Ice formation within a thin film flowing over a flat plate

We present a model for ice formation in a thin, viscous liquid film driven by a Blasius boundary layer after heating is switched off along part of the flat plate. The flow is assumed to initially be in the Nelson et al. (J. Fluid Mech., vol. 284, 1995, pp. 159–169) steady-state configuration with a constant flux of liquid supplied at the tip of the plate, so that the film thickness grows like in which the film and air are driven over the growing ice layer. Moreover, in the early time regime, there is an additional intermediate region in which the air–water interface propagates a slope discontinuity downstream due to the sudden onset of the ice at the switch-off point. For each regime, we present ice profiles and growth rates, and show that for large times, the film is predicted to rupture in the outer region when the slope discontinuity becomes sufficiently enhanced.