Salt evaporation (2D)

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The science

Water leaves a pan at a rate proportional to the vapour-pressure deficit: E = k (1 + 0.25 u) (a_w e_s(T) - RH e_s(T)), with the Magnus saturation pressure e_s = 0.6108 exp(17.27 T / (T + 237.3)) kPa, wind speed u, and a mass-transfer constant k = 0.12 kg/m2/h per kPa. Dissolved salt lowers the water activity: a_w = exp(-nu phi M_w m) with nu = 2 ions, M_w = 0.018015 kg/mol, molality m and an osmotic coefficient phi = 0.90 + 0.06 m fitted to NaCl data. At saturation (m = 6.1 mol/kg) this gives a_w close to the measured 0.753, so a saturated brine evaporates about a quarter slower than fresh water.

The salt stays behind: its mass is constant, so the concentration c = m_salt / m_water rises until it reaches the solubility c_sat(T) = 35.65 + 0.0075 T + 0.0004 T^2 g per 100 g water. After that every further kilogram of water removed forces its share of salt out as cubic NaCl crystals, so c stays pinned at c_sat and the crystal curve climbs.

Simplifications: the brine temperature equals the air temperature (no solar heating or cooling by evaporation), one salt only (real sea water also deposits gypsum first and bitter salts last), no rain, no diurnal cycle and no crystal-bed resistance. The drawing is a schematic.