Adler model

Because the Adler model is time dependent, it allows prediction of the impedance as well as the corresponding gaseous and solid-state concentration profiles within the electrode as a function of time. Under zero-bias conditions, the model predicts that the measured impedance can be expressed as a sum of electrolyte resistance (Aeiectroiyte), electrochemical kinetic impedances at the current collector and electrolyte interfaces (Zinterfaces), and a chemical impedance (Zchem) which is a convolution of contributions from chemical processes including oxygen absorption. solid-state diffusion, and gas-phase diffusion inside and outside the electrode. 

Figure 26. Predictions of the Adler model shown in Figure 25 assuming interfacial electrochemical kinetics are fast, (a) Predicted steady-state profile of the oxygen vacancy concentration ( ) in the mixed conductor as a function of distance from the electrode/electrolyte interface, (b) Predicted impedance, (c) Measured impedance of Lao.6Cao.4Feo.8-Coo.203-(5 electrodes on SDC at 700 °C in air, fit to the model shown in b using nonlinear complex least squares. Data are from ref 171.

However, as we saw in section 3.3 for platinum on YSZ, the fact that i—rj data fits a Butler—Volmer expression does not necessarily indicate that the electrode is limited by interfacial electrochemical kinetics. Supporting this point is a series of papers published by Svensson et al., who modeled the current—overpotential i—rj) characteristics of porous mixed-conducting electrodes. As shown in Figure 28a, these models take a similar mechanistic approach as the Adler model but consider additional physics (surface adsorption and transport) and forego time dependence (required to predict impedance) in order to solve for the full nonlinear i—rj characteristics at steady state. 

Another set of papers countering the conclusions of the Adler studies (as well as implicitly the Svens-son studies) were published by Liu and co-workers, who questioned the validity of the Adler model on several levels. As discussed elsewhere,... 

Inconsistency of performance with a bulk path at low vacancy concentration. A quantitative comparison between predictions of the Adler model and impedance data for LSC shows the poorest agreement (underprediction of performance) at low temperatures, high F02. and/or low Sr content. These are the conditions under which the bulk vacancy concentration (and thus also the ionic conductivity and surface exchange rate of oxygen with the bulk) are the lowest. These are exactly the conditions under which we would expect a parallel surface path (if it existed) to manifest itself, raising performance above that predicted for the bulk path alone. Indeed, as discussed more fully in section 5, the Adler model breaks down completely for LSM (a poor ionic conductor at open-circuit conditions), predicting an... 

Many mixing models which utilize the simplified concepts of micro-mixing and segregation have been introduced. Most notable of these are the two-environment models of Chen and Fan (19), Kearns and Manning (20), and others (21, 22), and the dispersion models of Spielman and Levenspiel (23), and Kattan and Adler (24). 

The overall system that we will analyze comprises the unbleached Kraft pulp line, chemicals and energy recovery zones of a specific paper mill (Melville and Williams, 1977). We will employ a somewhat simplified but still realistic representation of the plant, originally developed in a series of research projects at Purdue University (Adler and Goodson, 1972 Foster et al., 1973 Melville and Williams, 1977). The records of simulated operation data, used to support the application of our learning architecture, were generated by a reimplementation, with only minor changes, of steady-state models (for each individual module and the system as a... 

Pierre M. Adler, Ali Nadim, and Howard Brenner, Rheological Models of Suspensions Stanley M. Englund, Opportunities in the Design of Inherently Scfer Chemical Plants H. J. Ploehn and W. B. Russel, Interactions between Colloidal Particles and Soluble Polymers... 

Santschi PH, Li YH, Adler DM, Amdurer M, Bell J, Nyffeler UP (1983) The relative mobility of natural (Th, Pb and Po) and fallout (Pu, Am, Cs) radionuclides in the coastal marine-enviromnent - results from model-ecosystems (MERL) and Narragansett Bay. Geochim Cosmochim Acta 47 201-210... 

Pierre M. Adler, Ali Nadim, and Howard Brenner, Rheological Models of Suspenions... 

Figure 25. Adler s ID macrohomogeneous model for the impedance response of a porous mixed conducting electrode. Oxygen reduction is viewed as a homogeneous conversion of electronic to ionic current within the porous electrode matrix, occurring primarily within a distance A from the electrode/electrolyte interface (utilization region). (Adapted with permission from ref 28. Copyright 1998 Elsevier.)...

One limit of behavior considered in the models cited above is an entirely bulk path consisting of steps a—c—e in Figure 4. This asymptote corresponds to a situation where bulk oxygen absorption and solid-state diffusion is so facile that the bulk path dominates the overall electrode performance even when the surface path (b—d—f) is available due to existence of a TPB. Most of these models focus on steady-state behavior at moderate to high driving forces however, one exception is a model by Adler et al. which examines the consequences of the bulk-path assumption for the impedance and chemical capacitance of mixed-conducting electrodes. Because capacitance is such a strong measure of bulk involvement (see above), the results of this model are of particular interest to the present discussion. 

Bylaite, E., Adler-Nissen, J., and Meyer, A.S. Effect of xanthan on flavor release from thickened viscous food model systems, J. Agric. Food Chem., 53(9) 3577-3583, 2005. 

Instead of considering fluid in deadwater regions to be completely stagnant, an alternate view considers that there is a slow interchange or cross flow between the fluid in these regions and the active fluid passing through the vessel. With this approach Adler and Hovorka (A2) treated the combined model shown in Fig. 20. This consists of j identical units... 

A2. Adler, R. J., and Hovorka, R. B., A Finite-Stage Model for Highly Asymmetric Residence-Time Distributions, Preprint 3, Second Joint Automatic Control Conference, Denver, Colorado, June, 1961. 

Neftel, K.A, Adler, R H, Kaeppeli, L., et ah Stage fright in musicians a model illustrating the effect of beta blockers. Psychosom. Med. 44, 461-469, 1982. 

For this model, the current through the capacitor is given by (Adler et al., 2003) ... 

Tr(C) reported in Fig. 4.8, and corresponding to safe operative conditions according to the Adler and Enig criterion, are obtained with the Semenov number Se = 0.47, which is well above the maximum critical value provided by the Semenov criterion, Sec = 0.377, as given by (4.28). This difference mainly arises from the inclusion into the mathematical model of the terms accounting for consumption of reactant A. 

Dorfler, U., Adler-Kohler, R., Schneider, P., Scheunert, I., Korte, F. (1991) A laboratory model system for determining the volatility of pesticides from soil and plant surfaces. Chemosphere 23, 485-496. 

Figure 5- Models, a, general case. Fluid flows from left to right at constant velocity and is transferred from the E.E. (unshaded tubes, Min. Mix.) to the L.E. (shaded area, Max. Mix.). In the s(, a) space, a particle having a given residence time tg describes a trajectory between the plane a = 0 and the plane X = 0 b, a model of Spencer et stl. (68). Each particle stays in the E.E. for a duration proportional to its residence time c,r p model of Spencer et al. (68), which is also the series model of Weinstein and Adler (69) Each particle stays for a constant time in the E.E., provided tg> d, parallel model of Weinstein and Adler...

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