Flow zone

In continuous-flow zone electrophoresis the solute mixture to be separated is injec ted continuously as a narrow source within a body of carrier fluid flowing between two electrodes. As the solute mixture passes through the transverse field, individual components migrate sideways to produce zones which can then be taken off separately downstream as purified fractions. 

The trajectory followed by water in a filter mass it is not linear. Water is forced to follow the outlines of the grains that delineate the interstices. These changes in direction are also imposed on particles in suspension being transported by the water. This effect leads to the evacuation of particles in the dead flow zones. Centrifugal action is obtained by inertial force during flow, so the particles with the highest volumetric mass are rejected preferentially. 

The centerline temperature differential within the zone of fully established turbulent flow (Zone 3) of a nonisothermal jet can be derived using equations of momentum (Eq. (7.39)) and excessive heat conservation along the jet <. S... 

Kasicka, V., Pruslk, Z., Sazelova, P., Jiracek, J. and Barth, T., Theory of the correlation between capillary and free-flow zone electrophoresis and its use for the conversion of analytical capillary separations to continuous free-flow preparative processes. Application to analysis and preparation of fragments of insulin, ]. Chromatogr. A, 796, 211, 1998. 

Ns = number of sealing strips encountered by the bypass stream in the cross-flow zone,... 

The pressure drop in the cross-flow zones between the baffle tips is calculated from correlations for ideal tube banks, and corrected for leakage and bypassing. 

Bypassing will affect the pressure drop only in the cross-flow zones. The correction factor is calculated from the equation used to calculate the bypass correction factor for heat transfer, equation 12.30, but with the following values for the constant a. 

There will be no leakage paths in an end zone (the zone between tube sheet and baffle). Also, there will only be one baffle window in these zones so the total number of restrictions in the cross-flow zone will be Ncv +NWV. The end zone pressure drop APe will therefore be given by ... 

The bypass and leakage areas, window area, and the number of tubes and tube rows in the window and cross-flow zones can be determined precisely from the tube layout diagram. For preliminary calculations they can be estimated with sufficient accuracy by considering the tube bundle and shell geometry. 

The number of tubes in a cross-flow zone Nc is given by... 

Stirred tank performance often is nearly ideal CSTR or the model may need to take into account bypassing, stagnant zones or other parameters associated with the geometry and operation of the vessel and the agitator. Sometimes the vessel can be visualized as a zone of complete mixing in the vicinity of the impellers followed by a plug flow zone elsewhere, thus a CSTR followed by a PFR. 

A fluidized bed reactor has a substantial free space above the main level of the catalyst for purpose of disengaging entrainment. In this region plug flow may be assumed to prevail. An overall appropriate model accordingly will consist of well mixed and bypass zones in parallel followed by a plug flow zone. The fraction of flow in bypass is 1-a and the fraction of vessel volume in plug flow is 2. Find the transfer function and equations for the responses to step and impulse inputs of tracer. 

In laminar flow of Bingham-plastic types of materials the kinetic energy of the stream would be expected to vary from V2/2gc at very low flow rates (when the fluid over the entire cross section of the pipe moves as a solid plug) to V2/gc at high flow rates when the plug-flow zone is of negligible breadth and the velocity profile parabolic as for the flow of Newtonian fluids. McMillen (M5) has solved the problem for intermediate flow rates, and for practical purposes one may conclude... 

An interesting feature of the experimental results plotted in Fig. 6 is that the ratio c/u may be less than 1.5 under certain flow conditions. It will be shown later (Section IV, F) that the surface velocity of the film is equal to 1.5m, so that in this flow zone it appears that the surface waves move less rapidly than the surface of the film. Under these circumstances, the waves might tend to steepen at the upstream end, and the sudden transition from steep-fronted to steep-backed waves might explain the increase in the randomness of the waves in this flow zone, as illustrated by the standard deviation of the wavelengths mentioned in the last section. 

Detailed kinematic investigations of flow near the front of a stream were undertaken.284 A diagram of the experimental device is shown in Fig. 4.49. In the experimental procedure, a liquid was placed in a chamber with transparent walls above an aluminum piston, which was driven downwards by connection to a suitable drive. This resulted in the appearance of streams inside the liquid,and three different flow zones could be distinguished. The so-called "fountain effect discussed in Section 2.11 appeared near the free surface, while a reverse fountain flow was observed below the moving surface. It is interesting to note the movement of two liquids with different densities, when one liquid is used as a piston to push the other (analyzed experimentally and theoretically).285 If the boundary between the two liquids is stationary and the walls of the chamber move at constant velocity, then the pattern of flow is as shown in Fig. 4.50, where flow trajectories corresponding to front and reverse fountain effects are clearly shown. Two other flow patterns -developed flow inside the main part of the chamber and circulation near the surface of the aluminum piston - were also observed. 

A microfluidic system was made consisting of a Y-type channel structure and a packed bed of micro beads in a zone in the center of the outlet channel [162]. At the end of the micro-bead bed a weir is placed. The outlet channel then reopens to a larger flow zone which has several parallel micro channels, splitting the main flow into many sub-streams. These micro channels serve as spatially addressable detection lanes. 

Equation (5.2a) is valid for any DG/ i value, Reynolds number, turbulent flow zone, or laminar flow zone. First calculate a Reynolds number from DG/[i. Then use Kern s Fig. 24, which appears in App. A as Fig. A.l. You may also derive this value by using Eq. (5.2a) for Jh. This equation is simply a curve-fit to Kern s figure. 

For DG / p < 2100 Reynolds number, laminar flow zone, apply the following equation for inside tube wall h, value ... 

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