Solid fraction in dendritic solidification of a liquid

When a liquid is cooled below its equilibrium solidification temperature the solidification takes place as growing dendrites of microscopic scale. An essential feature of the material formed this way is its solid fraction f, which is less than unity due to liquid entrapped between the solid dendrites. In this letter, f in directional solidification of a pure liquid is solved analytically showing that f is independent of the growth conditions. In this sense, this solidification process is self-regulating and f is a material parameter. For water, as an example, the ice fraction is 70% in agreement with experimental data.