Multi-limit state analysis method for quantifying thickness of pre-melting layer at initial melting stage of salinized soil
By using interface pre-fusion theory and multi-limit state analysis, the problem of quantifying the thickness of the pre-fusion layer in the early stage of saline soil melting was solved, and accurate description and model establishment under different limit states were achieved, supporting multi-field coupled numerical simulation of saline soil engineering in cold regions.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- LANZHOU UNIV
- Filing Date
- 2026-01-16
- Publication Date
- 2026-05-01
AI Technical Summary
Existing technologies are insufficient to systematically quantify the coupling effects of multiple factors such as interfacial forces, salinity, and geometric curvature during freeze-thaw processes in complex saline soil systems. They are unable to accurately characterize the pre-melting behavior under different extreme states in the early stages of thawing, resulting in an inability to accurately describe the thickness of the pre-melting layer in the early stages of saline soil thawing.
Based on the theory of interface pre-melting, by clearly distinguishing different physical limit states, the supercooling-pre-melting layer thickness control equations of the planar pre-melting model and the spherical ice crystal model are established, and the calculation formulas for the pre-melting layer thickness under seven limit states are derived, including the influence of interfacial force, impurity concentration and ice crystal geometry.
It achieves a high-precision description of the pre-melting layer thickness in the early stage of saline soil melting, clarifies the relationship between the pre-melting layer thickness and supercooling under different extreme states, and provides key parameters and physical models for multi-field coupled numerical simulation of saline soil engineering in cold regions.
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Figure CN121958702A_ABST
Abstract
Description
A multi-limit state analysis method for quantifying the thickness of the pre-melting layer in the early stage of saline soil melting. Technical Field
[0001] This invention relates to a method for quantifying the thickness of the pre-melting layer in the early stage of thawing of saline soil in cold regions, specifically to a multi-limit state analysis method for quantifying the thickness of the pre-melting layer in the early stage of thawing of saline soil. Background Technology
[0002] With the advancement of engineering construction in cold regions, engineering problems in saline-permafrost areas are becoming increasingly prominent. During the freeze-thaw process, the presence of salt significantly exacerbates problems such as frost heave, thaw settlement, and salt heave, seriously threatening the stability of infrastructure. In the early stages of thawing, the nanoscale pre-thaw layer formed at the interface between ice crystals and soil particles is a key microstructure controlling the behavior of unfrozen water and the phase change process, and its thickness directly affects the engineering properties of the soil.
[0003] During freeze-thaw cycles, the thickness of the pre-melted layer is a key characteristic quantity describing the microscopic mechanism of the solid-liquid phase transition of water in soil, directly related to the release and absorption of latent heat of phase change. Existing research largely focuses on the macroscopic thermodynamic properties and engineering experience of permafrost, lacking in-depth exploration of interfacial pre-melting behavior during thawing, especially the stability and thickness evolution of the pre-melted layer under different physical limiting conditions (such as differences in interfacial force properties, extreme impurity concentrations, and changes in ice crystal geometry). Currently, commonly used theoretical methods to describe permafrost phase transitions include classical nucleation theory, pre-melting theory, and soil water potential theory. However, when applied to complex saline soil systems, these methods often struggle to systematically quantify the coupling effects of multiple factors such as interfacial forces, salinity, and geometric curvature, failing to accurately characterize the pre-melting behavior under different limiting states in the initial thawing stage.
[0004] This invention aims to achieve a refined and scenario-based quantification of the pre-melting layer thickness during the initial stage of saline soil melting. Specifically, based on interfacial pre-melting theory, this invention establishes corresponding analytical expressions for the pre-melting layer thickness by clearly distinguishing different physical limiting states (including the dominant interfacial force type, impurity concentration limit, and ice crystal geometry assumption), thereby achieving a high-precision description of pre-melting behavior under specific scenarios. This invention will contribute to deepening the understanding of the microscopic mechanism of saline soil melting and provide key theoretical parameters and physical models for multi-field coupled numerical simulation of saline soil engineering in cold regions. Summary of the Invention
[0005] To address the aforementioned issues, this invention discloses a multi-limit state analysis method for quantifying the thickness of the pre-melting layer in the early stage of saline soil thawing. Compared to other measurement methods, the method described in this invention is simple to calculate, and the physical meaning of each parameter is clear and easy to obtain.
