Hydrodynamic systems some useful parameters

The development of convective-diffusion theories is due principally to Prandtl9 and Schlichting10, and their application in electrochemistry to Levich11. Levich was the first to solve the equations for the rotating disc electrode. 

Besides the diffusion layer, of thickness 5, and the mass transfer coefficient, /cd, there are other parameters which are useful for describing hydrodynamic systems. 

The first is the concept of a hydrodynamic layer of thickness 5H, within which all velocity gradients occur. In practice one uses values that differ by 5 per cent from their values at infinite distance from the electrode surface, given that the components tend asymptotically to their values in bulk solution. It has been demonstrated that11 

We now define various dimensionless groups that are useful in mass transport problems  

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It was shown that for certain system parameters given by a critical Reynolds number, there is a possibility of propagation of the specific flow structures inside the liquid layer. The convection cells, which can appear, are similar to those observed in the Ryleigh-Benard experiment [9]. Such phenomenon can be very important for some air-water-phospholipid systems such as the pulmonary surfactant present in the natural mass exchanger - the lungs. The hydrodynamic system described in the piq er can be a very useful tool for explanation of convective diffusion-reaction transport process in case of interaction of allergens with pulmonary epithelium, causing atopy. 

The quasi-one-dimensional model used in the previous sections for analysis of various characteristics of fiow in a heated capillary assumes a uniform distribution of the hydrodynamical and thermal parameters in the cross-section of micro-channel. In the frame of this model, the general characteristics of the fiow with a distinct interface, such as position of the meniscus, rate evaporation and mean velocities of the liquid and its vapor, etc., can be determined for given drag and intensity of heat transfer between working fluid and wall, as well as vapor and wall. In accordance with that, the governing system of equations has to include not only the mass, momentum and energy equations but also some additional correlations that determine... 

Ralf Kuriyel (Millipore Corporation) addressed some of the issues related to the use of Dean vortices, formed during the flow of fluids in curved conduits, to enhance the performance of cross-flow filters by increasing the back transport of solutes. Results were presented on coiled hollow fibers with a varying radius of curvature, fiber diameter, and solution viscosity, to characterize the relationship between the back transport of solutes and hydrodynamic parameters. A performance parameter relating back transport to the Dean number and shear rate was derived, and a simple scaling methodology was developed in terms of the performance parameter. The use of Dean vortices may result in membrane systems with less fouling and improved performance. 

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