CN117054308A - Salinized soil supercooling degree prediction method based on crystallization dynamics - Google Patents
Salinized soil supercooling degree prediction method based on crystallization dynamics Download PDFInfo
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Abstract
The invention relates to a salinized soil supercooling degree prediction method based on crystallization kinetics, which comprises the following steps: firstly, obtaining a pore diameter distribution curve of a soil sample and a soil characteristic pore diameter; then obtaining the water content of the soil volume, and calculating the pore saturation; obtaining the salt content and the salt content of the soil, and calculating the water activity of the soil pore solution; and calculating to obtain the supercooling degree value of the soil sample at different freezing rates. According to the invention, based on the occurrence environment of unsaturated saline soil pore solution, the influence of nucleation, solution cooling, ice water interface, soil water adsorption, water-air interface and the like on the free energy of a system is considered, classical nucleation theory is introduced to deduce and establish a unsaturated saline soil pore solution nucleation model, and a saline soil (containing non-saline soil) soil supercooling degree prediction model applicable to an unsaturated state (containing saturated state) is established for the first time; the influence factors are clear and have clear physical meaning, and can be used for calculating and predicting the supercooling degree of the saline soil and the non-saline soil.
Description
Technical Field
The invention relates to the technical field of frozen soil engineering, in particular to a salinized soil supercooling degree prediction method based on crystallization kinetics.
Background
Unfrozen water refers to water which still exists in a liquid state in soil pores at a negative temperature, and is a key factor for determining the mechanical, permeation, heat transfer and other properties of frozen soil. The distribution of salinized soil and frozen soil areas is very wide in the world or in China. More and more projects will be carried out in salinized seasonal frozen soil areas. The influence of the freeze thawing circulation on unfrozen water of soil mainly comprises two forms of migration and phase change, and the two forms can finally cause undesirable geological phenomena such as frost heaving, thawing and settlement of soil body, lifting of salt on the surface of the earth and the like. If the soil pore solution is controlled not to freeze at a short-term negative temperature, the problems of agricultural and engineering diseases caused by freeze thawing circulation can be greatly reduced.
In the initial stage of freezing, the microscopic mechanism of supercooling effect of soil body is that nucleation of pore solution crystallization prevents freezing. The difference between the equilibrium freezing temperature and the lowest supercooling temperature of the soil is often defined as the supercooling degree of the soil. Regarding soil supercooling degree prediction, only a few scholars have proposed an empirical fitting model based on experimental data. However, these prediction methods based on empirical fitting are not physically significant enough and often lack universality. The reasons for this can be summarized in two ways: on the one hand, the factors influencing the supercooling degree of the soil sample are numerous, and not only the properties of the soil sample (salt content, water content, pore characteristics and the like) but also the cooling conditions of the external environment are included. On the other hand, based on the principle of conservation of energy and experimental means, the volume change of unfrozen water is analyzed, and the critical nucleation state of the pore solution of the frozen soil body forming stable crystal nucleus is difficult to analyze. In practical engineering application, the supercooling degree of the soil body usually takes an empirical value or directly ignores the supercooling effect. This is because of the lack of a good model for predicting the supercooling degree of the soil body, so that the frozen characteristic curve model used in the field of numerical simulation is difficult to describe the supercooling phenomenon of the soil water accurately. The research indicates that for the soil with higher salt content and smaller average pore diameter, the error between the SFCC model established by neglecting the supercooling effect and the actual test result is larger.
In summary, along with urgent needs of research and development and engineering construction, a theoretical model of supercooling degree of soil considering soil salinity needs to be proposed for filling theoretical vacancy. On one hand, the crystallization supercooling mechanism of soil pore water under the normal freezing action is studied in depth, and exploration of supercooling characteristics of unfrozen water is helpful for further establishing a high-precision SFCC model, and a more perfect theoretical basis can be laid for numerical calculation. On the other hand, by predicting the supercooling degree of the soil body and further researching the influence factors, the freezing control of the engineering structure and the pore water in the foundation of the engineering structure under the short-term negative temperature environment can be realized. Thus, the engineering plant is protected from engineering diseases derived from frequent freeze-thawing cycles caused by meteorological changes and day-to-night temperature differences.
For many years, the development and application of nucleation theory and crystallization kinetics in the fields of atmosphere, materials, foods and the like provide a new solution for interpreting thermodynamic conditions of critical nucleation states of soil pore water and revealing supercooled crystallization microscopic mechanisms thereof.
Disclosure of Invention
The invention aims to solve the technical problem of providing a method for predicting supercooling degree of a frozen soil body by taking aperture, salt content, water content, system cooling rate and other factors into consideration.