[0006] The objective of this invention is achieved through the following technical solution:
[0007] A multi-limit state analysis method for quantifying the thickness of the pre-melting layer in the early stage of saline soil thawing includes the following steps:
[0008] Step 1: Determine the basic pre-melting theoretical model and establish the undercooling-pre-melting layer thickness control equations for the planar pre-melting model and the spherical ice crystal model;
[0009] Step 1 includes the following sub-steps:
[0010] a. Determine the relationship between undercooling and pre-melted layer thickness under the planar pre-melting model. Introduce the pre-melting theory into the ice melting process in porous media and make the following assumptions for the planar pre-melting model: three layers—ice layer, pre-melted layer, and matrix layer—and calculate the undercooling. With pre-melt layer thickness The expression is as follows:
[0011] (1)
[0012] In the formula, The molar density of water molecules; The latent heat of phase transition of water molecules is approximately 6.01 kJ / mol under standard conditions. The number of moles of impurities per unit area; To balance the melting temperature; Here, denoted by Hamaker's constant, represents the interaction between the particle surface and the liquid caused by short-range van der Waals forces. This refers to the thickness of the pre-melt layer; It is a relative gas constant; It is the surface charge density; For electron charge, ; The vacuum permittivity, ; is the relative permittivity of the solvent; the relative permittivity of water is approximately 80 at room temperature. The Debye length of a monovalent ion. The unit is 1 / m.
[0013] b. Determine the expression for the relationship between undercooling and pre-melted layer thickness under the spherical ice crystal model. Consider the curvature of the ice-water interface in the actual soil-water environment, assuming the ice crystal has a radius of... The spherical shape, supercooling expression:
[0014] (2)
[0015] In the formula, Let be the radius of curvature of the ice-water interface; The molar density of ice crystals, and The relationship is ; These represent the number of moles of liquid and impurities in the entire system, respectively. This is the free energy at the ice-water interface.
[0016] Step 2: Determine the limiting case of pre-fusion layer thickness under the planar pre-fusion model;
[0017] Step 2 includes the following sub-steps:
[0018] a. Under the assumption of a planar interface and The relationship is determined by the nature of the dominant interfacial force. Based on formula (1), the formulas for calculating the thickness of the pre-fusion layer under the planar pre-fusion model in the following four extreme cases are derived.
[0019] b. Determine the pre-melt layer thickness in the absence of interfacial forces. When the effects of interfacial forces such as dispersion forces and surface charges are neglected, the system behavior is dominated by thermodynamic equilibrium, corresponding to a pure colligative effect. Radius of curvature The trend of change is entirely determined by the Gibbs-Thomson effect. Follow It increases and monotonically decreases. When When the radius of curvature approaches the value of the bulk freezing point depression caused by impurities, the radius of curvature diverges. The solid-liquid interface tends to be planar. Pre-melt layer thickness. The changing trend is determined by impurity concentration It is controlled together with the subcooling.
[0020]
[0021] at this time, When the impurity concentration is close to the initial concentration, and the colligative term is present at a relatively small degree of supercooling. It is dominant and has a large radius of curvature.
[0022] c. Determine the pre-melt layer thickness under the condition that only attractive dispersive forces are present. When the Hamaker constant... hour( An attractive dispersion force exists at the solid-liquid interface, which exerts a compressive effect on the pre-melted layer. Follow It increases while monotonically decreasing. Pre-melt layer thickness. The changes exhibit nonlinear characteristics and critical behavior. Due to the collapse or thinness of the pre-melt layer, the liquid phase mainly exists in the curvature-induced region, where the impurity concentration is very high, leading to significant colligative terms.
[0023]
[0024] at this time, The attractive dispersion force inhibits the formation of the pre-melt layer, making its thickness smaller than that in the pure colligative case.
[0025] d. Determine the pre-melt layer thickness under the condition that only repulsive dispersion forces are present. When the Hamaker constant... hour, The interfacial dispersion forces are repulsive, which helps stabilize the pre-melt layer. Still follow It increases while monotonically decreasing. Pre-melt layer thickness. The changes in [these] show greater stability.
