There are two models describing of the distribution of the tracer compound between the two phases (the precipitate and the solution):
* Doerner-Hoskins law (logarithmic):
* Berthelot-Nernst law:
where:
: a and b are the initial concentrations of the tracer and carrier, respectively;
: a − x and b − y are the concentrations of tracer and carrier after separation;
: x and y are the amounts of the tracer and carrier on the precipitate;
: D and λ are the distribution coefficients.
For D and λ greater than 1, the precipitate is enriched in the tracer.
Depending on the co-precipitation system and conditions either λ or D may be constant.
The derivation of the Doerner-Hoskins law assumes that there in no mass exchange between the interior of the precipitating crystals and the solution. When this assumption is fulfilled, then the content of the tracer in the crystal is non-uniform (the crystals are said to be heterogeneous). When the Berthelot-Nernst law applies, then the concentration of the tracer in the interior of the crystal is uniform (and the crystals are said to be homogeneous).  This is the case when diffusion in the interior is possible (like in the liquids) or when the initial small crystals are allowed to recrystallize. Kinetic effects (like speed of crystallization and presence of mixing) play a role.