Quasistatic solute diffusion

A quasistatic approximation to the solute field neglects its perturbation time derivative while retaining the interface motion in the solute balance. For steady pulling, a lateral wavenumber $k$ then has decaying exponent $q=(V+\sqrt{V^2+4D^2{k}^2})/(2D)$. It is justified when the interface growth time is long compared with the relevant solute diffusion time. Fixing the thermal field does not by itself impose this solutal timescale ordering.