Residence repartition

If uranium is internally cycled in coastal environments or if the riverine delivery of U shows some variability, residence time estimates (regardless of their precision) cannot be sensitive indicators of oceanic uranium reactivity. Based on very precise measurements of dissolved uranium in the open ocean, Chen et alJ concluded that uranium may be somewhat more reactive in marine environments than previously inferred. Furthermore, recent studies in high-energy coastal environments " indicate that uranium may be actively cycled and repartitioned (non-conservative) from one phase to the next. 

We say the solution is saturated if solute is partitioned between a liquid-phase solution and undissolved, solid material (Figure 5.16). In other words, the solution contains as much solute as is feasible, thermodynamically, while the remainder remains as solid. The best way to tell whether a solution is saturated, therefore, is to look for undissolved solid. If -Repartition) is small then we say that not much of the solute resides in solution, so most of the salt remains as solid - we say the salt is not very soluble. Conversely, most, if not all, of the salt enters solution if K(partition) is large. 

Eunction F (t) is directly connected to the residence time distribution. It is recognized as the repartition function of the residence time random variable. So, F(t) shows the fraction of the fluid elements that stayed in the device for a time less than or equal to t. Between F(t) and E(t) the following integral and differential link exists ... 

We can obtain the repartition function of the residence time for the model of perfect mixing flow from relations (3.67) and (3.62). This function is ... 

The residence time distribution E(t) and the residence time repartition will be obtained starting with the inverse transformation of the transfer function T(p) ... 

In order to solve the model equation, we must complete it with the univocity conditions. In some cases, relations (3.100)-(3.107) can be used as solutions for the model particularized for the process. The equivalence between both expressions is that c(x,t)/C(j appears here as P(x,t). Extending the equivalence, we can establish that P(x, t) is in fact the density of probability associated with the repartition function of the residence time of the liquid element that evolves inside a uniform porous structure. 

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