[0026]
[0027] at this time, Repulsive dispersion forces stabilize liquid films under high subcooling, with thicknesses ranging from... Increase slowly.
[0028] e. Determine the pre-melt layer thickness under the influence of surface charge. When surface charge exists at the solid-liquid interface... At this time, electrostatic forces and dispersing forces jointly regulate the pre-melting behavior, making the situation most complex. Still follow It increases and monotonically decreases. Ignoring colligative effects, the pre-melt layer thickness is obtained as follows:
[0029]
[0030] at this time, .
[0031] Step 3: Determine the limiting case of pre-melting layer thickness under the spherical ice crystal pre-melting model.
[0032] Step 3 includes the following sub-steps:
[0033] a. In the pores of actual porous media, ice crystals often exhibit a curved shape that encapsulates soil particles. Therefore, based on formula (2), the following formulas for calculating the pre-melting layer thickness of the spherical ice crystal model are derived for the following three extreme cases.
[0034] b. Determine the pre-melted layer thickness under the condition that only dispersion forces are involved. The interface is ice / quasi-liquid layer / soil particles, and the corresponding dispersion force is repulsive dispersion force ( It resists the thinning of the liquid film and promotes and stabilizes the presence of the pre-melted liquid film.
[0035]
[0036] at this time, .
[0037] c. Determine the pre-melted layer thickness under the condition that only the solute effect is involved. Dispersion forces play a dominant role, mainly manifested as attraction. .
[0038]
[0039] at this time, When the impurity concentration approaches infinity, the Debye length approaches zero, and the range of electrostatic repulsion becomes infinitesimally small. This weakens its ability to support the liquid film and resist dispersive attraction or ice phase attraction, and the electrostatic effect is completely suppressed by the high concentration of ions.
[0040] d. Determine the pre-melt layer thickness under the condition of electrostatic effect only. The contribution of electrostatic force is strongly dependent on the Debye length. As the Debye length approaches infinity, the strength and effective range of the electrostatic repulsion force are maximized.
[0041] (9)
[0042] at this time, The surface charge reaches the dominant limit.
[0043] The beneficial effects of this invention are:
[0044] This invention, based on pre-melting theory and a multi-limit state analysis framework, proposes a systematic method for quantifying the thickness of the pre-melting layer in the initial stage of saline soil thawing. It clarifies the correspondence between the pre-melting layer thickness and supercooling degree under seven limit states in planar and spherical ice crystal models, as well as the stability criteria, demonstrating strong applicability. This method takes into account the multiple influences of interfacial forces, impurity concentration, and ice crystal morphology during the freeze-thaw process of saline soil. The physical meaning of each limit state is clear, and the required parameters are easy to determine. In addition to the above-mentioned objectives, features, and advantages, this invention also has other objectives, features, and advantages. The invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description
[0045] Figure 1 is a flowchart of the method in this invention.
[0046] Figure 2 is a schematic diagram of the change in pre-fusion layer thickness under the planar pre-fusion model in this invention.
[0047] Figure 3 is a schematic diagram of the change in pre-melt layer thickness under the pure electrostatic effect case of the planar pre-melt model in this invention.
[0048] Figure 4 is a schematic diagram of the change in pre-melting layer thickness in the case of spherical ice crystal model with only dispersion force in this invention.
[0049] Figure 5 is a schematic diagram of the change in pre-melting layer thickness in the case of spherical ice crystal model with only solute effect in this invention. Detailed Implementation
[0050] Detailed Implementation Instructions
[0051] A multi-limit state analysis method for quantifying the thickness of the pre-melting layer in the early stage of saline soil thawing includes the following steps:
[0052] Step 1: Determine the basic pre-melting theoretical model and establish the undercooling-pre-melting layer thickness control equations for the planar pre-melting model and the spherical ice crystal model;
[0053] Step 1 includes the following sub-steps:
[0054] a. Determine the relationship between undercooling and pre-melted layer thickness under the planar pre-melting model. Introduce the pre-melting theory into the ice melting process in porous media and make the following assumptions for the planar pre-melting model: three layers—ice layer, pre-melted layer, and matrix layer—and calculate the undercooling. With pre-melt layer thickness The expression is as follows:
[0055] (1)
[0056] In the formula, The molar density of water molecules; The latent heat of phase transition of water molecules is approximately 6.01 kJ / mol under standard conditions. The number of moles of impurities per unit area; To balance the melting temperature; Here, denoted by Hamaker's constant, represents the interaction between the particle surface and the liquid caused by short-range van der Waals forces. This refers to the thickness of the pre-melt layer; It is a relative gas constant; It is the surface charge density; For electron charge, ; The vacuum permittivity, ; is the relative permittivity of the solvent; the relative permittivity of water is approximately 80 at room temperature. The Debye length of a monovalent ion. The unit is 1 / m.