In order to solve the problems, the method for predicting the supercooling degree of the saline soil based on crystallization kinetics comprises the following steps:
(1) And (3) performing a soil aperture analysis test to obtain a pore size distribution curve of a test soil sample, and obtaining a soil characteristic pore size.
(2) And (3) performing a soil water content measurement test to obtain the soil volume water content and the porosity, and calculating the pore saturation.
(3) And (3) carrying out a soil salinity analysis test to obtain the salt content and the salt content of the soil, and calculating the water activity of the soil pore solution.
(4) According to the calculation method, the supercooling degree value of the soil sample under different freezing rates is calculated.
The free energy change function delta G of the system in the nucleation process can be divided into the free energy change delta G of the solution main body molecules sln Nucleation leads to a change in the free energy of the nuclei Δg V Energy DeltaG generated at ice-water interface S And pore adsorption energy change amount Δg ls Free energy change ΔG of water molecules at interface with water vapor la Five parts:
ΔG＝ΔG sln +ΔG V +ΔG S +ΔG ls +ΔG la (1)
to determine the free energy change of the system during the phase transition, two boundary states are now defined. State a refers to the initial state (no ice water phase change), the instantaneous temperature is T 0 . At this time, the components in the solution are water molecules and solute molecules, and the molecular numbers are respectively as follows: n is n w And n y Chemical potential is mu w，1 And mu y，1 . State b refers to critical nucleation state with instantaneous temperature T sc . At this time, the components in the pores are crystal nucleus molecules, water molecules and solute molecules, and the molecular numbers can be expressed as follows: n is n germ 、(n w -n germ ) And n y The method comprises the steps of carrying out a first treatment on the surface of the Chemical potential is expressed as mu i 、μ w，1 And mu y，1 。
Thus, the free energy change ΔG of the main molecule of the solution in formula (1) sln Can be calculated by the following formula:
ΔG sln ＝n w (μ w，1 -μ w，0 )+n y (μ y，1 -μ y，0 ) (2)
the crystallization process results in a change in the molar composition of the liquid phase and a loss of entropy of the system, then the above formula can also be expressed as:
in the formula (3), n germ Indicating the total number of crystal nucleus molecules. Considering that the critical nucleation radius is far smaller than the pore size and the temperature and pore solution concentration change is very small, the calculation can be nearIt is thought that the solution activity is unchanged before and after crystallization. I.e. a w ≈a w，0 ，a y ≈a y，0 . Formula (3) can thus be further simplified as:
in the formula (4), v i For the average lattice volume occupied by ice molecules, the Zobrist equation can be used to calculate:
in the formula (5), N a Is the Avgalileo constant, ρ i0 At zero degree, ice density, ρ is taken i0 =0.9167g/cm 3 . In addition, relative temperature(T 0 0 degrees celsius, T is the actual temperature).
The amount of change in the free energy ΔG of the crystal nucleus molecule caused by nucleation during nucleation V Can be expressed as:
in formula (6), e li Represents the steady vapor pressure ratio of the solution and ice crystals produced at the same temperature and pressure. For solution-ice crystal systems, raoult's law was used for pore solutions (non-ideal dilute solutions):
in the formula (7), e i Representing the steady vapor pressure ratio of water to ice crystals produced at the same temperature and pressure, can be calculated by the following formula:
ln e i ≈(-210368-131.438T+3.32373·10 6 /T+41729.1lnT)/(RT) (8)
along with the growth of crystal nucleus, the ice water interface is also continuously outwardsExpansion, ΔG S Not only temperature but also crystal nucleus radius r germ Direct correlation can be calculated by the following formula:
σ iw indicating ice water interfacial tension, by DeMott&Rogers model calculations are shown below:
σ iw [J·m -2 ]＝28·10 3 +(T-T 0 )·0.25·10 -3 (10)
considering that the water-air interface is affected by saturation, assuming that the air-filled shape is similar to that of the pores (as shown in fig. 1), when the soil surface area in the pore unit is S s Pore saturation of S r At the time, the surface area of the soil particles and the interface area S of the water vapor la The relationship can be written approximately:
Koopmans&miller indicates the water gas interfacial tension sigma la About equal to ice water interfacial tension sigma in unsaturated soil iw 2.2 times of (a), thus can be directly referenced to sigma iw Model calculation sigma la 。
Thus, the free energy change AG of water molecules at the water-air interface can be obtained la ：
The adsorption effect of the soil particles and the wetting effect of the surface tension of the liquid water enable the combined water film to completely cover the surface of the soil particles, and the contact angle of the soil-water interface can be considered to be 180 degrees in calculation. Based on the theory of adhesion wetting in surface chemistry, the average binding force of soil particles to pore water can be calculated by the following formula:
in formula (13), the first term represents the inter-particle van der Waals forces action, and the second term represents the hydration structure force (the action is remarkable when h is less than 10 nm). Wherein h is the thickness of the adsorbed film, which can be measured by experimental methods such as acoustic interference, the film thickness is considered herein to be a function of pore saturationA H Is Hamaker constant (related to dielectric constant), which means the interaction between the particle surface and the liquid due to short range Van der Waals forces, A in soil applications H ＝-6·10 -20 J。/>For the interaction energy constant, 0.008N/m, h can be used 0 Length of attenuation for hydration, h 0 0.8nm may be taken.
