A two-reservoir recycling model for mantle-crust evolution.

The exact solutions for the isotopic compositions and the concentrations of the two-reservoir model for mantle-crust evolution are given for arbitrary rates of crustal growth and of back flow to the mantle. The critical parameters are the chemical fractionation factors for crustal growth and refluxing and the integrated fractional mass-removal rates from the crust and the mantle. For the case where refluxing is proportional to crustal growth, all the solutions reduce to simple analytic expressions. The expression for the mean age of the mass of the crust with refluxing is given. If refluxing is significant, the model shows that highly incompatible elements have short residence times in the mantle. With plausible concentration values, material balance implies that the continents were derived from only a small fraction of the mantle.