Parallel plate comparative analysis

Show that the analysis just derived for the circular channel has the correct parallel-plate limiting behavior for channel widths that are small compared to the radius, that is, small gaps where r0 - n (r,- + r0)/2. 

FIGURE 31.10 Comparative analysis of droplet formation mechanism (6kV applied potential, 2.5 cm electrode distance) (a) parallel plate setup and (b) positively charged needle setup. Note the formation of the jet spray in (h). (From Poncelet, D., Bugarski, B., Amsden, B., Zhu, J., Neufeld, R., and Goosen, M.F.A., Appl. Microbiol. BiotechnoL, 42 (2-3), 251-255, 1994. With permission.)... 

In the article on electro-osmosis (q.v.) a similar formula, but with 4 in place of the factor 6, is derived. Since electrophoresis is the reverse of electro-osmosis, the same expression should apply in both cases to the potential at the surface of shear between the two phases. The explanation of the apparent discrepancy is that instead of applying Stokes s law to a small sphere, the derivation of the electro-osmotic effect is based on the model of a parallel plate capacitor, i.e. on a large solid surface whose radius of curvature is negligible (compared with the thickness of the diffuse double layer). Closer analysis of the problem by Henry and Booth has shown that 4 is the correct factor for large particles, independent of their size and shape, but that for most systems, e.g. stable colloidal solutions, the factor varies between 4 and 6, depending on the size of the particle and the thickness of its atmosphere. 

Figure 10.22 The viscosity-temperature data set measured using thermomechanical analysis (TMA) parallel-plate viscometry of the National Bureau of Standards (NBS), USA, 710 glass is compared to the Vogel-Fulcher-Tammann [9] model issued by the NBS.

A second strategy relies on parallel experimentation. In this case, the same experimental step is performed over n samples in n separated vessels at the same time. Robotic equipment such as automated liquid-handlers, multi-well reactors and auto-samplers for the analysis are used to perform the repetitive tasks in parallel. This automated equipment often works in a serial fashion as, for example, a liquid handler with a single dispensing syringe filling the wells of a microtiter plate, one after another. However, the chemical formation of the catalyst or the catalytic reaction are run at the same time, assuming that their rate is slow compared to the time needed to add all the components. The whole process appears parallel for the human user whose intervention is reduced. 

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