Channel flow general geometry

Chapter 7 deals with the practical problems. It contains the results of the general hydrodynamical and thermal characteristics corresponding to laminar flows in micro-channels of different geometry. The overall correlations for drag and heat transfer coefficients in micro-channels at single- and two-phase flows, as well as data on physical properties of selected working fluids are presented. The correlation for boiling heat transfer is also considered. 

Channel flow between plane parallel electrodes is shown in Fig. 11. This geometry is similar to that of the disk in that an electrode and an insulator intersect in the same plane. Because of many geometric similarities, the general characteristics of the primary and secondary current distributions are similar. At the edges the local current density is infinite for the primary current distribution (Fig. 12). Increasing the kinetic limitations tends to even out the current distribution. The significant contrasts appear in a comparison of the tertiary current distributions. In channel flow, the fluid flows across the electrode rather than normal to it. Consequently, the electrode is no... 

Two-dimensional (2D) microfluidic systems that can produce highly monodisperse emulsion droplets have been intensively studied in various fields [59-63]. Confined microfluidic channels such as T-junctions [64-68], cross-junctions [69-71], flow-focusing geometries [72-79] and other co-flow geometries [67, 80, 81] are generally used. Under the conditions of low Reynolds and capillary numbers [66], highly monodisperse emulsion droplets are reproducibly formed in the channels, typically... 

It is noteworthy that several studies exhibit contradictory results for both the mechanical and thermal characteristics of the flow. This is generally due to differences in the many parameters that characterize these studies such as the geometry, shape and surface roughness of the channels, the fluid, the boundary conditions and the measuring methodology itself. These discrepancies indicate the need for extension of the experimental base to provide the necessary background to the theoretical model. 

For the study of flow stability in a heated capillary tube it is expedient to present the parameters P and q as a function of the Peclet number defined as Pe = (uLd) /ocl. We notice that the Peclet number in capillary flow, which results from liquid evaporation, is an unknown parameter, and is determined by solving the stationary problem (Yarin et al. 2002). Employing the Peclet number as a generalized parameter of the problem allows one to estimate the effect of physical properties of phases, micro-channel geometry, as well as wall heat flux, on the characteristics of the flow, in particular, its stability. 

A number of authors have considered channel cross-sections other than rectangular [102-104]. Figure 2.17 shows some examples of cross-sections for which friction factors and Nusselt numbers were computed. In general, an analytical solution of the Navier-Stokes and the enthalpy equations in such channel geometries would be involved owing to the implementation of the wall boundary condition. For this reason, usually numerical methods are employed to study laminar flow and heat transfer in channels with arbitrary cross-sectional geometry. 

Eqs. 7.22 and 7.24 represent the velocities due to screw rotation for the observer in Fig. 7.9, which corresponds to the laboratory observation. Eq. 7.25 is equivalent to Eq. 7.24 for a solution that does not incorporate the effect of channel width on the z-direction velocity. For a wide channel it is the z velocity expected at the center of the channel where x = FK/2 and is generally considered to hold across the whole channel. The laboratory and transformed velocities will predict very different shear rates in the channel, as will be shown in the section below relating to energy dissipation and temperature estimation. Finally, it is emphasized that as a consequence of this simplified screw rotation theory, the rotation-induced flow in the channel is reduced to two components x-direction flow, which pushes the fluid toward the outlet, and z-direction flow, which tends to carry the fluid back to the inlet. Equations 7.26 and 7.27 are the velocities for pressure-driven flow and are only a function of the screw geometry, viscosity, and pressure gradient. 

Consider the fully developed steady flow of an incompressible fluid through an annular channel, which has an inner radius of r, and an outer radius of r0 (Fig. 4.27). The objective is to derive a general relationship for the friction factor as a function of flow parameters (i.e., Reynolds number) and channel geometry (i.e., hydraulic diameter Dh and the ratio f A friction factor /, which is a nondimensional measure of the wall... 

In tortuous-path stacks there is no need for spacer screens as thicker membranes, narrow channels, and plenty of cross-straps are used. On the contrary, in sheet-flow stacks spacers of different geometry and thickness are necessary to prevent membrane contact (that would result in burning through), as well as to induce turbulence in the flowing solution (Kuroda et al., 1983). Spacers generally consist of a sealing frame and a net in the... 

To separate liquid distribution, entrance and collection effects, a short monolith piece was measured and deduced for the determination of the ki -value of the considered monolith section in developed laminar film regime. Figure 8.23 shows some results for monoliths of different channel geometry and diameter. In general, a slight increase of the mass transfer performance with liquid velocity is found. This can be related to a large amount to the increase in gas-liquid interface area for higher flows. 

If the geometry of an FFF channel is known exactly and a parabolic flow profile in the channel can be assumed (see Sect. 1.2), it is possible to make exact predictions about the separation of the sample as well as the separation efficiency. In this section, only the general theoretical expressions universally applicable to all FFF techniques operating in the normal mode are provided. Specialities of the different FFF methods are given during their detailed discussion in Sect. 2. 

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