Surface aging

An empirically determined relationship between drop weight and drop time does allow surface tensions to be determined for small surface ages [41],... 

If, on the other hand, it is assumed that contact times for the individual fluid elements vary at random, an exponential surface age distribution characterized by a fractional rate of renewal s may be used (34). This approach is caUed surface renewal theory and results in... 

The average transfer rate according to the Higbie model for surface age distribution then becomes ... 

In the Danekwens model of mass transfer it is assumed that the fractional rate of surface renewal s is constant and independent of surface age. Under such conditions the expression for the surface age distribution function is = If the fractional rate of surface renewal were proportional to surface age (say s — bt. where b is a constant), show that the surface age distribution function would then assume the form ... 

Experiments have been carried out on the mass transfer of acetone between air and a laminar water jet. Assuming that desorption produces random surface renewal with a constant fractional rate of surface renewal, v, but an upper limit on surface age equal to the life of the jet, r, show that the surface age frequency distribution function, 4>(t), for this case is given by ... 

The selectivity in a system of parallel reactions does not depend much on the catalyst size if effective diffusivities of reactants, intermediates, and products are similar. The same applies to consecutive reactions with the product desired being the final product in the series. In contrast with this, for consecutive reactions in which the intermediate is the desired product, the selectivity much depends on the catalyst size. This was proven by Edvinsson and Cybulski (1994, 1995) for. selective hydrogenations and also by Colen et al. (1988) for the hydrogenation of unsaturated fats. Diffusion limitations can also affect catalyst deactivation. Poisoning by deposition of impurities in the feed is usually slower for larger particles. However, if carbonaceous depositions are formed on the catalyst internal surface, ageing might not depend very much on the catalyst size. 

Surface bio-etching in nature. Defects created by a-rays or fission fragments at the surface of a mineral are easily etched by acidic water, zeroing the surface age. Biological etching in a worm that swallowed soils, might occur for surface defects. 

Surface renewal theory (Danckwerts, 1951) proposes that there is an infinite range of ages for elements of the surface and the surface age distribution function (t) can be expressed as... 

This is a dynamic method and can be used to measure y from first instants of formation up to greater surface ages depending on the flow rate. 

In the Danckwerts model of mass transfer it is assumed that the fractional rate of surface renewal, s is constant and independent of surface age. Under such conditions the expression for the surface age distribution function is s st. 

If the fractional rate of surface renewal were proportional to surface age (say, s = bt, where b is a constant), show that the surface age distribution function would then assume the form ... 

Figure 3.31 Correlation of the normalised dynamic surface pressure n(f)/neq at a surface age of 100 ms with the rate of foam formation dh/dt. The correlation holds for various systems (reproduced with permission [9]).

Here, we still find noritic material on the surface. Age determinations on selected Apollo 14 samples showed that the material of the Fra Mauro area underwent thermal metamorphism about 3.9 x 109 years ago93 The Imbrium collision is thought to have provided the required energy and is therefore dated accordingly by various authors93,94,95. ... 

The dynamic surface tension curve can be divided into three parts the first equilibrium state represents values at low surface ages (Region 1 in Fig. 7), a rate limiting state (Region 2 in Fig. 7), and the second equilibrium state represented by the static surface tension (Region 3 in Fig. 7). 

Parameters for transfer of uranium into and out of bone were assumed to be proportional to those of alkaline earth elements such as calcium (the U02 ion can substitute for the Ca "" ion at bone surfaces). Age-specific bone turnover rates developed for a generic alkaline-earth model (ICRP 1993) were incorporated into the uranium model to predict distribuhon to the tissues. As a result of this change, a greater proportion of uranium distributes to bone and a lesser proportion to soft tissues at ages under 25 years, compared to adults. 

An important issue for irradiation chemistry is the dose versus depth into the surface. This was computed by J. Cooper et oZ. and the results for Europa are shown in Fig. 3. Here the vertical axis is the time to achieve a dose of 100 eV per molecule in H2O. This is a useful form since we note below that radiation chemists typically give radiation effects as G-vaJues, the number of a particular molecular species created or destroyed for each 100 eV of energy deposited. Geologist have suggested that the youngest surface ages are 10 years on Europa/ hence, the significant dose, as... 

Jacobson A. D., Blum J. D., Chanberlain C. P., Poage M. A., and Sloan V. E. (2002) Ca/Sr and Sr isotope systematics of a Himalayan glacial chronosequence carbonate versus silicate weathering rates as a function of landscape surface age. Geochim. Cosmochim. Acta 66, 13-27. 

Crocker R. L. and Major J. (1955) Soil development in relation to vegetation and surface age at Glacier bay, Alaska. J. Ecol. 43, 427-448. 

The classic penetration model of Higbie (1935) is based on the assumption that all the fluid elements reside at the interface for the same length of time. The surface age distribution for this model is... 

Figure 9.3. Surface age distribution according to Danckwerts the elements undergo random surface renewal at frequency s.

The Danckwerts surface age distribution (Eq. 9.1.6) leads to an average value of the mass transfer coefficient given by... 

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