Modeling Interfacial Liquid Layers in Environmental Ices SUPPLEMENTARY MATERIAL Min H. Kuo, Samar G. Moussa, V. Faye McNeill* Department of Chemical Engineering, Columbia University, New York, New York 10027 *Author to whom correspondence should be addressed: [email protected]; phone (212) 854‐2869; FAX (212) 854‐3054
Derivation of BL Model
Additional symbols not listed in Table 1
Symbol Quantity f ice Fugacity of pure ice w ˆ brine Fugacity of water in brine layer f w vap f w Fugacity of water in vapor space above ice f Fugacity of pure liquid water w x Mole fraction of water in brine layer w ice H w Enthalpy of ice at T, P ice,0 H w Enthalpy of ice at reference state brine Partial molar enthalpy of water in brine layer H w liq,0 H w Enthalpy of water in unfrozen liquid solution at reference state brine H w Enthalpy change upon formation of brine layer vap H w Enthalpy change upon vaporization V ice Volume of ice at T, P w brine Vw Partial molar volume of water in brine layer fus Vw Volume change of fusion brine Vw Volume change upon formation of brine layer vap Vw Volume change upon vaporization
w Activity coefficient of water in brine m Molality of solute in brine layer [=] mole/kg water s Molar mass of water M w
S1
Derivation
At equilibrium (Tester and Modell, 1996),