A method, system, and storage medium for simulating interfacial hydrophobicity based on statistical thermodynamics and modified DLVO theory.

Abstract

This application provides a method, system, and storage medium for simulating interfacial hydrophobicity based on statistical thermodynamics and modified DLVO theory. The method first obtains flotation process parameters; then defines the water molecule ligand structure and energy state at the hydrophobic interface; the bulk phase of the hydrophobic interface is set as the first boundary condition, and the innermost edge closest to the hydrophobic interface is set as the second boundary condition. Combining the hydration of ions and water molecules, the ion distribution is calculated. The contact angle parameters of the innermost interface ligands and the interfacial potential, which change due to ion adsorption, are corrected. The hydrophobic surface potential and double-layer structure are corrected according to ion-induced theory, and the macroscopic physical properties of the interface after hydrophobic correction are calculated. The flotation effect under the parameter conditions is obtained based on the macroscopic physical properties of the interface. This calculation method can quantitatively analyze and numerically simulate interfacial interactions during flotation, providing a theoretical basis for process control in flotation practice.

Description

Technical Field

[0001] This application relates to the field of digital simulation technology of interface hydrophobicity, and in particular to a method, system and storage medium for simulating interface hydrophobicity based on statistical thermodynamics and modified DLVO theory. Background Technology

[0002] Interfacial hydrophobicity has significant theoretical and applied value in many fields, including chemistry, colloid science, materials science, environmental science, and life science, playing a crucial role, especially in mineral processing engineering. As one of the core driving forces of the flotation process, interfacial hydrophobicity directly determines whether mineral particles can selectively adhere to the surface of air bubbles in aqueous solution, achieving efficient separation of valuable minerals from gangue.

[0003] However, traditional theories can only describe van der Waals forces and electric double-layer forces at liquid-solid or liquid-liquid interfaces, failing to explain the additional attraction exhibited between hydrophobic particles and bubbles. Numerous experiments show that the strength and range of hydrophobic interactions far exceed predictions from DLVO theory, while existing molecular-scale hydrophobic theories suffer from oversimplification and struggle to accurately characterize the complex interfacial behavior in mineral processing. Current macroscopic DLVO theories, by neglecting the evolution of water molecule structures at hydrophobic interfaces, cannot describe long-range forces and vapor bridge effects, nor establish a correlation between interfacial physicochemical parameters and thermodynamic quantities, making it difficult to reveal the regulatory mechanisms of hydrophobicity. Furthermore, their treatment of ionic interactions is limited to the electrostatic shielding approximation, failing to quantify ion-induced interfacial water reconstruction behavior. Therefore, a more reasonable interfacial hydrophobic theoretical model is needed to address the aforementioned inaccuracies in hydrophobic interface simulations. Summary of the Invention

[0004] Purpose of the invention: This application discloses a method, system, and storage medium for simulating interface hydrophobicity based on statistical thermodynamics and modified DLVO theory. This calculation method can perform quantitative analysis and numerical simulation of interfacial interactions during flotation, providing a theoretical basis for process control in flotation practice.

[0005] This application discloses a method for simulating and calculating the hydrophobicity of interfaces based on statistical thermodynamics and modified DLVO theory, including the following steps:

[0006] Obtain flotation environment parameters, ion concentration, and ligand contact angle parameters;

[0007] Define the ligand structure and energy state of water molecules at hydrophobic interfaces;

[0008] The bulk phase based on the hydrophobic interface is set as the first boundary condition, and the innermost side closest to the hydrophobic interface is set as the second boundary condition. Combining the hydration of ions and water molecules, the ion distribution is calculated. The contact angle parameters of the innermost interface ligands and the interface potential that change due to ion adsorption are corrected. The hydrophobic surface potential and double layer structure are corrected according to the ion-induced theory. Then, the macroscopic physical property parameters of the interface after hydrophobic correction are calculated.

[0009] The flotation effect under parameter conditions is obtained based on the macroscopic physical property parameters of the interface.

