Nuclide equilibrium partitioning

If the rate of adsorption, the rate of desorption, and the equilibrium partitioning of a nuclide between a solid medium and solution are known, then the rate of migration of a nuclide through the medium can be predicted with the ARDISC model. 

Both dynamic melting and equilibrium transport melting require that the porosity when two nuclides are fractionated from one another is similar to the size of the larger of the partition coefficients for the two nuclides. Given the low values of the experimental determinations of Du and Dxh, the porosities required to explain the observational data in these models are generally less than 0.5% and often times closer to 0.1%. Such low porosity estimates have been criticized based on physical grounds given the low estimated mantle permeability derived from the extent of melt connection observed in experiments (Paul 2001). 

This bulk state of secular equilibrium applies to the total amount of the U-series nuclides, but does not necessarily say where the different elements reside within the system. If the bulk system has a single phase (such as a melt or a monomineralic rock) then that phase will be in secular equilibrium. If the material has multiple phases with different partitioning properties, however, the individual phases can maintain radioactive dis-equilibria even when the total system is in secular equilibrium. There are two basic sets of models that exploit this fact, the first assumes complete chemical equilibrium between all phases and the second assumes transient diffusion controlled sohd exchange. 

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