Supercooling, which usually occurs early in freezing, is mainly related to capillary water in the macropores of the soil, which makes the critical nucleation radius of the solution much smaller than the pore radius. Therefore, the equivalent water film thickness h may be considered to be unchanged during nucleation. When the equivalent aperture is r c When the adsorption energy change amount of the soil particles to the water molecules can be calculated as:
from the above, the binding energy of the soil particles to the pore water before and after nucleation is extremely small and negligible.
And (3) the following formulas (2) - (14) are obtained after finishing:
in crystallization kinetics, uniform nucleation refers to a process of gradually generating nuclei inside a solution due to molecular movement and combination of a parent phase under the condition of no crystallization induction. From the energy perspective, the free energy variation of the system
ΔG k Will follow the formation of crystal nucleusAnd the growth shows a trend of increasing and decreasing. And ΔG during crystallization k At maximum growth, corresponding to the "maximum nucleation potential barrier" across which stable nuclei are formed, also known as critical nucleation work ΔG * . The corresponding minimum equivalent nucleus radius is defined as critical nucleation radius r * . Thermodynamic conditions according to critical nucleation statesThe critical nucleation n can be obtained by combining (1) * Critical nucleation radius r * With the maximum potential energy barrier (critical nucleation work) Δg * Can be expressed as:
the embryo is widely distributed in the pore solution, and growth or extinction depends on whether stable crystal nucleus can be formed across the potential energy barrier of nucleation, and the generation quantity (effective crystallization probability) of the effective embryo is closely related to the salt content, the water content (saturation) and the pore size. On the one hand, the crystallization process of uniform nucleation has randomness, and the influence of the randomness on the nucleation process is difficult to accurately analyze based on thermodynamics and crystallization dynamics; on the other hand, the theoretical assumption of using the nucleation framework herein may result in significant errors when predicting very low saturation, very small pore soil supercooling. To solve the above problems, the relationship between the crystallization frequency and the cooling process (cooling rate), and the soil characteristics (salt content, water content and pore size distribution) can be expressed as follows:
at the same time let n l Introducing pore equivalent radius r for the amount of moisture in the pore unit c Can build n l And S is equal to r The relationship of (2) is as follows:
therefore, the minimum chemical potential barrier to be crossed for forming stable critical nucleiThe method comprises the following steps:
at the same temperature and pressure, the chemical potential of the ice molecules is lower than that of the water molecules, and the chemical potential of the ice molecules is the thermodynamic driving force for spontaneous phase change. The invention introduces molecular chemical potential to calculate the free energy difference between solid and liquid phases, which can be expressed by delta mu. As shown in formula (21) (wherein the ice phase is subscripted as i and the liquid phase is subscripted as l):
Δμ＝μ w (p w ，a w ，T)-μ i (p i ，T) (21)
the invention sets the solidifying point of deionized water as the analysis standard state [ T ] 0 (273.13K)、P 0 (101.013kPa)]Then the ice and water chemical potentials can be expressed as:
v in w 、V i Representing the molar volumes of liquid water and ice nuclei respectively,
representing the chemical potentials of deionized water and ice crystals, respectively, in a standard state. When the ice-water two phases are in a critical nucleation state, the phase change driving force and the chemical energy state are as follows:
the combined formulae (18) to (22) can be obtained:
we introduce Δs m For representing the entropy change during the phase change per mole of ice water, namely:
when the reference state of the solution is the normal pressure state, the pressure of the solution phase is considered to be almost unchanged from P before and after freezing w ＝P 0 This simplifies the formula (21) to:
introducing a Young-Laplace equation:
the soil body supercooling degree psi and the ideal supercooling degree psi can be obtained by combining (25) to (28) # The expression:
the invention derives a free energy function of a phase change process of the soil pore solution based on a soil pore solution crystallization microstructure in combination with a classical nucleation theory, determines critical nucleation work and critical nucleation radius required by the formation of stable crystal nuclei of the soil pore solution, establishes an effective nucleation probability expression for representing the relationship between the probability of forming the stable crystal nuclei, soil properties and environmental cooling conditions, and establishes a thermodynamic equilibrium equation in the critical nucleation state to obtain a theoretical calculation formula of the supercooling degree of the soil. The soil sample physical parameters required by the invention comprise a pore size distribution curve, the salt content of soil, the salt content and the water content, and in addition, the influence of the cooling rate on the supercooling degree of the soil body is considered. In summary, the invention has comprehensive consideration of objective influence factors and definite physical meaning, and can be used for predicting the supercooling degree of soil. In addition, the invention can provide theoretical basis for controlling the freezing process of the cold region agriculture and engineering soil, theoretical support for establishing a high-precision freezing characteristic curve model and theoretical reserve for perfecting a cold region engineering numerical calculation model.
