Rotating Channel Flow

Centrifugal flow Lab-CD Lab-disk Lab-on-a-Diskl Microfluidics on a CD Rotating channel flow... 

Current Meters. Various vane designs have been adapted for open-channel flow measurement. The rotating element is partially immersed and rotates rather like a water wheel. Operation is similar to that of vane anemometers. 

Substituting Eq. 7.18 into Eq. 7.3 and solving Eqs. 7.1 and 7.3 for V, 14, and Vp, the solution for the transformed boundary condition problem Is obtained, and the equations are shown by Eqs. 7.21, 7.23, and 7.26. These equations physically represent the flow due to rotation and pressure in the transformed frame of reference in Fig. 7.10. Equation 7.21 is the velocity equation for the x-direction recirculatory cross-channel flow for the observer attached to the screw, and Eq. 7.23 is the apparent velocity in the z direction for the observer attached to the moving screw. 

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. 

The screw rotation analysis leads to the model equation for the extruder discharge rate. There are now two screw-rotation-driven velocities, and and a pressure-driven velocity, Pp that affect the rate. and transport the polymer fluid at right angles to one another. In order to calculate the net flow from screw rotation It Is necessary to resolve the two screw-rotation-driven velocities into one velocity, Vpi, that can be used to calculate the screw rotation-driven flow down the screw parallel to the screw axis (or centerline) as discussed in Chapter 1 and as depicted in Fig. 7.14. The resolved velocity will then be integrated over the screw channel area normal to the axis of the screw. 

Equation A7.13 is the cross-channel flow in the transformed (Lagrangian) frame and concludes the derivation of Eq. 7.18. Equation A7.13 also applies to a physical device where the barrel is actually rotated. Transforming Eq. A7.13 to the laboratory (Eule-rian) reference frame as follows for a physical device where the screw is rotated ... 

In the previous problem we examined temperature profiles and reactant (SiH4) concentration profiles in a channel-flow chemical vapor deposition (CVD) reactor. At sufficiently high temperatures (and pressures) SM4 undergoes unimolecular decomposition into the species SiH2 and H2. This is followed by numerous reactions of the intermediate species [180]. One such intermediate species formed in the gas phase is Si (i.e., a gas-phase silicon atom). In this problem we consider the gas-phase formation and destruction reactions governing the spatial profiles of Si atoms in a rotating-disk CVD reactor. 

A number of micro mixers use secondary or rotational flows, which are, e.g., created by in-channel flow structures, to stretch and fold fluids. The mixing approach here superposes the rotation by a break-up step, which basically is a splitting step [146], This was done based on the analysis of elementary mixing steps and their corresponding transfer to low Reynolds number mixing. 

Figure 13 plots an example of the processed PIV frame. The turbulent velocity field and its boundaries, solid wall, and liquid-free surface are simultaneously shown in Figure 13. The turbulence structures such as the coherent vortical structure near the bottom wall and its modification after release from the no-slip boundary condition near the free surface of the open-channel flow, and the evolvement of the free-surface wave can be seen in Figure 13. This simultaneous measurement technique for free-surface level and velocity field of the liquid phase using PIV has been successfully applied to the investigation of wave-turbulence interaction of a low-speed plane liquid wall-jet flow (Li et al., 2005d), and the characteristics of a swirling flow of viscoelastic fluid with deformed free surface in a cylindrical container driven by the constantly rotating bottom wall (Li et al., 2006c).

Fig. 10.23 Co-rotating channels, (a) Contours of axial velocity at plane (I) (b) velocity vector at plane (I) (c) contours of axial velocity at plane (I) (d) velocity vectors at plane (II), in (mm/s). [Reprinted by permission from T. Katziguara, Y. Nagashima, Y. Nakano, and K. Funatsu, Numerical Study of Twin Screw Extruders by 3-D Flow Analysis - Development of Analysis Technique and Evaluation of Mixing Performance for Full Flight Screws, Polym. Eng. Sci., 36, 2142 (1996).]...

