Transient experiments diffusion

At a close level of scrutiny, real systems behave differently than predicted by the axial dispersion model but the model is useful for many purposes. Values for Pe can be determined experimentally using transient experiments with nonreac-tive tracers. See Chapter 15. A correlation for D that combines experimental and theoretical results is shown in Figure 9.6. The dimensionless number, udt/D, depends on the Reynolds number and on molecular diffusivity as measured by the Schmidt number, Sc = but the dependence on Sc is weak for... 

Channel techniques employ rectangular ducts through which the electrolyte flows. The electrode is embedded into the wall [33]. Under suitable geometrical conditions [2] a parabolic velocity profile develops. Potential-controlled steady state (diffusion limiting conditions) and transient experiments are possible [34]. Similar to the Levich equation at the RDE, the diffusion limiting current is... 

A similar method of analysis of transient state diffusion kinetics has been propos-ed 144,1491 based on the consideration that, in any experiment, the kinetic behaviour of the system represented by S(X), DT(X) will generally deviate from that of the corresponding ideal system represented by Se, De in either of two ways (i) ideal kinetics is obeyed, but with a different effective diffusion coefficient D , where n = 1,2,... denotes a particular kinetic regime (Dn is usually deduced from a suitable linear kinetic plot) or (ii) ideal kinetics is departed from, in which case one is reduced to comparison between the (non-linear) experimental plot and the corresponding calculated ideal line. 

In this type of experiment the NOE buildup tends to disappear with p/. In the steady state case, the saturation time is always long enough to allow spin / to cross-relax with other spins, even if pr is large. In transient experiments, the cross relaxation with spin / is by itself limited in time and, pj being the same, cross relaxation with other spins is drastically limited. In any case, spin diffusion is limited in that region of time in which NOE is growing (Fig. 7.6). Truncated and transient NOEs performed with short NOE buildup times are efficient in quenching spin diffusion. 

The available transport models are not reliable enough for porous material with a complex pore structure and broad pore size distribution. As a result the values of the model par ameters may depend on the operating conditions. Many authors believe that the value of the effective diffusivity D, as determined in a Wicke-Kallenbach steady-state experiment, need not be equal to the value which characterizes the diffusive flux under reaction conditions. It is generally assumed that transient experiments provide more relevant data. One of the arguments is that dead-end pores, which do not influence steady state transport but which contribute under reaction conditions, are accounted for in dynamic experiments. Experimental data confirming or rejecting this opinion are scarce and contradictory [2]. Nevertheless, transient experiments provide important supplementary information and they are definitely required for bidisperse porous material where diffusion in micro- and macropores is described separately with different effective diffusivities. 

The TEOM is a promising tool for investigation of the influence of coke on adsorption and diffusion in catalysts. As a consequence of high flow rates of the carrier gas through the sample bed, the technique minimizes the external mass and heat transfer limitations in transient experiments without affecting the accuracy of the measurements. The data are not influenced by buoyancy and flow patterns, which are significant when conventional methods are used. 

There are macroscopic (uptake measurements, liquid chromatography, isotopic-transient experiments, and frequency response techniques), and microscopic techniques (nuclear magnetic resonance, NMR and quasielastic neutron spectrometry, QENS) to measure the gas diffusivities through zeolites. The macroscopic methods are characterized by the fact that diffusion occurs as the result of an applied concentration gradient on the other hand, the microscopic methods render self-diffusion of gases in the absence of a concentration gradient [67]. 

A particular example of another transient experiment, which we find most useful, is the determination of diffusion coefficients using the rotation speed j step method [20]. The transient response of the limiting current at a rotating disc to a step in the rotation speed say from 5 to 7 Hz is a function pf the... 

