Field flow fractionation calculations

Water at 20°C is pumped through a thin rectangular (ribbon-shaped) field-flow fractionation channel at a flowrate of 1.00 mL/ min. The channel dimensions (see Figure 4.2) are length L — 40.0 cm, breadth b = 2.00 cm, and thickness w = 254 fim. Calculate the average and maximum flow velocities, (u) and uraM, and the pressure difference Ap in atmospheres needed to drive the flow. 

Calculation of Flow Properties and End Effects in Field-Flow Fractionation Channels by a Conformal Mapping Procedure, P. S. Williams, S. B. Giddings, and J. C. Giddings, Anal. Chem., 58, 2397 (1986). 

Field-flow fractionation experiments are mainly performed in a thin ribbonlike channel with tapered inlet and outlet ends (see Fig. 1). This simple geometry is advantageous for the exact and simple calculation of separation characteristics in FFF Theories of infinite parallel plates are often used to describe the behavior of analytes because the cross-sectional aspect ratio of the channel is usually large and, thus, the end effects can be neglected. This means that the flow velocity and concentration profiles are not dependent on the coordinate y. It has been shown that, under suitable conditions, the analytes move along the channel as steady-state zones. Then, equilibrium concentration profiles of analytes can be easily calculated. 

Another separation technique of particular application for proteins, high-molar-mass molecules, and particles is the general class known as field-flow fractionation (FFF) in its various forms (cross-flow, sedimentation, thermal, and electrical). Once again, MALS detection permits mass and size determinations in an absolute sense without calibration. For homogeneous particles of relatively simple structure, a concentration detector is not required to calculate size and differential size and mass fraction distributions. Capillary hydrodynamic fractionation (CHDF) is another particle separation technique that may be used successfully with MALS detection. 

Determine the elution volume. Refer to the example calculations in Chapter 32, p. 376, related to sedimentation field flow fractionation, then calculate the total adsorption and layer thickness. 

Protein adsorption to PS latex has also been determined by sedimentation field flow fractionation (SdFFF). The maximum surface coverages of P-casein and p-lactoglobulin on negatively charged PS latex calculated using this method were similar at around Img/m [19]. This figure, which was confirmed by amino acid analysis of the material irreversibly bound to the surface, was significantly lower... 

The presence of surface phenomena in SdFFF, except for being a main source of error in calculating physicochemical quantities, could also be a basis for a new separation method called Potential-Barrier Field-Flow Fractionation, which can separate colloidal particles of different size or of any physicochemical parameter involved in the potential energy of interaction between the particles and the FFF channel wall. ° The same method can be also used for the concentration and analysis of dilute colloidal samples, such as those of natural water, where particles are present in low... 

Electric Field-Flow Fractionation This method is similar to electrophoresis. The electric field is induced by charging the two parallel plates, as in Figure 13.20. The channel between the two plates is filled with buffer as in the case of electrophoresis. The value of X is calculated by using... 

Sedimentation Field-Flow Fractionation This method uses the centrifugal field to separate molecules. The value of A, is calculated by using... 

Flow Field-Flow Fractionation This method is similar to dialysis or ultrafiltration, with the solvent acting uniformly on all the solutes. The field is generated by the flow of the solvent. The separation is mainly determined by the diffusion coefficient or frictional coefficient. The value of X is calculated using... 

A magnetic field flow fractionation unit consisting of a square channel of 1 mm x 1 mm cross section is used to separate magnetic beads of different sizes. The magnetic susceptibility of magnetic bead is equal to 3500. The magnetic beads of 1 pm and 10 pm diameter are submerged in water with susceptibility of -9.035 x 10 . The 1 pm particle is deposited at a mean distance of 500 mm from the enhance of the channel. Calculate the distance at which the 10 pm particle will be deposited. 

In order to calculate the theoretical unattached fraction of radon progeny the appropriate differential equations must be developed to describe the net formation of unattached radon progeny. The system may be visualized schematically for RaA as illustrated in Fig. 2. It is assumed that there is no flow into or out of the system or removal by electric fields. The equations which describe the system presented in Fig. 2 are ... 

Fig. 5. Variation of the Sl80 and 8D values of the fluid delivered from well 131, located 500 m away from the re-injection site, during an injection test conducted in the peripheral area of Serrazzano in the Larderello field (open squares). The figure also shows graphically, and in arbitrary units, the flow rate Q of water re-injected into the well as a function of time, and the position of each sample collected. Theoretical isotopic pattern of the steam produced by re-injected water, assuming continuous steam separation at depth, is also reported. Since the actual evaporation temperature and the fraction of residual water are unknown, calculations were made for three different temperatures (140, 160, and 180 °C) and fractions (/w) of residual liquid water after boiling. Dashed line represents the hypothetical mixing between deep geothermal steam (W) and completely evaporated re-injected water (R).

Various forms of diffusion coefficients are used to establish the proportionality between the gradients and the mass flux. Details on determination of the diffusion coefficients and thermal diffusion coefficients is found in Chapter 12. Here, however, it is appropriate to summarize a few salient aspects. In the case of ordinary diffusion (proportional to concentration gradients), the ordinary multicomponent diffusion coefficients Dkj must be determined from the binary diffusion coefficients T>,kj. The binary diffusion coefficients for each species pair, which may be determined from kinetic theory or by measurement, are essentially independent of the species composition field. Calculation of the ordinary multicomponent diffusion coefficients requires the computation of the inverse or a matrix that depends on the binary diffusion coefficients and the species mole fractions (Chapter 12). Thus, while the binary diffusion coefficients are independent of the species field, it is important to note that ordinary multicomponent diffusion coefficients depend on the concentration field. Computing a flow field therefore requires that the Dkj be evaluated locally and temporally as the solution evolves. 

A variety of control schemes are shown separately in Figures 3.14 and 3.15 for the lower and upper sections of fractionators. To some extent, these sections are controllable independently but not entirely so because the flows of mass and heat are interrelated by the conservation laws. In many of the schemes shown, the top reflux rate and the flow of HTM to the reboiler are on flow controls. These quantities are not arbitrary, of course, but are found by calculation from material and energy balances. Moreover, neither the data nor the calculation method are entirely exact, so that some adjustments of these flow rates must be made in the field until the best possible performance is obtained from the equipment. In modern large or especially sensitive operations, the fine tuning is done by computer. 

Specific conversion rates are calculated in the usual way for a flow reactor k = (F/S) ln[(Ceq - C0)/(Ce<, - Cx)], where F is the flow rate (mol s 1), S the total catalyst surface (m2), C, the ortho-para equilibrium ratio at the reactor temperature, C0 the ratio for hydrogen entering the reactor and Cx the ratio for hydrogen leaving the reactor. For different samples of the same catalyst the zero field conversion reproducibility is seldom better than by a factor of 5, but the fractional change AkH = (kH - k0)/ko may often be reproduced to 5%. In some cases a change of 0.5% is measurable. (kH is the specific rate in a field H, k0 that in zero or negligible field). 

For these calculations, attention was limited to a temperature range of 950° to 1350°K, a pressure range of 300 mTorr to 7.6 Torr, and SiH4 mass fractions of 15 to 30% in H2. Under these conditions, the mass fraction of SiH2 formed was at most on the order of 10 3, so that the influence of the Yj s on the temperature distribution was small. To a good degree of approximation, the temperature was calculated to be linear. By the same token, the flow field which was easily calculated did not demonstrate any unique behavior. 

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