Hydrodynamic voltammetry — is a voltammetry technique featuring an electrolyte solution which is forced to flow at a constant speed to the electrode surface. -> mass transport of a redox species enhanced in this way results in higher current. The forced flow can be accomplished either by agitation of the solution (solution stirring, or channel flow), or the electrode (electrode rotation, see -> rotating disk electrode or vibration,... 

The characteristics of laminar flow can allow mathematical prediction of the solution velocity and this has led to a range of hydrodynamic devices which use forced convection as a transport component under laminar flow conditions, examples include, the -> rotating disk electrode [i],-> wall jet electrode [ii], and channel flow cell (see -> flow cell). 

More complicated 3D effects were studied in Refs. 6 and 7 with the help of 3D Monte Carlo digital simulation performed with a rather powerful computer (RISK System/6000). Sedimentation FFF with different breadth-to-width channel ratios and both codirected and counterdirected rotation and flow were studied. Secondary flow forming vortexes in the y-z plane is generated in the sedimentation FFF channel, both due to its curvature, and the Coriolis force caused by the centrifuge rotation. The exact structure of the secondary flow was calculated by the numerical solution of the Navier-Stokes equations and was used in the Monte Carlo simulation of the movement of solute molecules. 

The calculations discussed in this article were done using the equations just given [i.e., (A.8)-(A.ll)j. It is instructive, however, to examine a simple analytical representation of the tidal flow in the Sound. Let the Sound be represented by a closed channel. Flow into and out of the channel takes place only across one face. The channel is, of course, fixed on the Earth rotating in the lunar gravitational field. The water level in the channel is given by... 

For the electron transfer reaction, it was found that any excess energy in the process was statistically partitioned among all degrees of freedom of the complex and was manifested in the LIF spectra as rotational heating. Flow tube experiments tuned to different Br isotopes also showed a hydrogen-atom transfer channel in the HBr + HBr reaction. 

For basic studies the most suitable type is the rotating disc which is either placed in the end face of a rotating cylinder. Fig. 3.2, or is used as a free rotating system with an integral shaft. Fig. 3.3 [7]. Further models are the rotating cylinder, free or co-axial [11,12J, and pipe and channel flow [7,14]. 

In pilot and prodnction plants, the flow conditions are determined by the nature of the apparatus and process, bnt in laboratory tests, they have to be individnally chosen. To determine the effects of static on very gently moving media, it is snfflcient to stir the medinm with an agitator. If exposure of the material to flowing media is expected, special corrosion tests are essential for simulation, for example, circnlation tests with pipe or channel flow and nse of rotating discs or cylinders as specimens. 

Voltammetric techniques may be broadly divided into steady-slate techniques, such as channel flow cell [44 6], rotating disc [47, 48], or microelectrode [49] voltammetry at sufficiently low potential scan rate to give a current response independent of time, and transient techniques, such as cyclic voltammetry or chronoamperometry, giving a current response which is dependent on time. 

The relatively long equilibration time of the stagnant thin layer of the OTTLE or reflection cell does not allow one to study the kinetics of fast reactions. Alternatively, the forced convection regimes of the RDE and the channel-flow cell allow production of steady state currents, and both have been investigated with optical detection of electrogenerated species. Further details can be found in Chapter 2.4 in this volume. The rotating OTE was investigated early on and the theory has recently been expanded [204]. The electrode is used... 

Shear Stress Sensors, Fig. 8 Schematic of a static calibration apparatus (a) using a rotating disk and (b) long, high aspect ratio smooth channel flow... 

The rotating disc electrode (RDE) is the classical hydrodynamic electroanalytical technique used to limit the diffusion layer thickness. However, readers should also consider alternative controlled flow methods including the channel flow cell (38), the wall pipe and wall jet configurations (39). Forced convection has several advantages which include (1) the rapid establishment of a high rate of steady-state mass transport and (2) easily and reproducibly controlled convection over a wide range of mass transfer coefficients. There are also drawbacks (1) in many instances, the construction of electrodes and cells is not easy and (2) the theoretical treatment requires the determination of the solution flow velocity profiles (as functions of rotation rate, viscosities and densities) and of the electrochemical problem very few cases yield exact solutions. 

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