The time-dependent temperature distribution in a transient experiment is governed by Eq. 4, and usually the related parameter, thermal diffusivity. is obtained. However, under certain circumstanees the solution to the heat equation contains the thermal conductivity as well as the thermal diffusivity, and by choosing a suitable method the diffusivity can be eliminated from the answer. The more important methods are the line and plane source heater methods and arc described below. These arc not Standard methods, but they can be used where speed is more imp .>rtant than absolute accuracy, to give a conductivity value more quickly than the Standard methods. They can also be used to compare a range of materials. 

Some methods that are specifically for the detection of oxygen have been used the colorimetric method [42] the coulometric method [43] and another based on the phenomenon of radiothermoluminescence of polymers, as a function of oxygen content [44], The latter was used in a transient experiment and hence measured the diffusivity. but if the solubility is known, or can be measured, the permeability can be calculated. 

The single-pellet diffusion reactor can be employed for transient experiments. Cannestra et al. [65] give an example. Gas composition was measured at the center of one-dimensional pellets. The standard single-pellet diffusion reactor was modified to allow continuous gas analysis and miniaturized in order to reduce the time constants of gas flow mixing. A rather simple model for data evaluation used by the authors was not able to predict major features of the response measurments at the pellet center but gave qualitatively correct results of the external concentration responses. This demonstrates the necessity of an elaborate modeling of instationary multicomponent diffusion and porous structure for this type of reactor. 

While flow reactors operate at conditions that closely mirror the operating environment witnessed in practice, these reactors can typically only offer a global kinetic description and lack the details of elementary reaction steps and mechanism that reveal how materials operate on a more fimdamental level. If the goal is catalyst development, then one typically needs more detailed rate expressions that describe elementary reaction steps for the development of a mechanism. The goal is to understand not only more than just the properties of the catalyst but also how it functions. In order to understand such details, transient experiments will provide the most insight into the elementary steps as well as secondary processes (e.g., surface/bulk diffusion) that make up the complex catalytic system. 

The generation/collection (G/C) modes constitute a different SECM procedure that expands the applicability of the technique to a wide range of situations, hi these modes, the collector (either tip or substrate) works as an amperometric sensor that collects the products produced at the generator surface (either substrate or tip, respectively). Thus, the collector potential is controlled to electrochemically reaet with the generator-produced species. Typical collector responses used in G/C experiments are (a) voltammetric curves, where the collector potential is swept, and (b) diffusion-controlled limiting current vs. time curves. In contrast to the feedback mode where steady-sate responses are monitored, in G/C experiments, the current-time dependence is an important set of data to evaluate. The timescale of most of G/C transient experiments is much wider, possibly up to 100 sec. Moreover, as the tip-substrate distances increase, typical coupling and distortion of transient responses are not significant. 

The TAP reactor is very well suited for kinetic studies. At low pressure, all transport of gas-phase species is by (Knudsen) diffusion, thus ruling out any external mass transfer limitations. The diffusion as a random movement also eliminates all radial concentration gradients. Very low amounts of reactants are pulsed into the reactor, which are on the order of a few nanomoles. Thus, the amount of heat generated is very small even in the case of strongly exo- or endothermic reactions. Therefore, the reactor is operated isothermally and no heat transfer limitations occur. Concentration profiles inside the pores for transient experiments might arise even in the absence of chemical reaction. If significant diffusion of reactants and products inside the catalyst pores occurs, it will be revealed by the transient response and then needs to be addressed correctly by a modeling approach. This is often the case for microporous materials [26,27,72]. 

Another very important feature of transient experiments in the TAP-2 reactor is that they can be performed in different diffusion regimes, which are determined by the reactor geometry and the number of molecules pulsed. When the pulse size is below 10 molecules, gas transport in the micro-reactor occurs via Knudsen diffusion. This means that any collisions between gas-phase molecules are strongly minimized. Therefore, pure heterogeneously-catalysed reactions can be investigated. Transient experiments with higher pulse sizes (molecular diffusion) provide important information about the contribution of gas-phase processes to the overall reaction studied. 

This paper is focused on the determination of the diffusion and adsorption parameters of n-butane by transient experiments in several activated carbons prepared by phosphoric acid activation. 

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