According to the calculation method, the supercooling degree value of the soil sample under different freezing rates is calculated. The invention is based on the occurrence environment of unsaturated saline soil pore solution, considers the influence of nucleation action, solution cooling action, ice water interface action, soil water adsorption action, water-air interface action and the like on the free energy of a system, introduces classical nucleation theory deduction to establish a non-saturated saline soil pore solution nucleation model, and establishes a saline soil (non-saline soil) soil supercooling degree prediction model for the first time in a non-saturated state (saturated state). The method fully considers a plurality of influencing factors such as aperture, salt content type, water content, cooling rate and the like, has clear influencing factors and definite physical meaning, and can be used for calculating and predicting the supercooling degree of the saline soil and the non-saline soil. In addition, the invention can provide theoretical basis for controlling the freezing process of the cold region agriculture and engineering soil, theoretical support for establishing a high-precision freezing characteristic curve model and theoretical reserve for perfecting a cold region engineering numerical calculation model.
Compared with the prior art, the invention has the following advantages:
1. the invention is based on the occurrence environment of unsaturated saline soil pore solution, fully considers the influence of nucleation action, solution cooling action, ice water interface action, soil water adsorption action, water-air interface action and the like on the free energy of a system, introduces classical nucleation theory deduction to establish a unsaturated saline soil pore solution nucleation model, and establishes a saline soil (containing non-saline soil) soil supercooling degree theoretical model which can be used in an unsaturated state (containing saturated state) for the first time. The invention finally obtains the theoretical expression of the supercooling degree of the soil body, wherein the input parameters of the theoretical expression are the salt type, the salt content, the pore size distribution, the water content and the cooling rate of the soil body.
2. The method can be used for analyzing and calculating the supercooling degree of the salty soil and the non-salty soil, fully considers a plurality of influencing factors such as aperture, salt content type, water content, cooling rate and the like, and has clear influencing factors and definite physical meaning.
Drawings
The following describes the embodiments of the present invention in detail with reference to the drawings.
FIG. 1 is a microscopic schematic of a soil pore solution nucleation process.
FIG. 2 is a schematic view of the characteristic pore diameter of the soil sample.
FIG. 3 is a graph of freezing process analysis and supercooling degree.
FIG. 4 is a graph comparing measured data points to predicted results.
Description of the embodiments
The method for predicting the supercooling degree of the saline soil based on crystallization kinetics comprises the following steps:
(1) And (5) performing a soil aperture analysis test to obtain the aperture distribution curve and the soil characteristic aperture of the soil sample.
(2) And (5) performing a soil moisture content measurement test to obtain the soil volume moisture content, and calculating the pore saturation.
(3) And (3) carrying out a soil salinity analysis test to obtain the salt content and the salt content of the soil, and calculating the water activity of the soil pore solution.
(4) According to the calculation method, the supercooling degree value of the soil sample under different freezing rates is calculated.
FIG. 1 is a schematic diagram showing a nucleation process of a soil pore solution, wherein the free energy change function ΔG of the system in the nucleation process can be divided into the free energy change ΔG of the solution host molecules sln Nucleation leads to a change in the free energy of the nuclei Δg V Energy DeltaG generated at ice-water interface S And pore adsorption energy change amount Δg ls Free energy change ΔG of water molecules at interface with water vapor la Five parts:
ΔG＝ΔG sln +ΔG V +ΔG S +ΔG ls +ΔG la (1)
to determine the free energy change of the system during the phase transition, two boundary states are now defined. State a refers to the initial state (no ice water phase change), the instantaneous temperature is T 0 . At this time, the components in the solution are water molecules and solute molecules, and the molecular numbers are respectively as follows: n is n w And n y Chemical potential is mu w，1 And mu y，1 . State b refers to critical nucleation state with instantaneous temperature T sc . At this time, the components in the pores are crystal nucleus molecules, water molecules and solute molecules, and the molecular numbers can be expressed as follows: n is n germ 、(n w -n germ ) And n y The method comprises the steps of carrying out a first treatment on the surface of the Chemical potential is expressed as mu i 、μ w，1 And mu y，1 。
Thus, the free energy change ΔG of the solution host molecule during nucleation in formula (1) sln Can be calculated by the following formula:
ΔG sln ＝n w (μ w，1 -μ w， 0)+n y (μ y，1 -μ y，0 ) (2)
the crystallization process results in a change in the molar composition of the liquid phase and a loss of entropy of the system, then the above formula can also be expressed as:
in the formula (3), n germ Represents the total number of crystal nucleus molecules; a, a w Representing water activity, calculating the molar concentration of the pore solution according to the salt content, and passingAnd (5) calculating the Picter ion model. Considering that the critical nucleation radius is much smaller than the pore size and that the temperature and pore solution concentration change is very small, the solution activity before and after crystallization can be approximately considered to be approximately unchanged during calculation. I.e. a w ≈a w，0 ，a y ≈a y，0 . Formula (3) can thus be further simplified as:
in the formula (4), v i For the average lattice volume occupied by ice molecules, the Zobrist equation can be used to calculate:
in the formula (5), N a Is the Avgalileo constant, ρ i0 At zero degrees the ice density, ρ is preferably taken i0 ＝0.9167g/cm 3 ). In addition, relative temperature(T 0 0 degrees celsius, T is the actual temperature).