[0057] b. Determine the expression for the relationship between undercooling and pre-melted layer thickness under the spherical ice crystal model. Consider the curvature of the ice-water interface in the actual soil-water environment, assuming the ice crystal has a radius of... The spherical shape, supercooling expression:
[0058] (2)
[0059] In the formula, Let be the radius of curvature of the ice-water interface; The molar density of ice crystals, and The relationship is ; These represent the number of moles of liquid and impurities in the entire system, respectively. This is the free energy at the ice-water interface.
[0060] Step 2: Determine the limiting case of pre-fusion layer thickness under the planar pre-fusion model;
[0061] Step 2 includes the following sub-steps:
[0062] a. Under the assumption of a planar interface and The relationship is determined by the nature of the dominant interfacial force. Based on formula (1), the formulas for calculating the thickness of the pre-fusion layer under the planar pre-fusion model in the following four extreme cases are derived.
[0063] b. Figure 2 shows a schematic diagram of the pre-melt layer thickness variation under the planar pre-melt model described in this invention. It illustrates that the pre-melt layer thickness monotonically decreases with increasing undercooling in the absence of interfacial forces. The pre-melt layer thickness is determined in the absence of interfacial forces. When the effects of interfacial forces such as dispersion forces and surface charges are ignored, the system behavior is dominated by thermodynamic equilibrium, corresponding to a pure colligative effect. Radius of curvature The trend of change is entirely determined by the Gibbs-Thomson effect. Follow It increases and monotonically decreases. When When the radius of curvature approaches the value of the bulk freezing point depression caused by impurities, the radius of curvature diverges. The solid-liquid interface tends to be planar. Pre-melt layer thickness. The changing trend is determined by impurity concentration It is controlled together with the subcooling.
[0064]
[0065] at this time, When the impurity concentration is close to the initial concentration, and the colligative term is present at a relatively small degree of supercooling. It is dominant and has a large radius of curvature.
[0066] c. As shown in Figure 2, this invention presents a schematic diagram illustrating the variation of the pre-melted layer thickness under the planar pre-melted model. It describes how the pre-melted layer thickness monotonically decreases with increasing undercooling under the influence of only attractive dispersion forces. The pre-melted layer thickness under the condition of only attractive dispersion forces is determined. When the Hamaker constant... hour( An attractive dispersion force exists at the solid-liquid interface, which exerts a compressive effect on the pre-melted layer. Follow It increases while monotonically decreasing. Pre-melt layer thickness. The changes exhibit nonlinear characteristics and critical behavior. Due to the collapse or thinness of the pre-melt layer, the liquid phase mainly exists in the curvature-induced region, where the impurity concentration is very high, leading to significant colligative terms.
[0067]
[0068] at this time, The attractive dispersion force inhibits the formation of the pre-melt layer, making its thickness smaller than that in the pure colligative case.
[0069] d. Determine the pre-melt layer thickness under the condition that only repulsive dispersion forces are present. When the Hamaker constant... hour, The interfacial dispersion forces are repulsive, which helps stabilize the pre-melt layer. Still follow It increases while monotonically decreasing. Pre-melt layer thickness. The changes in [these] show greater stability.
[0070]
[0071] at this time, Repulsive dispersion forces stabilize liquid films under high subcooling, with thicknesses ranging from... Increase slowly.
[0072] e. Figure 3 shows a schematic diagram of the pre-melt layer thickness variation under the pure electrostatic effect scenario in the planar pre-melt model described in this invention. It illustrates how electrostatic repulsion generated by surface charges significantly thickens the liquid film at low undercooling, with the thickness varying with... Decrease and logarithmic growth. Determine the pre-melt layer thickness under the influence of surface charge. When surface charge exists at the solid-liquid interface. At this time, electrostatic forces and dispersing forces jointly regulate the pre-melting behavior, making the situation most complex. Still follow It increases and monotonically decreases. Ignoring colligative effects, the pre-melt layer thickness is obtained as follows:
[0073]
[0074] at this time, .
