Channel laminar flow

For most medium- and large-scale micromanifold structures, where one passage feeds multiple parallel channels, flow traverses through turbulent and transition flows in the micromanifold region. This fluid in turbulent to transition flow also turns in the micromanifold region as it drops flow into parallel microchannels, which are primarily in the laminar flow regime. 

With turbulent channel flow the shear rate near the wall is even higher than with laminar flow. Thus, for example, (du/dy) ju = 0.0395 Re u/D is vaHd for turbulent pipe flow with a hydraulically smooth wall. The conditions in this case are even less favourable for uniform stress on particles, as the layer flowing near the wall (boundary layer thickness 6), in which a substantial change in velocity occurs, decreases with increasing Reynolds number according to 6/D = 25 Re", and is very small. Considering that the channel has to be large in comparison with the particles D >dp,so that there is no interference with flow, e.g. at Re = 2300 and D = 10 dp the related boundary layer thickness becomes only approx. 29% of the particle diameter. It shows that even at Re = 2300 no defined stress can be exerted and therefore channels are not suitable model reactors. 

One way to ease any difficulties that may arise in fabricating a membrane, especially in design configurations that are not planar, is to go membraneless. Recent reports take advantage of the laminar flow innate to microfluidic reactors ° to develop membraneless fuel cells. The potential of the fuel cell is established at the boundary between parallel (channel) flows of the two fluids customarily compartmentalized in the fuel cell as fuel (anolyte) and oxidant (catholyte). Adapting prior redox fuel cell chemistry using a catholyte of V /V and an anolyte of Ferrigno et al. obtained 35 mA cmr at... 

Equation (4) states that the linear deposition rate vj is a diffusion controlled boundary layer effect. The quantity Ac is the difference in foulant concentration between the film and that in the bulk flow and c is an appropriate average concentration across the diffusion layer. The last term approximately characterizes the "concentration polarization" effect for a developing concentration boundary layer in either a laminar or turbulent pipe or channel flow. Here, Vq is the permeate flux through the unfouled membrane, 6 the foulant concentration boundary layer thickness and D the diffusion coefficient. 

Taylor (T4, T6), in two other articles, used the dispersed plug-flow model for turbulent flow, and Aris s treatment also included this case. Taylor and Aris both conclude that an effective axial-dispersion coefficient Dzf can again be used and that this coefficient is now a function of the well known Fanning friction factor. Tichacek et al. (T8) also considered turbulent flow, and found that Dl was quite sensitive to variations in the velocity profile. Aris further used the method for dispersion in a two-phase system with transfer between phases (All), for dispersion in flow through a tube with stagnant pockets (AlO), and for flow with a pulsating velocity (A12). Hawthorn (H7) considered the temperature effect of viscosity on dispersion coefficients he found that they can be altered by a factor of two in laminar flow, but that there is little effect for fully developed turbulent flow. Elder (E4) has considered open-channel flow and diffusion of discrete particles. Bischoff and Levenspiel (B14) extended Aris s theory to include a linear rate process, and used the results to construct comprehensive correlations of dispersion coefficients. 

Laminar flow. Think about water flowing slowly in a channel. Will the water in the center of the channel flow faster or slower than the water along the sides of the channel Experience teaches that water in the center of a channel will flow faster than along the sides of the channel. Moreover, if the water flow is really slow, the water creeping along the side of the channel will barely mix with the bulk of the water flowing in the center of the channel. This is called laminar flow. 

It is to be noted that, for laminar open channel flow, the Froude and Reynolds numbers are interrelated. Making use of (1), (3), and (19), it is easily shown that... 

Laminar flow reactors are equipped with microstructured reaction chambers that have the desired low Reynolds numbers due to their small dimensions. Mass transport perpendicular to the laminar channel flow is dominated by diffusion, a phenomenon known as dispersion. Without the influence of diffusion, laminar flow reactors could not be used in heterogeneous catalysis. There would be no mass transport from the bulk flow to the walls as laminar flow, in contrast to turbulent flow, cannot mix the flow macroscopically. 