Similarly, nucleation results in a change in the free energy of the nuclei molecule ΔG V Can be expressed as:
in formula (6), e li Represents the steady vapor pressure ratio of the solution and ice crystals produced at the same temperature and pressure. For solution-ice crystal systems, raoult's law was used for pore solutions (non-ideal dilute solutions):
in the formula e i Representing the steady vapor pressure ratio of water to ice crystals produced at the same temperature and pressure, can be calculated by the following formula:
lne i ≈(-210368-131.438T+3.32373·10 6 /T+41729.1lnT)/(RT) (8)
along with the growth of crystal nucleus, the ice-water interface is also continuously extended outwards, delta G S Not only temperature but also crystal nucleus radius r germ Direct correlation can be calculated by the following formula:
σ iw indicating ice water interfacial tension, by DeMott&Rogers model calculations are shown below:
σ iw [J·m -2 ]＝28·10 3 +(T-T 0 )·0.25·10 -3 (10)
considering the influence of saturation on the water-air interface, we assume that the air-filled shape is similar to that of the pores (as shown in FIG. 1), when the soil surface area in the pore unit is S s Pore saturation of S r At the time, the surface area of the soil particles and the interface area S of the water vapor la The relationship can be written approximately:
Koopmans&miller indicates the water gas interfacial tension sigma la About equal to ice water interfacial tension sigma in unsaturated soil iw 2.2 times of (a), thus can be directly referenced to sigma iw Model calculation sigma la 。
Therefore, we can obtain the free energy change amount delta G of water molecules at the water-air interface la ：
The adsorption effect of the soil particles and the wetting effect of the surface tension of the liquid water enable the combined water film to completely cover the surface of the soil particles, and the contact angle of the soil-water interface can be considered to be 180 degrees in calculation. Based on the theory of adhesion wetting in surface chemistry, the average binding force of soil particles to pore water can be calculated by the following formula:
in formula (13), the first term represents the inter-particle van der Waals forces action, and the second term represents the hydration structure force (the action is remarkable when h is less than 10 nm). Wherein h is the thickness of the adsorbed film, which can be measured by experimental methods such as acoustic interference, the film thickness is considered herein to be a function of pore saturationA H Is Hamaker constant (related to dielectric constant), which means the interaction between the particle surface and the liquid due to short range Van der Waals forces, A in soil applications H ＝-6·10 -20 J。/>For the interaction energy constant, 0.008N/m, h can be used 0 Length of attenuation for hydration, h 0 0.8nm may be taken.
Supercooling, which usually occurs early in freezing, is mainly related to capillary water in the macropores of the soil, which makes the critical nucleation radius of the solution much smaller than the pore radius. Therefore, the equivalent water film thickness h may be considered to be unchanged during nucleation. When the equivalent aperture is r c When the soil particle binding energy change amount can be calculated as:
from the above, the binding energy of the soil particles to the pore water before and after nucleation is extremely small and negligible.
