Slowly accreting ice due to supercooled water impacting on a cold surface

A theoretical model for ice growth due to droplets of supercooled fluid impacting on a subzero substrate is presented. In cold conditions rime (dry) ice forms and the problem reduces to solving a simple mass balance. In milder conditions glaze (wet) ice forms. The problem is then governed by coupled mass and energy balances, which determine the ice height and water layer thickness. The model is valid for "thin" water layers, such that lubrication theory may be applied and the Peclet number is small; it is applicable to ice accretion on stationary and moving structures. A number of analytical solutions are presented. Two- and three-dimensional numerical schemes are also presented, to solve the water flow equation, these employ a flux-limiting scheme to accurately model the capillary ridge at the leading edge of the flow. The method is then extended to incorporate ice accretion. Numerical results are presented for ice growth and water flow driven by gravity, surface tension, and a constant air shear.