Quasi-equilibrium state

The flux of 3H-labeled PNU-78,517 across MDCK cell monolayers shows the characteristic disparity between the kinetics of disappearance from the donor solution and appearance in the receiver sink (Fig. 32). Drug uptake is rapid and exponential with time and approaches a quasi-equilibrium state in contrast, the concomitant efflux of drug into the receiver is slow and linear. While maintaining a 3% bovine serum albumin (BSA) concentration in the donor and varying the BSA concentration between 0.5 and 5% in the receiver, the results show that the... 

As will be discussed in the following chapter, most combustion systems entail oxidation mechanisms with numerous individual reaction steps. Under certain circumstances a group of reactions will proceed rapidly and reach a quasi-equilibrium state. Concurrently, one or more reactions may proceed slowly. If the rate or rate constant of this slow reaction is to be determined and if the reaction contains a species difficult to measure, it is possible through a partial equilibrium assumption to express the unknown concentrations in terms of other measurable quantities. Thus, the partial equilibrium assumption is very much like the steady-state approximation discussed earlier. The difference is that in the steady-state approximation one is concerned with a particular species and in the partial equilibrium assumption one is concerned with particular reactions. Essentially then, partial equilibrium comes about when forward and backward rates are very large and the contribution that a particular species makes to a given slow reaction of concern can be compensated for by very small differences in the forward and backward rates of those reactions in partial equilibrium. 

For n-type semiconductor electrodes in which a redox reaction of cathodic hole iiyection reaches its quasi-equilibrium state at the electrode interface, the recombination current of iiqected holes (minority charge carriers) with electrons (minority charge carriers), w, is given by Eqn. 8-70 [Reineke-Memming, 1992] ... 

In the mechanism of the anodic iron dissolution, described in this section, the formation process of the intermediate of ferrous hydroxocomplexes, Eqn. 9-21a, is in the quasi-equilibrium state so that the Nemst equation applies between the adsorption coverage, 6p oa-, of the intermediate FeOH [d and the overvoltage, t). Accordingly, for the range of relatively low coverages of adsorption to which Langmuir s adsorption isotherm applies, we obtain Eqn. 9-22 ... 

Consider a micellar solution at equilibrium that is subject to a sudden temperature change (T-jump). At the new temperature the equilibrium aggregate size distribution will be somewhat different and a redistribution of micellar sizes will occur. Aniansson and Wall now made the important observation that when scheme (5.1) represents the kinetic elementary step, and when there is a strong minimum in the micelle size distribution as in Fig. 2.23(a) the redistribution of micelle sizes is a two-step process. In the first and faster step relaxation occurs to a quasi-equilibrium state which is formed under the constraint that the total number of micelles remains constant. Thus the fast process involves reactions in scheme (5.1) for aggregates of sizes close to the maximum in the distribution. This process is characterized by an exponential relaxation with a time constant Tj equal to... 

When the system has reached its quasi-equilibrium state a slower process, involving the relaxation to the true equilibrium, becomes measureable. This process involves a change in the number of micelles. The formation or dissolution of a micelle involves according to scheme (5.1) the appearence of aggregates of size at the minimum of the size distribution curve, and since these aggregates occur with low probability the process can be a very slow one. Aniansson and Wall showed that this process is also characterized by an exponential decay with a relaxation time r2,... 

Sparks and Jardine (1984) studied the kinetics of potassium adsorption on kaolinite, montmorillonite, and vermiculite (Fig. 2.1) and found that a single first-order reaction described the data well for kaolinite and smectite while two first-order reactions described adsorption on vermiculite. One will note deviations from first-order kinetics at longer time periods, particularly for montmorillonite and vermiculite, because a quasi-equilibrium state is reached. These deviations result because first-order equations are only applicable far from equilibrium (Skopp, 1986) back reactions could be occurring at longer reaction times. 

Two methods have been proposed for the preparation of organosilane monolayers. One is chemisorption from organosilane solution [4-6], and the other one is Langmuir-Blodgett (LB) method or water-cast method [7-23], Fig. 1 shows the film formation mechanism of the organosilane by LB method (a) and chemisorption method (b). In the case of LB method (Fig. 1(a)), the toluene solution of organotrichlorosilane was spread on the water surface (pH 5.8) at a controlled subphase temperature. To attain quasi-equilibrium state of the monolayer, the monolayer was kept on the water subphase under a given... 

To examine the dynamical aspect of the hysteretic behavior, we consider the system geometry shown in Fig. 4. The porous material of length L in the z-direction is bounded by the gas reservoirs at z = 0 and z = L. Periodic boundary conditions are imposed on the X and y-directions. In typical experimental situations, starting from a (quasi)-equilibrium state, the external vapor pressure of the gas reservoir is instantaneously changed by a small amount, which induces gradual relaxations of the system into a new state. This geometry was used in recent work on dynamics of off-lattice models of adsorption (Sarkisov and Monson,... 

In a quasi-equilibrium state, a -exponential function [20] whose tail is of power type is reported in the HMF model with a certain type of initial condition [15]. The initial condition known as waterbag seems special because it lies on a one-dimensional line on two-dimensional p-space. To check generality, we must compute distribution functions for another type of initial condition that spreads on two-dimensional subspace of the p-space. 

In order to calculate the spectrum, the chemical-shielding tensors of all spins, as well as their relative orientation and distances, have to be known. The assumption of a quasi-equilibrium state simplifies Equation (4.28) considerably. For long mixing times t , all elements in exp(Wr ,) have equal intensity. This leads to the following signal function for a single-crystallite orientation ... 

In the preceding sections it has also been shown that fundamental dynamic quasi equilibrium states exist between the activities of autotrophic and heterotrophic organisms, respectively. The unique role of ozone as indispensible protective agent has been discussed. 

The so-called kinetic methods for the determination of nitrate-melt acidities are based on this reaction the rate of N02 evolution from the melts is dependent only on their acidity. Further, in the process of reaction (1.2.6), the concentration of NOj cation decreases this causes a fall in the rate of nitrogen dioxide evolution. Finally, the latter becomes so slow that a series of sequential measurements of pO demonstrates that this parameter is constant, i.e. the system passes to a quasi-equilibrium state. The pO value measured under these conditions is the upper limit of the melt acidity, which is independent of the composition of the added strong acid. All the above-said allows us to explain the thermal dependence of the upper limit of acidity for nitrate melts observed in [67] the rise of the melt temperature results not only in the decrease of cation NOj stability but also in the increase of the rate of reaction (1.2.6). 

The same relations are valid also at small deviations of the adsorption layer from equilibrium. In this case the DL is in a quasi-equilibrium state (Dukhin Deijaguin 1974, Dukhin Shilov... 

Figure 10-11. Plasma conversion of methane results of experiments and simulations presented as the methane conversion dependence on specific energy input (1) thermodynamic calculations of the quasi-equilibrium states (2) experiments with purely thermal energy input (3, 6, 7) experiments with a discharge (4, 5) theoretical lines representing isotherms (fixed temperature 7).

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