Mass-age distributions

The observed Phanerozoic rock mass distribution appears to consist of two mass maxima separated by a minimum in the mass of rock preserved per unit time. Gregor (1985) has demonstrated that the mass-age distribution for Carboniferous and younger sediments has a log linear relationship such that ... 

Figure 10.2. Observed and model sedimentary rock mass-age distributions. Observed mass distribution is represented by stippled area. Dashed curve is a model calculation for constant deposition and destruction rates of sediments of all age groups, whereas the histogram represents the results of a model calculation in which variations in these rates are permitted. The mean age of the sedimentary rock mass is about 350 million years. (After Garrels et al., 1976.)...

Figure 10.3. Mass-age distribution of the Phanerozoic Systems plotted as the logarithm of the survival rate (S, mass of System divided by duration of Period) versus age. (After Gregor, 1985.)...

Figure 10.5. Mass-age distribution of carbonate rocks and other sedimentary rock types plotted as survival rate (S) versus age. Total rock mass data from Gregor (1985) and estimates of carbonate rock mass from Table 10.1.

Mass-age distribution and recycling rates Dolomite/calcite ratios Ooids and ironstones Calcareous shelly fossils The carbonate cycle in the ocean... 

The original concept of recycling, as developed by Garrels and Mackenzie (1971a), was based solely on the continental database assembled by the group at the Vernadsky Institute of Geochemistry in Moscow (Ronov, 1949, 1964, 1968, 1976, 1982, 1993). The former authors proposed that the present-day mass/age distribution of global... 

The above view is clearly supported by the mass/age distribution of lithologies within the same tectonic domain. For example, carbonates, chert, red clay, and terrigeneous sediments on the ocean floor (Hay et al., 1988) all have the same type of age distribution pattern that is controlled by a single variable, the rate of spreading and subduction of the ocean floor. This sedimentary mass also differs lithologically from its continental counterpart, because it is comprised of... 

Figure 6 The mass/age distribution of preserved sedimentary mass deposited on continental crust (vertical lines), basin of passive margins (black), and on the oceanic floor (cross-hatched) (courtesy of W. W. Hay).

Figure 8 Observed cumulative mass/age distributions of major sedimentary lithological types. Explanation of abbreviations gr denotes graywackes sh, shales ark, arkoses ss, sandstones dol, dolostones evap, evapor-ites Im, limestones phosp, phosphorites CB, continental basement P, platforms MOB, mature erogenic belts OD, oceanic domain (after Veizer, 1988c).

Crystal structures can indeed be predicted, if the word is taken in a sensible meaning. Compare this situation with astrophysics we know mass, age, distribution, speed, and spectral properties of galaxies, although we do not (and we do not need to) know the absolute position of each star in a galaxy. In a similar fashion, computational crystallography can easily predict the essential parameters of the bulk texture of organic matter in the solid state, although it cannot tell the exact position of each atom in a crystal structure. 

Thus the age distribution of the surface is of an exponential form. From equation 10.113 the mass transfer rate at unit area of surface of age r is given by ... 

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 ... 

Given that, from the penetration theory for mass transfer across an interface, the instantaneous rale ol mass transfer is inversely proportional to the square root of the time of exposure, obtain a relationship between exposure lime in the Higbie mode and surface renewal rate in the Danckwerts model which will give the same average mass transfer rate. The age distribution function and average mass transfer rate from the Danckwerts theory must be deri ved from first principles. 

In calculating Ihe mass transfer rate from the penetration theory, two models for the age distribution of the surface elements are commonly used — those due to Higbie and to Danckwerts, Explain the difference between the two models and give examples of situations in which each of them would be appropriate. 

In the Danckwerts model, it is assumed that elements of the surface have an age distribution ranging from zero to infinity. Obtain the age distribution function for this model and apply it to obtain the average, mass Iransfer coefficient at the surface, given that from the penetration theory the mass transfer coefficient for surface of age t is VlD/(7rt, where D is the diffusivity. 

Explain the basis of the penetration theory for mass transfer across a phase boundary. What arc the assumptions in the theory which lead to the result that the mass transfer rate is inversely proportional to the square root of the time for which a surface element has been expressed (Do not present a solution of the differential equal ion.) Obtain the age distribution function for the surface ... 

Danckwerts assumed a random surface renewal process in which the probability of surface renewal is independent of its age. If s is the fraction of the total surface renewed per unit time, obtain the age distribution function for the surface and show that the mean mass transfer rate Na over the whole surface is ... 

In the preceding sections it was always assumed that all drops of the dispersed phase had the same diameter, and that, for the case that there is segregation, a spread in the concentration distribution was only caused by a spread in age distribution. However, as pointed out before, a spread in the drop size distribution may also cause different concentrations in the drops, even when these drops have the same age. Generally this may be expected only when there is mass transfer limitation. 

Figure 17. Mass activity distribution maps for both new and aged MEAs showing impact of 200 unmitigated start-stop cycles. Test conditions rcen = 80 °C, dewpt = 85 °C (anode and cathode), P = 250/270 kPaa, s (anode/cathode), high stoichiometry flow for anode (H2) and cathode (O2).

E E(t) EDM EDTA EDX EHD EKI EO EOF ESI-MS Ez Activation energy Exit-age distribution function Electro-discharge machining Ethylene-diamine-tetraacetic acid Energy dispersive X-ray Electrohydrodynamic Electrokinetic instability Electroosmotic-Electroosmotic flow Electrospray ionization mass spectrometry Electric field... 

These trends in lithologic features of the sedimentary rock mass can be a consequence of both evolution of the surface environment of the planet and recycling and post-depositional processes. It has been argued (e.g., Mackenzie, 1975 Veizer, 1988) that both secular and cyclic evolutionary processes have played a role in generating the lithology-age distribution we see today. For the past 1.5-2.0 billion years, the Earth has been in a near present-day steady state, and the temporal distribution of rock types since then has been controlled primarily by... 

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. 

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