Concentration pulse

For a short description of the aims of experimental concentration cycling with respect to citraconic acid formation, see [13]. It is also demonstrated there that the response to rectangular concentration pulses for a given reactor configuration of a multi-channel-stack micro reactor can be improved by increasing the number of platelets and channels (while reducing their diameter). Such behavior was shovm for an incompressible fluid, i.e. is not solely related to the above-mentioned reaction. 

Square Concentration Pulses in Oxidation Catalysis over Perovskite-type Oxides of Manganese and Iron... 

A square concentration pulse flow technique has been developed to study the kinetics of catalytic reactions over catalysts which change their stoichiometry in response to the reaction conditions. The technique makes it possible to obtain hysteresis-free kinetics data while greatly reducing the time during which the catalyst is exposed to the reaction mixture. 

There are many facets of this study which we feel merit further investigation. In particular it is necessary to consider am extension of the proposed model, which in its present form is confined to the performance of a simple column, to cover the behaviour of any set of columns since it is column sets which are normally used. In addition, it is important to consider the input to the model which should be truly representative of polymers with a molecular weight distribution and not merely a concentration pulse of perfectly monodisperse polymer. In relation to this latter suggestion it would be significant if it were possible to link this model to the very real problem of deconvolution, i.e. the removal of instrumental and column broadening from the observed chromatogram to produce the true molecular weight distri-... 

Fig. 4.33 Shift of concentration pulses (Dirac impulses) for an aspect ratio of 0.1 in the water-acetone system (arrows indicate the individual peak maximum the hatched line connects the peak maxima).

Atmospheric inputs, particularly wet deposition, are variable in both space and time. Thus the atmosphere provides higher concentration pulses to the surface waters than mean atmospheric concentrations suggest, and may impose localised non-steady state conditions in surface waters which have the potential to promote phytoplankton growth (Owens et al., 1992 Michaels et al., 1993). 

Not only concentration pulses have been used as input signals. Wojciechowski used temperature ramps with his temperature scanning reactor [99, 103] and Kobayashi and Kobayashi [104] applied concentration step functions. Typical process parameters, which can be changed, are the pressure, the temperature or the composition of the gas mixture. Fast mixture or pressure pulses can be realized by the injection of reaction gas into the system by a micro-dispense valve. An appropriate flow sensor will then record the transition into the next stationary mode. 

Oh, Se H., Hegedus, L. L., Baron, K. and Cavendish, J. C., "Carbon Monoxide Oxidation in An Integral Reactor. Transient Response to Concentration Pulses in the Regime of Isothermal Multiplicities" Proc. ISCRE5 ACS Symposium Series 65,... 

Rapid desorption, which maximizes the output concentration pulse... 

The ultimate goal of a basic study of separations is to obtain a description of how component concentration pulses (zones or peaks) move around in relationship to one another. The flux density J tells how solute moves across boundaries into and out of regions, but it does not detail the ebb and flow of concentration. To do the latter we must transform J into a form that directly yields concentration changes. The procedure followed below for this is standard in many fields. It is followed, for example, in treatments of heat conduction and diffusion [14,15]. We shall continue to simplify our treatment to one dimension. 

We note that (7, v, and D may vary with x in some systems, but these variations are negligibly slow compared to the rapid variation of c with x associated with sharp concentration pulses. More complicated are variations of U, v, and D with concentration. However, since sample amounts are generally small in analytical separations, the concentration dependence can usually be ignored. 

Equations 3.30 and 3.31 are the basic differential equations for separation systems when solved, they show how concentration varies with time and distance, that is, the way in which concentration pulses move and evolve with the passage of time. 

The first moment, which is simply the position of the center of gravity of the concentration pulse, is zero because the zero of coordinate axis y is arbitrarily fixed at the center of gravity (see Eq. 3.36). In fact all odd moments are zero if c(y, t) is a Gaussian or other symmetrical function about y = 0. For asymmetric zones the value of the third moment becomes a measure of the asymmetry. More specifically, asymmetry is often measured by a normalized third moment called the skew, defined as (y3)/(y2)3/2. The flattening of a zone is measured by excess, ( y ) y2)2) - 3. Both skew and excess are zero for Gaussians as shown in Figure 5.2. 

Solute is introduced into a chromatographic column as a squareshaped concentration pulse, which occupies an initial width w on the column. Calculate the second moment about the mean (the variance a2) in terms of w. Calculate [Pg.109]

Chapter 5 dealt with the evolution of thin starting zones into concentration pulses distributed along a single axis. This treatment is appropriate for some important analytical separation methods, such as column chromatography carried out in thin one-dimensional tubes. However, as an alternate method... 

Nonlinear and dynamic models of desorption are used in the sequel. Mathematical justification of the boundary-value problems for the TDS-degassing method of metal saturated with hydrogen is given in [6,7]. The work [4] was a starting point of the results presented here. Algorithm of parameter identification for the model of hydrogen permeability of metals for the concentration pulses method [5] is presented in [8],... 

Gabis I.E. (1999) The method of concentration pulses for studying hydrogen transport in solids, J. Technical Physics 44(1) 90-94. 

The samples without defensive film coat were studied by the method of concentration pulses (MCP) at pressure 0.2 Torr within the range of temperatures 370 -596 °C in order to determine the hydrogen permeability parameters of stainless steel (12X18H10T). The knowledge of these parameters allowed to simplify the problem of parameter identification for titanium nitride. The samples with titanium nitride covering were studied by method of permeability at pressures 0.5-249 Torr and the temperatures 380-670 °C. 

To describe the hydrogen transfer in material without defensive coat for the concentration pulses method we used the model... 

The estimation of parameters D, b, s, a, a2 in model (11) - (17) of the hydrogen transfer in stainless steel was made by the identification algorithm based on the Fourier series. The detailed description of the algorithm is in [3, 4]. The experimental data got by the concentration pulses method were used for identification. In addition the estimations of s, X = Db1/2 were received by isotherms for the permeability method [3, 4]. Below we describe the identification algorithm based on the Fourier series. 

Popov V.V., Gabis I.E., Sidorov N.I., Zaika Yu.V. (2005) Studying hydrogen permeability by method of concentration pulses, Journal of Alloys and Compounds (at press). 

Various reactors can be used for dynamic experiments. The application of recycle reactors to the investigation of the underlying reaction networks has been demonstrated by Bennett [58], who operated a recycle reactor with the dynamic method by superimposing reactant concentration pulses on the inlet stream. To ensure that the amounts of gaseous components adsorbed on the catalyst are appreciable compared to the amounts of measurable components flowing, the ratio of the catalyst to total reactor volume was made as high as possible. A reactor system, designed for transient experiments, has been described by Bennett et al. [43]. 

Harlicl PJ.E. and Tezel, F.H., A Novel Solution Method for Interpreting Binary Adsorption Isotherms from Concentration Pulse Chromatography Data , Adsorption, 6 (2000), pp.293-309... 

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