Estimating Unfrozen Water Content in Frozen Soils Based on Soil Particle Distribution

Evaluating the potential of capillary rise for the migration of Pt nanoparticles in Luvisols and Phaeozems (Western Siberia)

“…(1) In soil horizons without macropores, colloidal particles can migrate with both lateral and vertical flows of capillary water. Transfer of colloids can be expected even in "warm" permafrost, where, as is known, capillary moisture is in an unfrozen state (Ming et al, 2020;Qiu et al, 2020) and migrates to the freezing front. The revealed process can explain the accumulation of dissolved and colloidal forms of elements in dispersed ice below the active layer in the peat deposit of Cryic Histisols (Lim et al, 2021).…”

An algorithmic framework for computational estimation of soil freezing characteristic curves

“…This equation models the equilibrium between two phases of the same substance in terms of temperature and pressure. We reiterate the conversion process from SWCC to SFCC, following the previous studies 7,8,20,21,37 …”

“…Therefore, at the onset of freezing, we refer this initial matric suction as “intrinsic matric potential,” which can be described as, $$\begin{equation} p_a -p_{_{w0}}=\psi ^*|_{(1-S_a)}, \end{equation}$$where $$\psi ^*|_{(1-S_a)}$$, $$p_a$$, $$p_{l0}$$ are the intrinsic matric potential in unsaturated unfrozen soil, air pressure, and initial water pressure at the onset of freezing, respectively. After substituting Equation (6) into Equation (5) as the boundary followed by adding $$p_c$$ to both sides of the equation, we may express the difference between ice and water pressures, 21 that is, $$\begin{equation} p_c-p_w = -\frac{\rho _wL_{wi}}{T_f^*}(T-T_f)+\psi ^*|_{(1-S_a)}-\frac{\rho _w-\rho _c}{\rho _c}(p_c-p_a). \end{equation}$$Here, $$T_f$$ is the freezing temperature.…”

“…Substitution of Equations (9) and (10) into Equation (7) allows us to model ice–water potential in terms of intrinsic matric potential and temperature 21 as, $$\begin{equation} p_c - p_w =\frac{1}{1+\frac{(\rho _w-\rho _c)\sigma _{iw}}{\sigma _{aw}-\sigma _{iw}}} {\left(-\frac{\rho _w L_{wi}}{T^*_f}(T-T_f) + \psi ^*|_{(1-S_a)} \right)}. \end{equation}$$Here $$T_f$$ indicates the freezing temperature of pore water, and this equation is only applicable when the temperature of the soil is below the freezing temperatures ($$T \le T_f$$).…”

“…Generally, freshwater freezes at 273.15 K under atmospheric pressure. According to Kurylyk and Watanabe 8 and Qiu et al., 21 the freezing point of liquid water within a specific pore space is associated with a particular freezing potential, which can be approximated as, $$\begin{equation} T_f = \frac{T_f^*}{\rho _w L_{wi}}(p_c-p_w). \end{equation}$$We may further consider the freezing point depression under unsaturated soil condition by combing Equations (9), (10), (6) , and (12), that is, $$\begin{equation} T_f= \frac{\sigma _{iw}}{\sigma _{aw}}\frac{T^*_f}{\rho _wL_{wi}}\psi ^*|_{(1-S_a)}.$$…”