Rayleigh fractionation describes the evolution of a system with multiple phases in which one phase is continuously removed from the system through fractional distillation. It is used in particular to describe

isotopic enrichment Isotope separation is the process of concentrating specific isotopes of a chemical element by removing other isotopes. The use of the nuclides produced is varied. The largest variety is used in research (e.g. in chemistry where atoms of "marker" ...

or depletion as material moves between reservoirs in an equilibrium process. Rayleigh fractionation holds particular importance in

hydrology Hydrology () is the scientific study of the movement, distribution, and management of water on Earth and other planets, including the water cycle, water resources, and environmental watershed sustainability. A practitioner of hydrology is call ...

and

meteorology Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did no ...

as a model for the isotopic differentiation of

meteoric water Meteoric water is the water derived from precipitation (snow and rain). This includes water from lakes, rivers, and icemelts, which all originate from precipitation indirectly. While the bulk of rainwater or meltwater from snow and ice reaches the ...

due to condensation.

The Rayleigh equation

The original Rayleigh equation was derived by

Lord Rayleigh John William Strutt, 3rd Baron Rayleigh, (; 12 November 1842 – 30 June 1919) was an English mathematician and physicist who made extensive contributions to science. He spent all of his academic career at the University of Cambridge. Am ...

for the case of fractional distillation of mixed liquids. This is an exponential relation that describes the partitioning of isotopes between two reservoirs as one reservoir decreases in size. The equations can be used to describe an

isotope fractionation Isotope fractionation describes fractionation processes that affect the relative abundance of isotopes, phenomena which are taken advantage of in isotope geochemistry and other fields. Normally, the focus is on stable isotopes of the same element. ...

process if: (1) material is continuously removed from a mixed system containing

molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...

s of two or more isotopic species (e.g., water with ¹⁸O and ¹⁶O, or sulfate with ³⁴S and ³²S), (2) the

fractionation Fractionation is a separation process in which a certain quantity of a mixture (of gases, solids, liquids, enzymes, or isotopes, or a suspension) is divided during a phase transition, into a number of smaller quantities (fractions) in which the ...

accompanying the removal process at any instance is described by the fractionation factor a, and (3) a does not change during the process. Under these conditions, the evolution of the isotopic composition in the residual (reactant) material is described by:

\frac = \left(\frac \right)^

where R = ratio of the isotopes (e.g., ¹⁸O/¹⁶O) in the reactant, R⁰ = initial ratio, X = the concentration or amount of the more abundant (lighter) isotope (e.g.,¹⁶O), and X⁰ = initial concentration. Because the concentration of X >> Xh (heavier isotope concentration), X is approximately equal to the amount of original material in the phase. Hence, if

f = X/X^0

= fraction of material remaining, then:

R = R^0 f^

For large changes in concentration, such as they occur during e.g. distillation of heavy water, these formulae need to be integrated over the distillation trajectory. For small changes such as occur during transport of

water vapour (99.9839 °C) , - , Boiling point , , - , specific gas constant , 461.5 J/( kg·K) , - , Heat of vaporization , 2.27 MJ/kg , - , Heat capacity , 1.864 kJ/(kg·K) Water vapor, water vapour or aqueous vapor is the gaseous pha ...

through the atmosphere, the differentiated equation will usually be sufficient.

References

{{Reflist Chemistry Hydrology Atmospheric_chemistry

The Rayleigh equation

See also

References