Transient behaviour

Microelectrodes with several geometries are reported in the literature, from spherical to disc to line electrodes each geometry has its own critical characteristic dimension and diffusion field in the steady state. The difhisional flux to a spherical microelectrode surface may be regarded as planar at short times, therefore displaying a transient behaviour, but spherical at long times, displaying a steady-state behaviour [28, 34] - If a... 

A transformer has both dielectric capacitances and electromagnetic inductances. Surge transference thus depends on the electrostatic and electromagnetic transient behaviour of these parameters as noted below. 

Table 3.4 Transient behaviour of a seeond-order system...

The position of the closed-loop poles in the. v-plane determine the nature of the transient behaviour of the system as can be seen in Figure 5.5. Also, the open-loop transfer function may be expressed as... 

Strictly speaking, all perturbations must be time-dependent we cannot arrange for them to have been in existence since t = —oo and we must instead switch them on. As in an electrical circuit, such switching-on causes initial transient behaviour that eventually dies away to leave a steady state. 

How can we confirm this sacrificial promoter model By simply looking at the r vs t transient behaviour of Figure 4.13 or of any galvanostatic NEMCA experiment upon current interruption (1=0). 

Complex models are often slow in execution owing to the large number of equations involved and the large range of time constants. Under these circumstances it is often useful to approximate the transient behaviour of the full model by a simpler model representation which is faster to compute. Such simplifications are commonly achieved by a combination of first-order lags and time delays and are often represented in Laplace transform form, especially when the sub-model is to be used as part of a control engineering application. 

Relaxation methods are not competitive with the steady-state methods in the use of computer time, because of slow convergence. However, because they model the actual operation of the column, convergence should be achieved for all practical problems. The method has the potential of development for the study of the transient behaviour of column designs, and for the analysis and design of batch distillation columns. 

C Hosokawa, H Tokailin, H Higashi, and T Kusumoto, Transient behaviour of thin film electroluminescence, Appl. Phys. Lett., 60 1220-1222, 1992. 

The general equation of convective diffusion in liquids, equation (15), is a second-order, partial differential equation with variable coefficients. Its solution yields the spatial distribution of c, as a function of time, namely its transient behaviour. On an analytical level, solution of equation (15) into the transient c(t) is possible only for a number of relatively simple systems with well-defined geometry and flow properties. The problem is greatly simplified if the concentration function Cj(x,y,z) is essentially independent of time t, i.e. in the steady-state. Then equation (15) reduces to ... 

If, at large time intervals, flux data do not change within the experimental error, the steady-state hypothesis is the simplest option. A possible check on that hypothesis would be to analyse the data in comparison with the transient behaviour as derived from the general expressions given above for given values of k and Ku. 

Hlavacek, V. (1977). Analysis of a complex plant—steady state and transient behaviour. I Plant data estimation and adjustment. Comput. Chem. Eng. 1, 75-100. 

The main assumptions of the method are not explicitly declared. For example, Rogers does not discuss the problems with respect to the conflict between the transient behaviour of a batch process and the implicit steady-state assumption of the mass balance. However, the mathematical model behind the mass-balance method is quite clear. The work does not include any uncertainty propagation analysis of the mass-balance method. 

We are thus, in many instances, more interested in the transient behaviour early in a reaction than we are in the more easily studied final or equilibrium state. With this in mind, we shall be concerned in our early chapters with simple models of chemical reaction that can satisfy all thermodynamic requirements and yet still show oscillatory behaviour of the kind described above in a well-stirred closed system under isothermal or non-isothermal conditions. 

If the computations are made with all the data taken from Table 2.1, however, a remarkable difference appears (Fig. 2.4). There is an initial transient behaviour during which the concentrations of the intermediates move quickly to the appropriate pseudo-stationary values. The PSS curves... 

Kay, S. R. and Scott, S. K. (1988). Multiple stationary states, sustained oscillations and transient behaviour in autocatalytic reaction diffusion equations. Proc. R. Soc., A418, 345-64. 

Ertl, G. (1989). The oscillatory catalytic oxidation of carbon monoxide on platinum surfaces. In Spatial inhomogeneities and transient behaviour in chemical kinetics, (ed. P. Gray, G. Nicolis, F. Baras, P. Borckmans, and S. K. Scott), ch. 37, pp. 563—76. Manchester University Press. 

Prior to the establishment of the steady states discussed in Sect. 4.2, the cell must pass through transient states which are more difficult to treat. Moreover, to delineate the transient behaviour, we would need to specify the exact electrical constraints. We shall therefore content ourselves here with deriving the general relationship that is obeyed during the transient phase, but we shall not solve this relationship. 

I. The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts (2 vols.). Vol. 1 The Theory of the Steady State. VoL 2 Questions of Uniqueness, Stability, and Transient Behaviour. Oxford Clarendon Press, 1975. 

Forced oscillations of chemical reactors. In P. Gray et al. (eds.), Spatial Inhomogeneities and Transient Behaviour in Chemical Kinetics., Manchester Manchester University Press, 1990. 

P. Marjanovic, Modelling the transient behaviour of blow tank pneumatic conveying system. Powder handling and processing, Trans. Tech. Pub. 5 (3) (1993) 219-226. 

In conclusion, it must be noted that the equations to describe the transient behaviour of heterogeneous catalytic reactions, usually have a small parameter e = Altsot/Alt t. Here Atsot = bsS = the number of active sites (mole) in the system and Nfot = bg V = gas quantity (mole). Of most importance is the solution asymptotes for kinetic equations at A/,tsot/7Vtflt - 0, 6S, bg and vin/S being constant. Here we deal with the parameter SjV which is readily controlled in experiments. The case is different for the majority of the asymptotes examined. The parameters with respect to which we examine the asymptotes are difficult for control. For example, we cannot, even in principle, provide an infinite increase (or decrease) of such a parameter as the density of active sites, bs. Moreover, this parameter cannot be varied essentially without radical changes in the physico-chemical properties of the catalyst. Quasi-stationarity can be claimed when these parameters lie in a definite range which does not depend on the experimental conditions. 

Derwent R.G. Collins W.J. Johnson C.E. and Stevenson D.S. (2001). Transient behaviour of tropospheric ozone precursors in a global 3-D CTM and their indirect greenhouse effects. Clim. Change, 49(4), 463-487. 

Figure 6 Calculation results of transient behaviour of primary coolant pressure, heat transfer tube temperature of PPWC and IHX, RPV temperature and fuel temperature...

A comparison of the results of a theoretical treatment of the transient behaviour of iron catalysts with experimental data shows that the low turnover frequencies found for those catalysts cannot be the result of a low rate constant for the propagation reaction. To obtain accurate data for the transient period, which lasted less than 20 s, a reaction system with very little axial dispersion was built. 

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