Flow instabilities curved tubes

Our main concern here is to present the mass transfer enhancement in several rate-controlled separation processes and how they are affected by the flow instabilities. These processes include membrane processes of reverse osmosis, ultra/microfiltration, gas permeation, and chromatography. In the following section, the different types of flow instabilities are classified and discussed. The axial dispersion in curved tubes is also discussed to understand the dispersion in the biological systems and radial mass transport in the chromatographic columns. Several experimental and theoretical studies have been reported on dispersion of solute in curved and coiled tubes under various laminar Newtonian and non-Newtonian flow conditions. The prior literature on dispersion in the laminar flow of Newtonian and non-Newtonian fluids through... 

Further details of the mass transfer enhancement techniques in membrane separation processes are reported by Belfort and Al-Bastaki and Abbas. In this entry, the focus is on the flow instabilities produced by Dean vortices in curved and coiled tubes because of their advantages over the other techniques, viz., lower axial dispersion, better radial mixing, residence time distribution closer to plug flow, higher mass... 

Unstable branches on the P(Q) curve and the appearance of hysteresis loops can occur for various reasons usually connected with an increase in viscosity. Thus, a non-monotonic P(Q) curve was first encountered in an analysis of the flow of a hot inert (non-reactive) liquid in a cold tube when the viscosity of the liquid was strongly dependent on temperature.190 The intense dissipative heat output may have been the reason for the instability in the flow of an inert liquid.191 In both cases, the reason for the nonmonotonic in P(Q) dependence was the strong dependence of viscosity on temperature, which is equivalent here to time dependence for viscosity. Detailed investigations of the hysteresis transitions shown in Fig. 4.24 proved that they have a wave character 192 in this case, the transition occurs at a constant flow rate. 

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