The spread and vaporisation of cryogenic liquids on water

The literature on the spread and vaporisation of cryogenic liquids on water is reviewed and a new model proposed. The model incorporates the features o T001 List of symbols Symbols C p Heat capacity. g Acceleration due to gravity. G m Molar vaporisation rate. h Latent heat with two suffices denoting phase change. h Pool thickness (no suffices). i Enthalpy. k, K Constants. K A, K B Functions of pool temperature and composition. k w Thermal diffusivity of water. l Depth in water where temperature is constant. L Length scale of an oil spill. L m Molar liquid spill rate. L wi Latent heat of fusion of ice. M Pool mass, M 0 initially. M s, M v Mass spilled, mass vaporised. q Heat flux to cryogenic liquid. r Radial co-ordinate R, R * Radius of pool. t Time. T Temperature. U Velocity. W m Number of moles of material in the pool. x A Molar methane portion of liquid pool ( x B, ethane). x AS Molar methane portion of spilling liquid. y A Molar methane portion of vapour ( y B, ethane). z Vertical coordinate. δ Vapour layer thickness. Δ T Temperature difference. ϵ Ice layer thickness. θ Temperature relative to freezing point of water. λ Effective thermal conductivity. μ Viscosity. ϱ Density. σ Surface tension. ø Heat flux to liquid pool = q. Suffices A Average (or methane fraction with x, y). B Boiling point of cryogen (or ethane fraction with x, y). fc Film collapse. fg Liquid to vapour phase change. F Freezing of water. i Ice. l, L Liquid. lv Liquid to vapour phase change. LE Leading edge. m Molar. O Initial o Oil. p Pool. s Spilling liquid. v Vapour. w Water.