[0010] Preferably, the water molecule ligand structure at the interface includes monomers, dimers, cyclic structures, and cage structures; the energy state of the ligand includes the interface hydrogen bond state, dipole-dipole interaction energy, and gas monomer energy.

[0011] Preferably, the thermodynamic parameters are calculated as follows: based on the ion distribution, the bulk ligand distribution and bulk energy of the first boundary condition are calculated using the Boltzmann distribution. According to the corrected contact angle parameter of the innermost interface ligand, a ligand transformation model over time is constructed to calculate the second boundary condition. Through the inverse ligand transformation process and the application of boundary condition constraints, a ligand spatial evolution model is formed. Combined with the two-level system, the thermodynamic parameters at the interface are calculated.

[0012] The boundary condition constraints include the energy difference between the first and second boundary conditions, ligand structure, and energy cutoff.

[0013] Preferably, the thermodynamic parameters at the interface include the hydrogen bond energy, entropy, chemical potential, density potential, and evaporation at the interface.

[0014] Preferably, the macroscopic physical properties include vibration frequency, dielectric constant, refractive index, and interfacial hydrophobicity.

[0015] Preferably, the corrected van der Waals force and electrostatic force are calculated using the corrected vibration frequency, dielectric constant, and refractive index. The corrected interfacial hydrophobic energy is superimposed with one or more of the corrected van der Waals force and electrostatic force to simulate the interaction forces between different types of hydrophobic interfaces, between interfaces and bubbles, between interfaces and particles, and between bubbles and particles.

[0016] This application also discloses a simulation and calculation system for interface hydrophobicity based on statistical thermodynamics and modified DLVO theory, including...

[0017] The parameter input module is configured to take flotation environment parameters, ion concentration, and ligand contact angle parameters as input.

[0018] The calculation module is configured to define the structure and energy state of water molecule ligands at the hydrophobic interface; the bulk phase of the hydrophobic interface is set as the first boundary condition, and the innermost side of the hydrophobic interface is set as the second boundary condition. Combined with the hydration of ions and water molecules, the ion distribution is calculated, the contact angle parameters of the innermost interface ligands and the interface potential that change due to ion adsorption are corrected, and the hydrophobic surface potential and double layer structure are corrected according to the ion-induced theory. Then, the macroscopic physical property parameters of the interface after hydrophobic correction are calculated.

[0019] The output module is configured to visualize and output the macroscopic physical property parameters of the hydrophobic reaction interface, reflecting the flotation effect under the obtained parameter conditions.

[0020] Furthermore, the calculation module can also be configured to calculate the bulk ligand distribution and bulk energy of the first boundary condition based on the ion distribution and Boltzmann distribution when calculating thermodynamic parameters. Based on the corrected contact angle parameter of the innermost interface ligand, a ligand transformation model over time is constructed to calculate the second boundary condition. Through the inverse ligand transformation process and the application of boundary condition constraints, a ligand spatial evolution model is formed. Combined with the two-level system, the thermodynamic parameters at the interface are calculated. The boundary condition constraints include the energy difference between the first and second boundary conditions, the ligand structure, and the energy cutoff.

[0021] Furthermore, the calculation module can also be configured to calculate the corrected van der Waals force and electrostatic force using the corrected vibration frequency, dielectric constant, and refractive index, and to calculate the superposition of the corrected interface hydrophobic energy with one or more of the corrected van der Waals force and electrostatic force, in order to simulate the interaction forces between different types of hydrophobic interfaces, between interfaces and bubbles, between interfaces and particles, and between bubbles and particles.

[0022] This application also discloses a storage medium for a method of simulating interface hydrophobicity based on statistical thermodynamics and modified DLVO theory. The storage medium is used to store computer program instructions capable of implementing the above-mentioned method of simulating interface hydrophobicity based on statistical thermodynamics and modified DLVO theory.

[0023] Beneficial effects: First, this interface hydrophobicity simulation calculation system can accurately simulate and dynamically predict the interaction behavior under different interface types and environmental parameters using the above-mentioned interface hydrophobicity simulation calculation method, and can provide reliable theoretical tools and technical support for mineral flotation engineering applications.