[0075] Step 3: Determine the limiting case of pre-melting layer thickness under the spherical ice crystal pre-melting model.
[0076] Step 3 includes the following sub-steps:
[0077] a. In the pores of actual porous media, ice crystals often exhibit a curved shape that encapsulates soil particles. Therefore, based on formula (2), the following formulas for calculating the pre-melting layer thickness of the spherical ice crystal model are derived for the following three extreme cases.
[0078] b. As shown in Figure 4, this invention presents a schematic diagram of the pre-melting layer thickness variation under the condition of dispersion force alone in the spherical ice crystal model. The pre-melting layer thickness is determined under the condition of dispersion force alone. The interface is ice / quasi-liquid layer / soil particles, and the corresponding dispersion force is repulsive dispersion force (…). It resists the thinning of the liquid film and promotes and stabilizes the presence of the pre-melted liquid film.
[0079]
[0080] at this time, .
[0081] c. As shown in Figure 5, this invention presents a schematic diagram of the pre-melted layer thickness variation under the solute effect alone scenario in the spherical ice crystal model. It describes the process where the electrostatic effect's range tends to infinitely small as the impurity concentration approaches infinity. The pre-melted layer thickness is determined under the solute effect alone scenario. Dispersion forces dominate, primarily manifesting as attraction. .
[0082]
[0083] at this time, When the impurity concentration approaches infinity, the Debye length approaches zero, and the range of electrostatic repulsion becomes infinitesimally small. This weakens its ability to support the liquid film and resist dispersive attraction or ice phase attraction, and the electrostatic effect is completely suppressed by the high concentration of ions.
[0084] d. Determine the pre-melt layer thickness under the condition of electrostatic effect only. The contribution of electrostatic force is strongly dependent on the Debye length. As the Debye length approaches infinity, the strength and effective range of the electrostatic repulsion force are maximized.
[0085] (9)
[0086] at this time, The surface charge reaches the dominant limit.
[0087] During the initial phase transition of thawing saline soils in cold regions, the formation and evolution of the pre-melted layer at the interface between ice crystals and soil particles significantly affect the unfrozen water content and the phase transition process. Furthermore, the properties of interfacial forces and impurity concentration also regulate the stability and thickness of the pre-melted layer. Therefore, through thermodynamic equilibrium analysis, the analytical relationship between the pre-melted layer thickness and supercooling under different limiting states can be defined and derived. To systematically quantify the influence of interfacial conditions on pre-melting behavior, seven limiting states are defined for the analysis of pre-melted layer thickness in saline soils, including: four cases under a planar model with no interfacial forces, only attractive dispersion forces, only repulsive dispersion forces, and the presence of surface charges; and three cases under a spherical ice crystal model: ideal purity, high impurity concentration, and low impurity concentration.
[0088] Figure 1 shows a flowchart of the method described in this invention. It illustrates the specific conditions corresponding to seven extreme cases.
[0089] Figure 2 shows a schematic diagram of the pre-melt layer thickness variation under the planar pre-melt model described in this invention. It illustrates the pre-melt layer thickness under conditions without interfacial forces. With supercooling It increases and monotonically decreases, with the rate of decrease gradually slowing down. In the same... Down, with impurity surface density Proportional ( The higher the curve, the higher the position. When the solidification point of the bulk phase approaches the value determined by the impurity concentration, d approaches a finite value determined by the initial impurity concentration, and collapse will not occur.
[0090] Figure 2 shows the effect of no electrostatic force and attractive dispersion force. Follow The decreasing trend is more pronounced, exhibiting significant nonlinear characteristics. There exists a critical supercooling degree ( ).when hour, Follow Increase and decrease; when hour, Discontinuous collapse (or a sharp decrease to near zero) will occur, indicating that the pre-melted layer is unstable under strong attraction.
