Differential flow technique

Figure 3.7. Differential flow technique for gas adsorption (after Nelsen and Eggertsen, 1958).

In DTA, temperature is monitored. In DSC, heat flow is monitored. The data obtained are similar. DTA can be considered a more global term, covering all differential thermal techniques, while DSC is a DTA technique that gives calorimetric (heat transfer) information. 

The reaction was conducted in a differential flow reactor, with gas-chromatographic analysis of the reaction mixture. The individual interactions of CO and 02 with the catalyst were studied by a pulse technique. 

The F( + )d methods, like techniques in the F(+)cd class, require differential flow for separation. However the nature of the differential flow differs in the two cases. Since the F(+)d methods induce enrichment only at an interface between two phases, the sole requirement of differential flow is that one phase assumes motion relative to another phase. It is usually an easy matter to instigate the relative motion of phases. 

Another commonly-used normalisation procedure is to use the relative flow technique. In this method the elastic differential cross section for a particular species may be obtained by comparing the scattered intensity under the same conditions with that from another target with a known cross section. It is important to ensure, for both the gas under study and the reference gas, that the electron flux density and distribution, the detector efficiency, and the target beam flux distribution are the same for both gases during the measurement. 

The I/O expansion factor will not be much different from the molar expansion fee-tor but it may be measurable. If so, it may provide a simple way of measuring net desorption rates. The kind of device that would make this technique viable is a differential flow rate or differential flow velocity meter. Since temperature does not enter into equation 5.69, this device would compare the flow rates of the inlet and a cooled outlet stream at a convenient common temperature, say the temperature at which inlet flow is metered. 

A comprehensive GC X 2GC technique with differential flow modulation has been developed for rapid analysis of VOCs. " In comprehensive GC X 2GC, two secondary columns of different polarities are used, requiring a GC with two detectors to monitor the column effluents. The flow-switching device is a modification of the unit developed by Sacks and Akard " for high-speed chromatography. The flow of carrier gas to the columns is controlled by a three-port solenoid valve placed outside the GC oven and not in the sample flowpath. Parallel and serially positioned tee unions control the flows of carrier and auxiliary gases and interface the primary column effluent to the secondary columns. Bueno and Seeley " used a 5.0 m X 0.25 mm i.d. capillary column with a... 

The adsorption of three argon/nitrogen binary mixtures at 310 K and up to 0.6 bar are presented. A continuous, quasi-equilibrium flow technique of adsorptive introduction was used to allow high-resolution isotherms to be obtained. These are compared to differential enthalpies of adsorption determined using adsorption microcalorimetry. 

The term DTA is used either as a general term for differential thermal techniques (including DSC) or for those techniques that measure temperature differences but are not designed to measure the heat flow. Figure 7.17 shows the... 

Calorimetry of liquids and solutes has been revolutionized in recent years by the combination of the differential scanning technique, in which some difference between a sample and a standard is observed, with the continuous flow of fluids through the calorimeter. Instead of having two mineral samples ( 5.6.2), two columns or tubes are used, through which a reference solution and a sample solution flow at a controlled rate (Figure 5.12). As before, the difference in the power required to keep the columns at the same temperature is directly related to the difference in the heat capacities of the two fluids. See Wood (1989) for a history of the development of these methods and then-advantages. 

This chapter discusses finite-difference techniques for the solution of partial differential equations. Techniques are presented for pure convection problems, pure diffusion or dispersion problems, and mixed convection-diffusion problems. Each case is illustrated with common physical examples. Special techniques are introduced for one- and two-dimensional flow through porous media. The method of weighted residuals is also introduced with special emphasis given to orthogonal collocation. 

Finally, Rivkin et al. (1986) also used the capillary flow technique to measure the viscosity of aqueous boron solutions, at temperatures up to 623 K and at pressures up to 30 MPa. In this case they employed a platinum capillary of 500 nun length and 0.3 nun ID, placed in a liquid thermostat in which temperature was controlled with an uncertainty of 0.03 K. A prunp-flowmeter was used to measure the volume of the fluid flowing through the capillary tube at each given temperatme and pressure. The pressure drop across the capillary ends was measmed with a compensation-type differential mercmy pressure gauge with a movable elbow. The details of the experimental apparatus and measurement procedme are given in Rivkin et al. (1979). 

A recent innovation is the static mercury drop electrode [55]. The mercury flow to the capillary is controlled by an electromagnetic valve opened periodically for a short time only so that a mercury drop of a constant area is formed. The current is registered some time after the drop formation when the charging current is reduced practically to zero and does not interfere. The measurement is performed by d.c. or differential pulse technique and the sensitivity of the measurement is highly increased. A chromatographic detector with SMDE is manufactured commercially [ 54 ] ... 

The forcing functions used to initiate chemical relaxations are temperature, pressure and electric held. Equilibrium perturbations can be achieved by the application of a step change or, in the case of the last two parameters, of a periodic change. Stopped-flow techniques (see section 5.1) and the photochemical release of caged compounds (see section 8.4) can also be used to introduce small concentration jumps, which can be interpreted with the linear equations discussed in this chapter. The amplitudes of perturbations and, consequently of the observed relaxations, are determined by thermodynamic relations. The following three equations dehne the dependence of equilibrium constants on temperature, pressure and electric held respectively, in terms of partial differential equations and the difference equations, which are convenient approximations for small perturbations ... 

Polyisobutylene has been taken as an example. For samples of molecular weight M , > 9,300, the temperature positions of the TSC peaks associated with Tg and T// are practically constant, as in other "non-flow techniques" such as adiabatic or differential scanning calorimetry. 

The transition temperatures deduced from this work have been compared with values from "non-flow" and "flow" techniques. In Figure 7, transition temperatures, Tg and T/i, have been plotted against log M . TSC data are in good agreement with values from other "non-flow" techniques such as Differential Scanning Calorimetiy (DSC) and Adiabatic Calorimeby (AC). The solid line in Fig. 7 mimics the leveling off of Tg and T// above M. Measures involving "flow" like Torsional Braid Analysis (TBA) and Mdt Viscosity (MV) show a specific bdiavior for T/ above (dashed line in Fig. 7). 

The simplicity gained by choosing identical weight and shape functions has made the standard Galerkin method the most widely used technique in the finite element solution of differential equations. Because of the centrality of this technique in the development of practical schemes for polymer flow problems, the entire procedure of the Galerkin finite element solution of a field problem is further elucidated in the following worked example. 

---