Supercooled droplets (liquid below 0 °C) are carried by the airflow around the leading edge, modeled here as a cylinder of radius R (the leading-edge radius). Air follows the classic potential-flow field around a cylinder:
u_x = 1 − (x²−y²)/(x²+y²)²
u_y = −2xy/(x²+y²)² (lengths in units of R, speed in units of V)
Droplets don't follow the air exactly — inertia carries them across curving streamlines toward the surface. Each droplet relaxes toward the local air velocity over a Stokes relaxation time τ = ρ_water·d²/(18·μ_air), giving the dimensionless Stokes number:
St = τ·V / R
dV_drop/dT = (u_air − V_drop) / St (T = t·V/R)
Small St (small droplets, low speed) → droplets hug the streamlines and mostly miss the surface, so collection efficiency β is low. Large St (big droplets, high speed) → droplets fly nearly straight and strike a wide swath of the nose. The fraction of spawned droplets that actually reach the cylinder, binned by impact angle from the stagnation point, is β(φ) — this sim computes it the same way real trajectory codes (e.g. LEWICE) do, by integrating individual droplet paths.
Whether the caught water freezes on contact (rime) or spreads into a film that runs back before freezing (glaze) is set by a simplified energy balance: colder air and lower water flux favor rime, while forced convection removes heat at a rate ∝ √V and must keep up with the latent-heat load ∝ LWC·V·β₀:
n ≈ min(1, k·(−T_amb) / (LWC·√V·β₀))
Rime ice (n → 1) is opaque, rounded and hugs the wetted region. Glaze ice (n → 0) is glassy, and unfrozen runback water refreezes at the edge of the film — producing the characteristic double "horn" shape modeled here as extra deposition beyond the main wetted band. This is why glaze icing is more aerodynamically dangerous: it grows further aft, disrupting the boundary layer over a wider chord.