[0091] Figure 3 shows a schematic diagram of the pre-melt layer thickness variation under the pure electrostatic effect scenario in the planar pre-melt model described in this invention. It illustrates the effect of impurity concentration... As the concentration of ions increases, the pre-melted layer thickness curve shifts downwards overall. This indicates that the dissolved ions have a significant shielding effect on the interfacial electrostatic potential: the higher ionic strength compresses the electric double layer, weakens the electrostatic repulsion between surface charges, and thus reduces the electrostatic support required to maintain the same liquid film thickness. This manifests as a decrease in electrostatic support at the same supercooling degree. The value decreases. In In a smaller area (near the pre-melt initiation point), electrostatic repulsion forces... Its contribution is absolutely dominant, and it can significantly thicken the liquid film, making... The value is much larger than that in the case of no interface force or only dispersion force.
[0092] Figure 4 shows a schematic diagram of the pre-melting layer thickness variation under the condition of only dispersion force in the spherical ice crystal model described in this invention. It illustrates the effect of small radius of curvature. Under the conditions, Follow The curve showing the change exhibits a segment with a positive slope. In the same... Below, ice crystal radius The smaller the curvature (the greater the curvature), the thicker the pre-melt layer. The larger it is. At the same time, exceeding a certain degree of supercooling... The range and the change in pre-melted layer thickness gradually level off. Since the dispersion force is repulsive, all curves change smoothly, indicating that the repulsive force also plays a stabilizing role in spherical geometry. Specifically, for high curvature (small radius)... For ice crystals, the system can respond to the increase in supercooling by increasing the thickness of the pre-melted layer, thereby balancing the thermodynamic barrier raised by curvature and phase change.
[0093] Figure 5 shows a schematic diagram of the pre-melting layer thickness variation in the spherical ice crystal model described in this invention under the condition of only solute effect. The radius is described. The smaller the curvature (the greater the curvature), the thicker the pre-melt layer. The larger the overall size, and Follow The faster the growth rate, the higher the rate of increase. Exceeding a certain degree of supercooling ( After this, the pre-melting theory fails. This indicates that in the spherical ice crystal model, the direction of the pre-melting layer thickness variation with supercooling is not determined by the properties of the interfacial forces (attraction or repulsion), but rather by the geometric curvature of the ice crystal. The coupling effect between phase change thermodynamics and phase change thermodynamics.
[0094] In summary, the multi-limit state analysis method for quantifying the pre-melting layer thickness in the early stage of saline soil melting proposed in this invention can systematically predict the evolution law and stability critical conditions of the pre-melting layer thickness for cold-region saline soils with different interface properties, different salt concentrations and different ice crystal morphologies. Applying the multi-limit state analysis framework of this invention to the evaluation and prediction of actual saline soil melting phase transition behavior is feasible.
Claims
1. A multi-limit state analysis method for quantifying the thickness of the pre-melting layer in the early stage of saline soil melting, characterized in that, The following steps are required: Step 1: Determine the basic pre-melting theoretical model and establish the supercooling-pre-melting layer thickness control equations for the planar pre-melting model and the spherical ice crystal model; Step 2: Determine the limiting case of pre-melting layer thickness under the planar pre-melting model; Step 3: Determine the limiting case of pre-melting layer thickness under the spherical ice crystal pre-melting model.
2. The multi-limit state analysis method for quantifying the thickness of the pre-melting layer in the early stage of saline soil thawing according to claim 1, characterized in that: Step 1 includes: a. Determining the relationship between undercooling and pre-melting layer thickness under the planar pre-melting model, introducing the pre-melting theory into the ice melting process in porous media, and making the assumptions of the planar pre-melting model: three layers: ice layer, pre-melting layer, and matrix layer, and calculating the undercooling. With pre-melt layer thickness The expression is as follows: (1) In the formula, The molar density of water molecules; The latent heat of phase transition of water molecules is approximately 6.01 kJ / mol under standard conditions. The number of moles of impurities per unit area; To balance the melting temperature; Here, denoted by Hamaker's constant, represents the interaction between the particle surface and the liquid caused by short-range van der Waals forces. This refers to the thickness of the pre-melt layer; It is a relative gas constant; It is the surface charge density; For electron charge, ； The vacuum permittivity, ； is the relative permittivity of the solvent; the relative permittivity of water is approximately 80 at room temperature. The Debye length of a monovalent ion. a. The unit is 1 / m; b. Determine the expression for the relationship between supercooling and premelted layer thickness under the spherical ice crystal model, considering the curvature of the ice-water interface in the actual soil-water environment, assuming the ice crystal has a radius of... The spherical shape, supercooling expression: (2) In the formula, The radius of curvature of the ice-water interface; The molar density of ice crystals, and The relationship is ； These represent the number of moles of liquid and impurities in the entire system, respectively. This is the free energy at the ice-water interface.