And (3) the following formulas (2) - (14) are obtained after finishing:
in crystallization kinetics, homogeneous nucleation means that the solution is internally moved by the parent phase molecules under conditions of no crystallization inductionAnd combining with the gradual nucleation process. From an energetics perspective, the free energy variation ΔG of the system k The crystal nucleus will be formed and grown in a first increasing and then decreasing trend. And ΔG during crystallization k At maximum growth, corresponding to the "maximum nucleation potential barrier" across which stable nuclei are formed, also known as critical nucleation work ΔG * . The corresponding minimum equivalent nucleus radius is defined as critical nucleation radius r * . Thermodynamic conditions according to critical nucleation statesThe critical nucleation n can be obtained by combining (1) * Critical nucleation radius r * With the maximum potential energy barrier (critical nucleation work) Δg * Can be expressed as:
the embryo is widely distributed in the pore solution, and growth or extinction depends on whether stable crystal nucleus can be formed across the potential energy barrier of nucleation, and the generation quantity (effective crystallization probability) of the effective embryo is closely related to the salt content, the water content (saturation) and the pore size. On the one hand, the crystallization process of uniform nucleation has randomness, and the influence of the randomness on the nucleation process is difficult to accurately analyze based on thermodynamics and crystallization dynamics; on the other hand, the theoretical assumption of using the nucleation framework herein may result in significant errors when predicting very low saturation, very small pore soil supercooling. To solve the above problems, an effective crystallization probability P is introduced for describing the crystallization frequency and the cooling process (cooling rate C T ) Soil characteristics (salt content, water content and characteristic pore diameter r) c ) The relationship between these can be expressed as follows:
when calculating the characteristic pore diameter of the soil sample, the median value of the pore diameter distribution curve can be taken as the characteristic pore diameter of the soil sample, and the implementation process is shown in figure 2. At the same time let n l Introducing pore equivalent radius r for the amount of moisture in the pore unit c Can build n l And S is equal to r The relationship of (2) is as follows:
therefore, the minimum chemical potential barrier to be crossed for forming stable critical nucleiThe method comprises the following steps:
at the same temperature and pressure, the chemical potential of the ice molecules is lower than that of the water molecules, and the chemical potential of the ice molecules is the thermodynamic driving force for spontaneous phase change. The invention introduces molecular chemical potential to calculate the free energy difference between solid and liquid phases, which can be expressed by delta mu. As shown in formula (21) (wherein the ice phase is subscripted as i and the liquid phase is subscripted as l):
Δμ＝μ w (p w ，a w ，T)-μ i (p i ，T) (21)
the invention sets the solidifying point of deionized water as the analysis standard state [ T ] according to the calculation requirement 0 (273.13K)、P 0 (101.013kPa)]Then the ice and water chemical potentials can be expressed as:
v in w 、V i Representing the molar volumes of liquid water and ice nuclei respectively, representing the chemical potentials of deionized water and ice crystals, respectively, in a standard state. When the ice-water two phases are in a critical nucleation state, the phase change driving force and the chemical energy state are as follows:
the combined formulae (18) to (22) can be obtained:
we introduce Δs m For representing the entropy change during the phase change per mole of ice water, namely:
when the reference state of the solution is the normal pressure state, the pressure of the solution phase is considered to be almost unchanged from P before and after freezing w ＝P 0 This simplifies the formula (21) to:
introducing a Young-Laplace equation:
during nucleation in the initial stage of freezing, deionized water freezing temperature T 0 Equilibrium freezing temperature T f Pore minimum supercooling temperature T sc Soil body supercooling degree psi and ideal supercooling degree psi # The relationship of (2) can be represented by figure 3. According to FIG. 3, the desired supercooling degree ψ can be obtained by combining (25) to (28) # And soil supercooling degree psi expression:
example 1
Model result verification
According to the invention, the actual measurement data of the supercooling degree of soil of a plurality of groups of scholars are selected for verification, and the physical parameters of the corresponding soil sample are arranged as shown in the following table:
/>
the data in the above table includes various soil types (sandy soil, silty soil and silty clay), salt conditions (no salt, naCl single salt, na) 2 SO 4 Mono-salt, naCl-Na 2 SO 4 Double salt), water content and soil sample under the condition of temperature reduction, has stronger representativeness. According to the prediction method, the prediction value of the supercooling degree of the soil body can be calculated by inputting the sample parameters. Finally, the error is calculated by comparing with the measured data, and an 'invention prediction effect analysis chart' (fig. 4) is obtained. As can be seen from fig. 4, the prediction errors of the 46 groups of soil samples are all less than 2 ℃; wherein, 36 groups of soil sample errors are less than 1 ℃ (accounting for 78.2% of total sample number), 29 groups of soil sample errors are less than 0.5 ℃ (accounting for 63% of total sample number), mean Absolute Error (MAE) =0.66 ℃, root Mean Square Error (RMSE) is 0.726 ℃. As a physical model, the calculation results of the invention show higher reliability for samples with different water content, salt type, soil type and cooling rate.
In conclusion, the calculation method disclosed by the invention is wide in applicability, clear in physical meaning and high in calculation precision, and can meet the calculation requirement of the supercooling degree of the saline soil. Finally, it is noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the technical solution of the present invention, which is intended to be covered by the scope of the claims of the present invention.
