Application of the Generalized Clapeyron Equation to Freezing Point Depression and Unfrozen Water Content

• Published in: Water resources research 2018-11, Vol.54 (11), p.9412-9431
• Main Authors: Zhou, Jiazuo, Wei, Changfu, Lai, Yuanming, Wei, Houzhen, Tian, Huihui
• Format: Article
• Language: English
• Subjects: Atmospheric models; Atmospheric temperature; Capillary pressure; Dilution; Freezing; Freezing point; Frozen ground; Heat and mass transfer; Heat transfer; Interactions; Mass transfer; Melting points; Mental depression; Modelling; Moisture content; Overburden; Pore pressure; Pore water; Pressure; Saline soils; Sodium carbonate; Sodium chloride; Soil; Soil conditions; Soil freezing; Soil water; Solutions; Thermal cycling; Water content
• ISSN: 0043-1397; 1944-7973
• DOI: 10.1029/2018WR023221

Freezing point and unfrozen water content are key parameters in modeling the heat and mass transfer under the cyclic change of atmosphere temperature. It is theoretically revealed the relation between the measured pore pressure and true pore pressure with physicochemical interactions. A new generalized Clapeyron equation is derived, which addresses the relationship among the measured pore water, ice‐liquid capillary pressure, and pore solution concentration for the frozen soil. The generalized Clapeyron equation is applied to derive the expressions for the freezing point and unfrozen water content in frozen soils at various thermodynamical conditions. The freezing point of soil is calculated and compared with the experimental results, showing that the freezing point depression becomes more pronounced as water content decreases and solution concentration increases. It is also shown that the NaCl solution with relatively high concentration in soil pore approximates the ideal dilute solution while Na2CO3 and some other solutions in soil are significantly different than the ideal dilute solution. Upon assuming the unfrozen water content is only determined by the capillary pressure, the Clapeyron equation links the soil water characteristic curve into the soil freezing characteristic curve. The unfrozen water content in the saline frozen soil and the frozen soil under overburden pressure is also calculated according to the expression derived from the generalized Clapeyron equation. Key Points The generalized Clapeyron equation addresses the osmosis and ice‐liquid capillary pressure The equation is applied to estimate the freezing point and unfrozen water content Capillary pressure is independent of solute content in the soil with NaCl solution