3. The multi-limit state analysis method for quantifying the thickness of the pre-melting layer in the early stage of saline soil thawing according to claim 1, characterized in that: Step 2 includes: a. Under the assumption of a planar interface and The relationship is determined by the nature of the dominant interfacial force. Based on formula (1), the following four limit cases are used to derive the formulas for calculating the thickness of the pre-melting layer under the planar pre-melting model; b. Determine the thickness of the pre-melting layer in the case of no interfacial force. When the effects of interfacial forces such as dispersion force and surface charge are ignored, the system behavior is dominated by thermodynamic equilibrium, corresponding to pure colligative effect, radius of curvature The trend of change is entirely determined by the Gibbs-Thomson effect. Follow Increases and monotonically decreases, when When the radius of curvature approaches the value of the bulk freezing point depression caused by impurities, the radius of curvature diverges. The solid-liquid interface tends to be planar, and the pre-melt layer thickness is... The trend of change is determined by impurity concentration Controlled in conjunction with subcooling: at this time, When the impurity concentration is close to the initial concentration, and the colligative term is under relatively small supercooling conditions, Dominant, with a large radius of curvature; c. Determine the pre-melt layer thickness under the condition that only attractive dispersion forces exist, when the Hamaker constant... hour( An attractive dispersion force exists at the solid-liquid interface, which exerts a compressive effect on the pre-melted layer. Follow The pre-melt layer thickness increases and decreases monotonically. The changes exhibit nonlinear characteristics and critical behavior. Due to the collapse or thinness of the pre-melted layer, the liquid phase mainly exists in the curvature-induced region, where the impurity concentration is very high, leading to significant colligative terms. at this time, d. Determine the pre-melt layer thickness when only repulsive dispersion forces are present, given the Hamaker constant. hour, The interfacial dispersion forces are repulsive, which helps stabilize the pre-melt layer. Still follow The pre-melt layer thickness increases and decreases monotonically. The changes exhibit stronger stability: at this time, Repulsive dispersion forces stabilize liquid films under high subcooling, with thicknesses ranging from... Increase slowly; e. Determine the pre-melt layer thickness under the influence of surface charge, when surface charge exists at the solid-liquid interface. At this time, electrostatic forces and dispersing forces jointly regulate the pre-melting behavior, making the situation most complex. Still follow As the coefficient increases and monotonically decreases, ignoring the colligative effect, the pre-melt layer thickness can be obtained as follows: at this time, 。 4. The method based on the thickness of the pre-melting layer in the initial stage of saline soil thawing according to claim 1, characterized in that: Step 3 includes: a. In the pores of actual porous media, ice crystals often present as curved surfaces enveloping soil particles. Therefore, based on formula (2), the following three extreme cases are used to derive the calculation formulas for the pre-melting layer thickness of the spherical ice crystal model; b. Determine the pre-melting layer thickness under the condition of only dispersion force, where the interface is ice / quasi-liquid layer / soil particles, and the corresponding dispersion force is repulsive dispersion force ( This helps to resist thinning of the liquid film and promotes and stabilizes the presence of the pre-melted liquid film. at this time, c. Determine the pre-melted layer thickness under the condition of solute effect only, where dispersion force plays a dominant role, mainly manifested as attraction. ， at this time, When the impurity concentration approaches infinity, the Debye length approaches zero, and the effective range of the electrostatic repulsion force becomes infinitesimally small, weakening its ability to support the liquid film and resist dispersive attraction or ice phase attraction. The electrostatic effect is completely suppressed by the high concentration of ions. d. Determining the pre-melted layer thickness under the condition of only electrostatic effect, the contribution of the electrostatic force strongly depends on the Debye length. When the Debye length approaches infinity, the strength and effective range of the electrostatic repulsion force are maximized. (9) At this time, The surface charge reaches the dominant limit.