Solute distribution curves from several hundred ice columns doped with small amounts of HCl, HF, NH4OH, and NH4F were investigated with the log linear approximate solution to the one-dimensional diffusion equation, discussed in an earlier paper. This led to the discovery of spontaneous convective effects which can be separated from a genuine concentration dependence of the distribution coefficient. The solutes studied show specific characteristics with respect to solubility in ice and concentration dependence of the distribution coefficient. These characteristic properties should eventually be correlated with specific structural relationships of these solutes (and the defects they create) to the ice lattice. The method of interpretation may be useful for unraveling the freezing history of natural ices of dilute solute content. The most direct and accurate method for measuring the distribution coefficient of (nonvolatile) solutes is by a combination of intense stirring and slow freezing rates.
The purpose of this work was to find a method suitable for analyzing experimental data of solute redistribution at the ice/water phase boundary at (quasi) equilibrium, when solute transport is controlled by (one-dimensional) diffusion and the distribution coefficient is concentration dependent. A careful study of the models proposed by earlier workers led to the formulation of an approximate log linear solution to the appropriate diffusion and continuity equations. Its validity was checked and justified by a numerical model of the rigorous analytical solutions available for the case of a concentration independent distribution coefficient. The approximate log linear solution is valid nearly over the whole range including the region approaching steady state, but not at the very beginning of freezing. It provides a straightforward method for analyzing experimental solute distribution curves. Its usefulness will be demonstrated subsequently by applying it to experimental data.
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