Regime transition, theoretical analysis

A theoretical analysis has been carried out for galvanostatic and potentiostatic pulse regimes [27]. The idea that developed is a bit the same as backflushing with pressure driven-membrane operation such as microfiltration or ultrafiltration. The time dependencies of the extent of the concentration polarization near the membrane surface during the pulse are described theoretically for both pulse regimes and a qualitative discussion of the pause duration is presented. The main characteristic of the non-stationary process is the transition time between the state without polarization and the state with stationary polarization. 

Besides cell thickness d of the nematic layer, which has almost no effect in the case ei = es = 0, reveals a strong influence on EC for finite flexocoefficients. This is demonstrated in the lower panel of Fig. 4.5, where for d = 10 /Ltm the conductive branch is totally absent. Then, as with the conductive regime, one can find a transition from oblique to normal dielectric rolls above a Lifshitz frequency In a recent experiment the oblique dielectric rolls at small w have indeed been observed. The threshold characteristics Uc and qc and the obliqueness angle a. could be well reproduced by a theoretical analysis of the nemato-electrohydrodynamic equations including flexopolarization. ... 

The flow patterns observed in vertical upward flow of a gas and Newtonian liquid are similar to those shown in Figme 4.1 and are described in detail elsewhere [Bamea and Taitel, 1986]. Taitel etal. [1980] have carried out a semi-theoretical study of the fimdamental mechanisms responsible for each flow pattern, and have derived quantitative expressions for the transition from one regime to another. This analysis shows a strong dependence on the physical properties of the two phases and on the pipe diameter. Figure 4.3 shows their map for the flow of air-water mixtures in a 38 nun diameter pipe. 

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