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Analyte cross-sectional area

Conventionally, analytical SEC columns have been produced with an internal diameter of 7.5 mm and column lengths of 300 and 600 mm. In recent years environmental and safety issues have led to concerns over the reduction of organic solvent consumption, which has resulted in the development of columns for organic SEC that are more solvent efficient (13). By reducing the internal diameter of the column, the volumetric flow rate must be reduced in order to maintain the same linear velocity through the column. This reduction is carried out in the ratio of the cross sectional areas (or internal diameters) of the two columns. Eor example, if a 7.5-mm i.d. column operates at 1.0 ml/min, then in order to maintain the same linear velocity through a 4.6-mm i.d. column the flow rate would be... [Pg.364]

All solutions of Eqs. (3) such as that by Yu and Sparrow (Yl) yield the velocity profiles in each phase as a function of the interfacial position h and the pressure drop. The volumetric flow rates Qt and Q are obtained by integrating each velocity profile over the respective phase cross-sectional area. The ratio of the flow rates can then be determined as a function of only the interfacial position, and since the volumetric flow rates are known, this yields an implicit fourth order equation for the interfacial position h. The holdups Rt and Rn can be calculated once the interfacial position is known. Since each equation for the volumetric flow rates is linear with respect to the pressure drop, once the interfacial position is known the pressure drop may be easily computed. An analytical procedure for determining pressure drop and holdup for turbulent gas-laminar liquid flows has been developed by Etchells (El) and verified by comparison with experimental data in horizontal systems (A7). [Pg.19]

The classical FEE retention equation (see Equation 12.11) does not apply to ThEEE since relevant physicochemical parameters—affecting both flow profile and analyte concentration distribution in the channel cross section—are temperature dependent and thus not constant in the channel cross-sectional area. Inside the channel, the flow of solvent carrier follows a distorted, parabolic flow profile because of the changing values of the carrier properties along the channel thickness (density, viscosity, and thermal conductivity). Under these conditions, the concentration profile differs from the exponential profile since the velocity profile is strongly distorted with respect to the parabolic profile. By taking into account these effects, the ThEEE retention equation (see Equation 12.11) becomes ... [Pg.349]

The Reynolds number, based on a hydraulic diameter, is Reo = puD/fi. In general the hydraulic diameter is given as D = 4AC/P, where Ac is the channel cross-sectional area. For a laminar flow, an analytic solution for flow in cylindrical tubes provides... [Pg.657]

Fig. 4.23 also indicates a slight decrease of the signal plateau which, at a first glance, was unexpected. In the following, a reactive dispersion model given in ref. [37] is applied to deduce rate constants for different reaction temperatures. A trapezoidal response function will be used. The temperature-dependent diffusion coefficient was calculated according to a prescription by Hirschfelder (e.g., [80], p. 68 or [79], p. 104] derived from the Chapman-Enskog theory. For the dimensionless formulation, the equation is divided by M/A (with M the injected mass and A the cross-section area). This analytical function is compared in Fig. 4.24 with the experimental values for three different temperatures. The qualitative behavior of the measured pulses is well met especially the observed decrease of the plateau is reproduced. The overall fit is less accurate than for the non-reactive case but is sufficient to now evaluate the rate constant. [Pg.114]

Figure 1.3. Thin fused silica capillary tubes similar to (and frequently smaller than) those shown here are often used for the analytical-scale separation of complex mixtures by chromatography and electrophoresis. The inside diameters of these capillaries are only 220 /im (lower two) and 460 fim (upper). The diameters of the smaller tubes are 680 times less than that of the LC column shown in Figure 1.2. The cross-sectional area, roughly proportional to separative capacity, is over 400,000 times less. (Photo by Alexis Kelner.)... Figure 1.3. Thin fused silica capillary tubes similar to (and frequently smaller than) those shown here are often used for the analytical-scale separation of complex mixtures by chromatography and electrophoresis. The inside diameters of these capillaries are only 220 /im (lower two) and 460 fim (upper). The diameters of the smaller tubes are 680 times less than that of the LC column shown in Figure 1.2. The cross-sectional area, roughly proportional to separative capacity, is over 400,000 times less. (Photo by Alexis Kelner.)...
Examination of Fig. 37 shows that, at generation 8, the surface area per Z group in PAMAM dendrimers approaches the cross-sectional area of the amine-terminated branch segment (ca. 33 A2) of the surface cell. Curve B assumes quantitative reactions and 100% branching ideality at each stage. Since our present analytical methods assure branching ideality detection limits of no more than 95%, curve A may more nearly approximate experimental congestion levels. [Pg.286]

As far as the conversion of the analytical response is concerned, the most used detectors in GrFFF have been, until now, conventional ultraviolet (UV) detectors commonly used for HPLC. With this type of detector, the amount of particles with diameter di is proportional to the detector response at the zth point. With particulate samples, in fact, because of UV detector optics, the response is a turbidity signal read within an angle between the incident light and the photosensor (i.e., usually smaller than —10°) rather than the absorbance. This turbidity signal can be assumed to be directly proportional to the sum of all cross-sectional areas of the particulate sample components at any time. The validity of the above assumption, in the case of particles which are about 10-fold larger than the incident wavelength, is discussed elsewhere [6]. The mass frequency function can thus be expressed as [7]... [Pg.1110]

Both injection techniques have been shown to suffer from the effects of analyte diffusion, specially when the clean capillary is initially introduced into the sample solution. Diffusion occurs across the boundary area between analyte and buffer, which is defined by the cross-sectional area of the capillary. Both techniques also suffer from the effects of inadvertent hydrodynamic flow that results from the reservoir liquid levels being at slightly different levels. While these effects are significant for the buffer-filled capillaries used in capillary zone electrophoresis, they are both much less important when the capillary is filled with a gel. [Pg.231]

The boundary conditions are zero velocity at the walls and zero slope at any planes of symmetry. Analytical solutions for the velocity profile in square and rectangular ducts are available but cumbersome, and a numerical solution is usually preferred. This is the reason for the transient term in Equation 16.7. A flat velocity profile is usually assumed as the initial condition. As in Chapter 8, is assumed to vary slowly, if at all, in the axial direction. For single-phase flows, u can vary in the axial direction due to changes in mass density and possibly to changes in cross-sectional area. The continuity equation is just AcUp = constant because the cross-channel velocity components are ignored. [Pg.579]


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Analytic sectionally

Cross-sectional area

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