Transport monotonously decreasing

This equation should be fulfilled at least in one point for x + D > 0. To note y is here the rate of cleavage. Hence, there are no limitations for its value. Eq. (22) shows that the condition for obtaining a maximum when we have a single cleavage center is independent of the actual form of the transport rate function, but is rather dependent on its slope. This would suggest that it is possible to obtain a peak in the length distribution even when the transport rate function is monotonically decreasing, and indeed that is what we find from our numerical simulations. 

Fig. 14.6 (a) Monotonously decreasing transport rate function v(x) = v (x). The vertical lines show the location of the point where the condition for the maximum in the length distribution (Eq. 22) holds and the location of the cleavage centre. The parameters are D = 15 and y = 0.001. 

Most experimental kinetic curves are rather smooth, i.e, the concentration of adsorbate in solution monotonically decreases, but some kinetic curves reported in the literature have multiple minima and maxima, which are rather unlikely to be reproducible. Such minima and maxima represent probably the scatter of results due to insufficient control over the experimental conditions. For instance use of a specific type of shaker or stirrer at constant speed and amplitude does not necessarily assure reproducible conditions of mass transfer. Some publications report only kinetic data—results of experiments aimed merely at establishing the sufficient equilibration time in equilibrium experiments. Other authors studied adherence of the experimentally observed kinetic behavior to theoretical kinetic equations derived from different models describing the transport of the adsorbate. Design of a kinetic experiment aimed at testing kinetic models is much more demanding, and full control over all parameters that potentially affect the sorption kinetics is hardly possible. 

The correlations for and deduced from the HFD-B potential have been accepted as the basis for the description of the dilute-gas transport data. The functionals 6 and 6, defined by equations (14.5), ate monotonically decreasing functions of the reduced temperature r = in the range 0.5 < T < 15 and are to within 0.1%... 

If the unsaturated zone is composed of relatively fine sediment (silt and fine sands) a quasi-uniform seepage flow can be assumed for the unsaturated zone in humid climate zones over long time spans. Therefore, the transport of infiltration water can be simulated in PHREEQC as a monotonous movement in accordance with the "piston flow model. A constant flow of infiltration water of 0.5 m per year is assumed for the following simulation. Furthermore, it is considered simplistically that the infiltrating precipitation has a tritium activity of 2000 TU (tritium units) over a period of 10 years. Then, it is assumed that the tritium activity decreases to zero again. 

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