Oscillatory instability and minimum undercooling criterion in directional solidification

We show in this paper that, when small Peclet number effects are taken into account, steady state deep cells which satisfy the minimum undercooling criterion never undergo an oscillatory instability. However, if the stability criterion for the oscillatory mode found in this limit is extended to Peclet number of order unity, deep cells may become unstable if:

a criterion which can be directly tested on the existing experimental data. Here Δ is the tip undercooling, U the interface velocity, K the partition coefficient and v the control parameter, ratio between thermal and diffusive lengths.