Rayleigh condensation

The isotopic composition of the vapor and condensate are simply offset at any given height in the atmosphere by the appropriate equilibrium fractionation factor and hence the derivative of the isotopic composition for the vapor and condensate with respect to elevation are identical as described below by Equation (1). Open system distillation, as modeled by Rayleigh condensation, removes the condensate as it condenses from the vapor leaving the isotopic composition of the residual vapor progressively depleted in lsO and 2H. We use Q = -In(p/ps)... 

Differential condensation in which the liquid separates from the vapour from which it has condensed. This process is analogous to differential, or Rayleigh, distillation, and the condensation curve can be calculated using methods similar to those for determining the change in composition in differential distillation see Volume 2, Chapter 11. 

Rayleigh distillation is a process in which the condensate is immediately removed from the vapor after formation (by fallout of rain and snow in the meteorological case) and leads to a higher... 

A number of investigators attempted to verify the Rayleigh limit using Millikan condensers and quadrupoles (Doyle et ai, 1964 Abbas and Latham, 1967 Berg et al., 1970), but these studies were not sufficiently precise because... 

Of special interest in stable isotope geochemistry are evaporation-condensation processes, because differences in the vapour pressures of isotopic compounds lead to significant isotope fractionations. For example, from the vapour pressure data for water given in Table 1.2, it is evident that the lighter molecnlar species are preferentially enriched in the vaponr phase, the extent depending upon the temperature. Such an isotopic separation process can be treated theoretically in terms of fractional distillation or condensation under equilibrium conditions as is expressed by the Rayleigh (1896) equation. For a condensation process, this equation is... 

Fig. 1.4 5 0 in a cloud vapour and condensate plotted as a function of a fraction of remaining vapour in a cloud for a Rayleigh process. The temperature of the cloud is shown on the lower axis. The increase in fractionation with decreasing temperature is taken into account (after Dansgaard 1964)... 

In this equation, ,/ and mi/2 are the masses of the two isotopes making up RZ1, and the terms are condensation coefficients for the two isotopes, which are determined experimentally and are typically close to 1. Equation (7.2.1) is valid if a is independent of the evolving composition of the evaporating liquid, and the diffusive transport rate is fast enough to keep the liquid homogeneous. The last condition is violated in solids, where diffusion is very slow relative to the evaporation rate, so solids do not undergo Rayleigh distillation. 

Earlier in this chapter, we discussed isotopic fractionation during evaporation. Under appropriate conditions, where the condensed phase remains isotopically well mixed and the gas phase is removed from the system to prevent back reaction, Rayleigh distillation will occur (Box 7.2), resulting in a condensed phase that is isotopically heavy relative to the starting composition (Fig. 7.9). Isotopic fractionation can occur during both condensation and evaporation, as demonstrated by experiments (Richter el al., 2002). But it is not necessary that isotopes fractionate during evaporation or condensation. It depends on the details of the process. If evaporation occurs into a gas phase that is sufficiently dense, back reactions between gas and liquid can reduce the isotopic fractionation to near the equilibrium value, which is very small. For example, sulfur in chondrules does not show the isotopic fractionation (Tachibana and Huss, 2005) expected during evaporation from a liquid. Also, evaporation from a solid does not produce isotopic fractionation in the solid because diffusion is much too slow to equilibrate the few layers of surface atoms that are fractionated with the bulk of the material. 

We have seen that elements can be separated based on their volatility, either through gas-solid or gas-liquid reactions. There are many types of reactions that form a continuum between equilibrium condensation (or its inverse, evaporation) on the one hand and purely kinetically controlled reactions, such as Rayleigh distillation, on the other. In some cases, isotopic fractionation can assist in identifying the processes involved. 

The Rayleigh model was developed for a single stage batch distillation-where a liquid mixture is charged in a still and a vapour is produced by heating the liquid. At any time, the vapour on top of the liquid is in equilibrium with the liquid left in the still. The vapour is removed as soon as it is produced but no part of the vapour is returned as reflux to the still after condensation. 

In his famous and extremely short essay entitled The principle of similitude Lord Rayleigh [4] discussed 15 different physical problems which can be condensed to laws by using dimensional analysis without performing any experiments. The last of these examples concerned the Boussinesq problem of the steady-state heat transfer from a fixed body to a ideal liquid flowing with the velocity of v. 

If no liquid is kept within the cloud ( l = 0), these equations correspond to the classical Rayleigh model, and to a closed system if all liquid is kept. The isotopic composition of the precipitation can be calculated all along the condensation process, if the amount of water leaving the cloud at each step is known. The largest range of 5-variation corresponds to the immediate removal of the condensate (Rayleigh process), and there is a decrease of this range by about a factor of 2, when all liquid formed is kept in the cloud (Jouzel, 1986). 

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