Claims (5)
1. The method for predicting the supercooling degree of the saline soil based on crystallization dynamics is characterized by comprising the following steps of:
(1) Performing a soil aperture analysis test to obtain an aperture distribution curve of a soil sample and a soil characteristic aperture;
(2) Performing a soil moisture content measurement test to obtain the soil volume moisture content, and calculating the pore saturation;
(3) Performing a soil salinity analysis test to obtain soil salt content and salt content, and calculating the water activity of a soil pore solution;
(4) According to the calculation method, the supercooling degree value of the soil sample under different freezing rates is calculated.
2. The method for predicting the supercooling degree of the saline soil based on crystallization kinetics according to claim 1, wherein the method comprises the following steps: by analyzing the nucleation process in the initial stage of freezing the soil pore solution, dividing the free energy change function delta G of the system in the nucleation process into: solution host molecule free energy change ΔG sln Nucleation leads to a change in the free energy of the nuclei Δg V Energy DeltaG generated at ice-water interface S And pore adsorption energy change amount Δg ls Free energy change ΔG of water molecules at interface with water vapor la Five parts:
ΔG＝ΔG sln +ΔG V +ΔG S +ΔG ls +ΔG la (1)
to determine the phase change processThe free energy change of the system now defines two boundary states, state a refers to the initial state, and the instantaneous temperature is T 0 At this time, the components in the solution are water molecules and solute molecules, and the molecular numbers are respectively as follows: n is n w And n y Chemical potential is mu w，1 And mu y，1 State b refers to critical nucleation state, and the instantaneous temperature is T sc At this time, the components in the pores are crystal nucleus molecules, water molecules and solute molecules, and the molecular numbers can be expressed as follows: n is n germ 、(n w -n germ ) And n y The method comprises the steps of carrying out a first treatment on the surface of the Chemical potential is expressed as mu i 、μ w，1 And mu y，1 ；
Thus, the free energy change ΔG of the main molecule of the solution in formula (1) sln Can be calculated by the following formula:
ΔG sln ＝n w (μ w，1 -μ w，0 )+n y (μ y，1 -μ y，0 ) (2)
the crystallization process results in a change in the molar composition of the liquid phase and a loss of entropy of the system, then the above formula can also be expressed as:
in the formula (3), n germ Indicating the total number of crystal nucleus molecules. Considering that the critical nucleation radius is far smaller than the pore size and the change of the temperature and the concentration of the pore solution is very small, the solution activity before and after crystallization can be approximately considered to be unchanged during calculation; i.e. a w ≈a w，0 ，a y ≈a y，0 . Formula (3) can thus be further simplified as:
in the formula (4), v i For the average lattice volume occupied by ice molecules, the Zobrist equation can be used to calculate:
in the formula (5), N a Is the Avgalileo constant, ρ i0 At zero degree, ice density, ρ is taken i0 ＝0.9167g/cm 3 In addition, relative temperature(T 0 0 degrees celsius, T is the actual temperature);
the amount of change in the free energy ΔG of the crystal nucleus molecule caused by nucleation during nucleation V Can be expressed as:
in formula (6), e li Representing the steady vapor pressure ratio of a solution, ice crystals, produced at the same temperature and pressure, using Raoult's law for the pore solution (non-ideal dilute solution) for a solution-ice crystal system:
in the formula (7), e i Representing the steady vapor pressure ratio of water to ice crystals produced at the same temperature and pressure, can be calculated by the following formula:
ln e i ≈(-210368-131.438T+3.32373·10 6 /T+41729.1lnT)/(RT) (8)
along with the growth of crystal nucleus, the ice-water interface is also continuously extended outwards, delta G S Not only temperature but also crystal nucleus radius r germ Direct correlation can be calculated by the following formula:
σ iw indicating ice water interfacial tension, by DeMott&Rogers model calculations, e.g.The following is shown:
σ iw [J·m -2 ]＝28·10 3 +(T-T 0 )·0.25·10 -3 (10)
considering that the water-air interface is affected by saturation, assuming that the air-filled shape is similar to that of the pores, when the soil surface area in the pore unit is S s Pore saturation of S r At the time, the surface area of the soil particles and the interface area S of the water vapor la The relationship can be written approximately:
Koopmans&miller indicates the water gas interfacial tension sigma la About equal to ice water interfacial tension sigma in unsaturated soil iw 2.2 times of (a), thus can be directly referenced to sigma iw Model calculation sigma la ；
Therefore, the free energy change amount DeltaG of water molecules at the water-air interface can be obtained la ：
The adsorption effect of the soil particles and the wetting effect of the liquid water surface tension enable the combined water film to completely cover the surface of the soil particles, the contact angle of the soil-water interface can be considered to be 180 degrees in calculation, and the average binding force of the soil particles to pore water can be calculated by the following formula based on the adhesion wetting theory in surface chemistry:
