shaped Nautamix vessel (Fig. 37c and d). Blending occurs by the downward movement at the outer walls of the vessel. The vessel serves the dual purposes of blending and storage. In these mixers the screw impeller actively agitates only a small portion of the mixture and natural circulation is used to ensure all the mixture passes through the impeller zone. In the case of Nautamix, an Archimedian screw lifts powder from the base of a conical hopper while progressing around the hopper wall. 

FIGURE 6.14 Archimedian growth spiral (top) Schematic presentation of Archimedian growth. Redrawn, with permission from Burton et aL [56], (bottom) iral growth on rare earth crystal. Printed, with permission ftom Tdkdorf and Welz [58]. 

Early research on the BZ reaction was concerned mainly with spirals of approximately Archimedian shape where the spiral tip moves steadily on a circular path around its rotation center. It was soon noticed that the spiral geometry and the dynamics of the tip motion become more complex when the excitability of the solution is changed [19-22]. 

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