Secondary flow component

Data for the bulk fluid, line A, indicate that vz varies as a function of z but maintains a value near 0.75 of maximum velocity. The periodicity of vx and vy is clearly evident in the graph of line A and a 1800 out of phase coupling of the components is seen with one positive when the other is negative. This indicates a preferred orientation to the plane of the oscillatory flow and this feature was seen in all the biofilms grown throughout this study. The secondary flow components are 0.1-0.2 of the maximum axial velocity and are spatially oscillatory. The significant non-axial velocities indicate non-axial mass transport has gone from diffusion dominated, Pe = 0, in the clean capillary, to advection dominated, Pe 2 x 103, due to the impact of the biofilm. For comparison, the axial Peclet number is Pe L 2x 10s. Line B intersects areas covered by biomass and areas of only bulk... 

The lack of hydrodynamic definition was recognized by Eucken (E7), who considered convective diffusion transverse to a parallel flow, and obtained an expression analogous to the Leveque equation of heat transfer (L5b, B4c, p. 404). Experiments with Couette flow between a rotating inner cylinder and a stationary outer cylinder did not confirm his predictions (see also Section VI,D). At very low rotation rates laminar flow is stable, and does not contribute to the diffusion process since there is no velocity component in the radial direction. At higher rotation rates, secondary flow patterns form (Taylor vortices), and finally the flow becomes turbulent. Neither of the two flow regimes satisfies the conditions of the Leveque equation. 

Various arrangements at the bottom of the inner cylinder are available in Figure 3.2 an indentation is provided so that an air gap is formed and shearing in the sample below the inner cylinder is negligible. Another arrangement is to make the bottom of the inner cylinder a cone. When one of the cylinders is rotated, a Couette flow is generated with fluid particles describing circular paths. The only non-zero velocity component is ve and it varies in the r-direction. In order to minimize secondary flow (Taylor vortices) it is preferable that the outer cylinder be rotated however, in most commercial instruments it is the inner cylinder that rotates. In this case, the fluid s velocity is equal to IXR, at the surface of the inner cylinder and falls to zero at the surface of the outer cylinder. The shear stress is uniform over the curved surface of the inner cylinder and over the outer cylinder (to the bottom of the annular gap). 

Figure 1.56 Scenario 2 vertical z-components of the flow lead to species penetration and induce secondary flows, (a) and (b) show fluid trajectories of one species for the cross-sectional area at the mixing channel front and the whole T-channel design (c) gives a mass-fraction contour plot of the other species at the outlet face [68] (by courtesy of Elsevier Ltd.).

Another difference between the extruders and continuous mixers, pointed out by Valsamis and Canedo, is that, in the former, channel solids and melt flow dominate, and flow over screw flights is a secondary effect (except for power calculations). In contrast, the circumferential flow in CMs (and internal mixers) over the wing tips is the major flow component. Thus, while wing tips and screw flights appear to be equivalent machine elements, their role and function are quite different. The wing tips provide high shear... 

Flow field-flow fractionation (flow FFF or FIFFF) is one of the FFF subtechniques in which particles and macromolecules are separated in a thin channel by aqueous flow under a field force generated by a secondary flow. As with other FFF techniques, separation in FIFFF is based on the applied force directed across the axis of separation flow. In FIFFF, this force is generated by cross-flow of liquid delivered across the channel walls. In order to maintain the uniformity of cross-flow moving in a typical rectangular channel, two ceramic permeable frits are used as channel walls and the flow stream enters and exits through these walls. The force applied in FIFFF is a Stokes force that depends only on the sizes of sample components. 

The path of a typical fluid element is a superposition of the recirculating secondary flow and the primary flow in the axial direction. The result is a helical motion as the fluid element moves through the tube. In addition to the secondary flow, however, the curvature of the tube axis also contributes the modification, (4-91), in the axial profile. When (4-91) and (4-80) are combined in the asymptotic form, (4-76), the axial velocity component takes the form... 

To date no numerical simulation of the acoustic streaming flow associated with application to the microfluidics has been successfully performed. The simulation can be performed only with the streaming flow by using the governing equation given as Eq. 27, but we also need to solve the full unsteady Navier-Stokes equations including not only the primary oscillatory flow component but also the secondary steady flow component. In this case locally fine grids must be adopted to deal with the thin Stokes layer adjacent to the solid surface. 

Optical Coherence Tomography and Optical Doppler Tomography, Fig. 6 ODT images of secondary flow in a meandering square microchaimel as shown in Fig. 3. The measured z components of the flow velocity V ixjtz) in the area of interest was projected into different cross-sectional planes, where the z axis is perpendicular to the microchannel plane (x-y plane) and along the direction... 

Distillation is a process that separates the components in a mixture by boiling point. At the heart of a distillation system is the column. Distillation columns come in two basic designs plate and packed. Flow arrangements vary from process to process. The symbols allow the technician to identify primary and secondary flow paths. The two standard symbols for distillation columns are shown in Figure 7-13. A distillation system is a complex arrangement of equipment and instruments. In most cases, all of the equipment covered in this text could be found in service within a distillation system. 

It is well known [7] that a secondary flow is created at bends with a small radius of curvature, due to inertial forces acting on the central part on the flow with the largest velocity. This results in a redistribution of the two liquid components and possibly a larger contact area. At sharp comers one could even expect local turbulence, since the sharp comer may act as a slit-type orifice if the Reynolds number exceeds the corresponding transition number 15. 

In microfluidics the flow is normally laminar but non-laminar flow can occur in components with short channels or orifices, at Reynolds numbers as low as 15 [1]. In our experiments the Reynolds numbers were all below 150 and we observed non-laminar flow conditions where secondary flow and presumable local turbulence was generated at sharp comers in the zigzags of the mini-channel. The maximum Reynolds numbers of the mixing experiments are plotted as a function of the ratio of the length between bends to the hydraulic diameter (L/Dj ) in figure... 

If the inner cylinder spins fast enough, an instability is triggered, which gives rise to a secondary flow made up of counter-rotating toroidal vortices stacked vertically inside the gap. The total solution is, therefore, not in the form given by [7.24] instead, it has non-zero Ur and Mz velocity components. The Couette instability has prompted a number of studies to be taken up. 

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