in the formula (13), the first term represents the van der Waals force action between particles, the second term represents the hydration structure force, wherein h is the adsorption film thickness, which can be measured by an experimental method such as acoustic interference, the water film thickness is a function of the pore saturation,A H for Hamaker constant, the dielectric constant is related to, indicating interaction between particle surface and liquid due to short range Van der Waals forces, A in soil applications H ＝-6·10 -20 J。/>For the interaction energy constant, 0.008N/m, h can be used 0 Length of attenuation for hydration, h 0 0.8nm can be taken;
the supercooling phenomenon occurring at the initial stage of freezing is usually mainly related to capillary water in the macropores of the soil, which makes the critical nucleation radius of the solution much smaller than the pore radius, so the equivalent water film thickness h can be considered as unchanged in the nucleation process, when the equivalent pore diameter is r c When the adsorption energy change amount of the soil particles to the water molecules can be calculated as:
the constraint energy of soil particles before and after nucleation to pore water is extremely small and negligible;
and (3) the following formulas (2) - (14) are obtained after finishing:
in crystallization kinetics, uniform nucleation refers to the process of gradually generating crystal nuclei in the solution due to the movement and combination of parent phase molecules under the condition of no crystallization induction, and the free energy change delta G of the system is in terms of energy science k Will show a trend of increasing and decreasing with the formation and growth of crystal nucleus, and ΔG in the crystallization process k At maximum growth, corresponding to the "maximum nucleation potential barrier" across which stable nuclei are formed, also known as critical nucleation work ΔG * The corresponding minimum equivalent nucleus radius is defined as the critical nucleation radiusr * According to thermodynamic conditions of critical nucleation states, i.e.The critical nucleation n can be obtained by combining (1) * Critical nucleation radius r * With the maximum potential energy barrier (critical nucleation work) Δg * Can be expressed as:
the embryo is widely distributed in the pore solution, the growth or the extinction depends on whether stable crystal nucleus can be formed across the nucleation potential energy barrier, and the generation quantity of the effective embryo, namely the effective crystallization probability, is closely related to the salt content, the water content, namely the saturation degree and the pore size, and the effective crystallization probability P is established for describing the relationship between the crystallization frequency and the temperature reduction process and the soil characteristics, and can be expressed as follows:
at the same time let n l Introducing pore equivalent radius r for the amount of moisture in the pore unit c Can build n l And S is equal to r The relationship of (2) is as follows:
therefore, the minimum chemical potential barrier to be crossed for forming stable critical nucleiThe method comprises the following steps:
at the same temperature and the same pressure, the chemical potential of the ice molecules is lower than that of water molecules, which is the thermodynamic driving force for spontaneous phase change, and meanwhile, the free energy difference between the solid phase and the liquid phase is calculated by introducing the chemical potential of the molecules, which can be represented by delta mu, as shown in a formula (21), wherein the index of the ice phase is i, and the index of the liquid phase is l:
Δμ＝μ w (p w ，a w ，T)-μ i (p i ，T) (21)
setting the solidifying point of deionized water as the analysis standard state, namely T 0 ＝273.13K、P 0 = 101.013kPa, then the ice, water chemical potential can be expressed as:
v in w 、V i Representing the molar volumes of liquid water and ice nuclei respectively, respectively representing chemical potentials of deionized water and ice crystals in a standard state, and when the ice-water two phases are in a critical nucleation state, the phase change driving force and the chemical energy state:
the combined formulae (18) to (22) can be obtained:
we introduce Δs m For representing the entropy change during the phase change per mole of ice water, namely:
when the reference state of the solution is the normal pressure state, the pressure of the solution phase is considered to be almost unchanged from P before and after freezing w ＝P 0 This simplifies the formula (21) to:
introducing a Young-Laplace equation:
the soil body supercooling degree psi and the ideal supercooling degree psi can be obtained by combining (25) to (28) # The expression:
3. the method for predicting the supercooling degree of the saline soil based on crystallization kinetics according to claim 2, wherein the method comprises the following steps: the provided soil pore solution freezes the initial crystallization nucleation microscopic model to obtain the Gibbs free energy function of the system in the nucleation process, solves to obtain critical nucleation conditions, and finally establishes an equation based on the thermodynamic equilibrium relation of ice-water two phases to deduce the theoretical expression of the supercooling degree of the soil body.
4. The method for predicting the supercooling degree of the saline soil based on crystallization kinetics according to claim 2, wherein the method comprises the following steps: the initial state is ice-water-free phase change.
5. The method for predicting the supercooling degree of the saline soil based on crystallization kinetics according to claim 2, wherein the method comprises the following steps: the temperature reduction process is the temperature reduction rate, and the soil characteristics comprise salt content, water content and pore size distribution.
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