The Co-rotating Disk Pump

For the JMP configuration, it is easy to show that the corresponding equations are 

The increase in the drag-flow rate has a profound effect on performance. For a given flow rate q, the optimum gap size in SMP and JMP configurations can be obtained by differentiating Eqs. E6.10-2 and E6.10-4, respectively, with respect to H to give Hopt = 3q/Vo and Hopt = 3q/2Vo- Next we substitute these values in Eqs. E6.10-2 and E6.10-4 and find that the ratio of pressure rises is 

Similarly, we find that the maximum flow-rate ratio for a given pressure rise is 

For non-Newtonian Power Law model fluids, these ratios are 

for Newtonian fluids, the pressurization capability of the optimized JMP is eight times that of the SMP, and for non-Newtonian fluids, the ratio exhibits a minimum at n = 0.801 and rises to 11.59 at it — 0.25 whereas, the flow rate at fixed pressure rise for Newtonian fluids is 81 2 — 2.83 times in JMP as compared to SMP, and for non-Newtonian fluids with n = 0.25 it rises to 7.25. Clearly, the JMP configuration is about an order of magnitude more efficient then the SMP one. Moreover, the specific power input in a JMP configuration for Newtonian fluids is one-half that of the SMP, and for n — 0.25, it is one-fifth the corresponding ratios for specific power dissipated into heat are, one-quarter and 1/25, respectively. 

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Fig. E6.7 The synthesis of the co-rotating-disk pump, (a) The building block (b) two corotating disks form the moving planes (c) front view of the processor showing the inlet and outlet ports separated by the channel block (d) side view of the pump.

Fig. 6.31 Schematic view of a co-rotating-disk pump, (a) The disks are attached to a rotating shaft and placed within a harrel having an inlet and an outlet port, separated by a channel block attached to the stationary barrel. The space between inlet and outlet ports, the disks, and the channel block form the processing chamber, (b) parallel arrangements of the disks (c) wedge-shaped disks.

FIGURE 3.29 A schematic view from above the disk of a passive capillary burst valve. A liquid flows in a channel or capillary and is pinned at the discontinuity where the channel meets a chamber or a wider channel. Sufficient fluidic pressure must be exerted by the centrifugal pump to overcome the pressure of curved liquid surfaces and to wet the walls of the chamber with liquid. This pressure is achieved at a characteristic rate of rotation or burst frequency, C0c, above which the liquid exits the channel and enters the chamber. CO, depends on the hydraulic diameter (dH) of the capillary and the amount of liquid in the channel and therefore provides a means of gating the flow of liquid [1042]. Reprinted with permission from the American Chemical Society. 

Passive capillary burst valves were fabricated on a plastic disk in which centrifugal liquid pumping was used to transport fluids, as shown in Figure 3.29. When the angular velocity (co) is less than the critical value (coc), the liquid cannot enter the big chamber. When co > coc, the liquid then bursts into the chamber. A wider channel would require less force to burst through and hence a lower rotation rate or a lower centrifugal force was used for the valve to burst open [226,453,454,1042],... 

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