Slow Migration of Brine Inclusions in First-Year Sea Ice

The paper derives the sharp-interface (Stefan-type) limit using matched asymptotics in whiskered coordinates x = γ(p) + H^{-1} z n near Γ, with ∇ and Δ expansions (3.3)–(3.4), and normal velocity Vn = −H^{-1} ż (3.5) . It obtains the outer equations (1 + b(Θ0) χ1) ∂t Θ0 = σθ ΔΘ0 and ∂t N0 = σN ∇·(∇N0 + δg e3 N0) (3.27)–(3.28), continuity of temperature (3.32), an interfacial salt conservation condition ż0/H N0 = σN^2 (∇N0 + δg e3 N0)·n (3.50), and the Fredholm-solvability velocity law ż0 = κ0 − ||Φ′||_{L2}^{−2}(B(Θ0) + N0) (3.53), summarized as (4.1)–(4.7) . The candidate solution reproduces these results with the same scaling, profile problem Φ̃'' = W0'(Φ̃) (3.7), and solvability argument, correctly placing b(·) in the enthalpy and B(·) = β(θ^2 − θ_*^2)/(2θ) in the velocity law (2.27) . Minor notational differences (e.g., σN versus σN^2 on the interface flux) aside, the derivations align point-by-point.