The flow in the feed channels is laminar, as is to be expected [41 ]. Owing to the size of the mixing chamber and the high fluid velocities, liquid mixing is expected to have a fast transition from laminar to turbulent Evidence for this is given below. Different from conventional micro mixers, the primary vortices are in the range of about 100 pm, hence smaller than usual. Thus, mixing is different and should be faster. 

Time resolution can also be limited by the parabolic flow profile of a confined fluid in the low Reynolds number (laminar flow) regime. The fluid velocity at the walls approaches zero. If the probe beam sample molecules spread over the entire width of a channel, their differing velocities must be considered. Those in close proximity to the walls travel very slowly, whereas those at the center of the channel flow most rapidly. To compensate for this effect, we flow an extra layer of buffer against the walls... 

Some of the more commonly used methods of obtaining solutions to problems involving natural convective flow have been discussed in this chapter. Attention has been given to laminar natural convective flows over the outside of bodies, to laminar natural convection through vertical open-ended channels, to laminar natural convection in a rectangular enclosure, and to turbulent natural convective boundary layer flow. Solutions to the boundary layer forms of the governing equations and to the full governing equations have been discussed. 

This program does a steady state simulation of the current at a narrow band electrode at the bottom of a channel with laminar flow of electrolyte through it, as discussed in Chap. 13, page 241. It is done as a march along X, the direction of flow. 

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). 

The first test is to compare a turbulent channel flow studied in the previous section and a laminar flow. A three dimensional Poiseuille flow in a pipe geometry was used as test case. The flow is laminar and the Reynolds number based on the bulk velocity and diameter is approximately 500. The bound-... 

Transport of heat or mass to the wall of a single, circular channel under laminar flow conditions is known as the classical Graetz problem [10]. For heat transport only, the energy equation contains axial convection and radial conduction ... 

The evolution of the Poiseuille number f Re) as a function of the Reynolds number is shown on figure 12. It is observed that the classical value for the laminar regime is obtained if the Reynolds number is less than 2000. The laminar turbulent transition occurs for the conventional value. The authors [22] investigated the entrance effects. They conclude that the friction factor is insensitive to the channel height and that there was no sign of a faster transition to turbulence compared to conventional channel flows. 

Cotta, R.M. and Ozisik, M.N. (1986) Transient Forced Convection in Laminar Channel Flow witii Stepwise Variations of Wall Temperature, CanJ. Chem. Eng., Vol. 64, pp. 734-742. 

Equipment designs based on indirect conduction usually transfer the heat from the primary heat transfer fluid to the intermediate wall within some kind of internal duct or channel. Transfer coefficients for these cases depend on the nature of the flow (laminar or turbulent) and the geometry of the duct or channel (short or long). Expressions for evaluating the transfer coefficients for these cases are available in standard texts. An expression for the convective thermal resistance can be generated similar to that derived for the conductive resistance ... 

Finally, mention should be made of a new generation of channel flow cells, in which the electrochemically generated species are transported by a laminar flow from the working electrode to an optically transparent part of the cell [316-318]. 

Under the impact of the cross-flow, the biopoly-mers/particles are forced in the direction of the membrane. To ensure that the analytes do not pass through the membrane, different pore sizes can be used. In this way, the analytes can be selectively rejected and it is possible to remove low-molecular compounds before the separation. The analytes diffusion back from this membrane is counteracted by the cross-flow, where, after a time, a dynamic equilibrium is established. The medium equilibrium height for smaller sized analytes is located higher in the channel than for the larger analytes. The smaller sized analytes are traveling in the faster velocity lines of the laminar channel flow and will be eluted first. As a result, fractograms, which... 

Flow FFF is one of a family of techniques which allows the fractionation of macromolecules based on size-related parameters. A detailed explanation of the mechanism and theory appears elsewhere in this encyclopedia. Fractionation is achieved by the application of a field (cross-flow) perpendicular to the channel flow [4]. Components showing greater response to the force exerted by the field are displaced further from the center of channel flow and toward the channel wall. Because the laminar flow through the channel produces a parabolic flow profile, the elution order of components is determined by their relative displacement. The size-... 

In (1.196) the quantities c,n,m still depend on the type of flow, laminar or turbulent, and the shape of the surface or the channel over or through which the fluid flows. Correspondingly, the mean Sherwood number can be written as... 

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