[0024] Second, this method for simulating and calculating interfacial hydrophobicity establishes an ion-induced theory to quantitatively calculate and describe the effects of hydrophobic interactions on ion distribution, surface charge density, and potential. It then systematically corrects the double-layer model, van der Waals forces, and surface potential in the traditional DLVO theory, ultimately forming a unified interfacial hydrophobic-DLVO model. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in this application, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0026] Figure 1 This is a flowchart illustrating the workflow of a simulation calculation method for interface hydrophobicity based on statistical thermodynamics and modified DLVO theory, as described in this application.

[0027] Figure 2 This is a theoretical schematic diagram of a method for simulating and calculating the hydrophobicity of an interface based on statistical thermodynamics and modified DLVO theory, as proposed in this application.

[0028] Figure 3 This is a structural diagram of the hydrogen bond energy states of water molecules with different ligands in the technical solution disclosed in this application.

[0029] Figure 4 This is a verification diagram showing the decreasing trend of dielectric constant of the hydrophobic interface in the technical solution disclosed in this application.

[0030] Figure 5 This is a schematic diagram of the vapor bridge situation at the hydrophobic interface in the technical solution disclosed in this application.

[0031] Figure 6 This is a diagram verifying the trend of vapor bridging force at the hydrophobic interface in the technical solution disclosed in this application.

[0032] Figure 7 This is a diagram verifying the trend of vapor bridging force at the hydrophobic interface in the technical solution disclosed in this application.

[0033] Figure 8 This is a schematic diagram of the hydrophobic interface nanobubbles used in the verification experiment of the technical solution disclosed in this application.

[0034] Figure 9 This is a schematic diagram of the structure of an interface hydrophobicity simulation calculation system based on statistical thermodynamics and modified DLVO theory according to this application.

[0035] Figure 10 This is a schematic diagram of the input interface of an interface hydrophobicity simulation calculation system based on statistical thermodynamics and modified DLVO theory according to this application.

[0036] Figure 11 This is a schematic diagram of the average vibrational frequency of hydrogen bonds in the output interface of an interface hydrophobicity simulation calculation system based on statistical thermodynamics and modified DLVO theory, as described in this application.

[0037] Figure 12 This is a schematic diagram of the output interface covalent bond frequency simulation of an interface hydrophobicity simulation calculation system based on statistical thermodynamics and modified DLVO theory according to this application.

[0038] Figure 13 This is a schematic diagram of the output interface refractive index simulation of an interface hydrophobicity simulation calculation system based on statistical thermodynamics and modified DLVO theory according to this application.

[0039] Figure 14 This is a schematic diagram of the surface charge density induced by hydrophobic interaction in the output interface of an interface hydrophobicity simulation calculation system based on statistical thermodynamics and modified DLVO theory, as described in this application.

[0040] Figure 15 This is a schematic diagram of the surface potential induced by hydrophobic interaction at the output interface of an interface hydrophobicity simulation calculation system based on statistical thermodynamics and modified DLVO theory, as described in this application.

[0041] Figure 16 This is a schematic diagram of the interface hydrophobicity simulation in the output interface of the interface hydrophobicity simulation calculation system based on statistical thermodynamics and modified DLVO theory of this application.

[0042] Figure 17 This is a schematic diagram of the interface hydrophobicity simulation under the ion-induced adsorption interface energy in the output interface of the interface hydrophobicity simulation calculation system based on statistical thermodynamics and modified DLVO theory of this application. Detailed Implementation

[0043] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0044] It should be noted that the use of designations such as [first], [second], [third], and [fourth] in this application does not represent any order, quantity, or importance; they are merely used to distinguish different parts. The directional designations such as [up], [down], [left], and [right] in this application are only for reference to the accompanying drawings. Therefore, the designations, directional designations, and positional relationship designations used are for the purpose of explaining and understanding this application, and not for limiting this application. In the drawings, structurally similar units are represented by the same labels.

[0045] Studies have shown that interfacial hydrophobicity primarily stems from changes in the hydrogen bond structure of water molecules at the hydrophobic interface. Compared to bulk water, the interfacial water hydrogen bond network is more fragile, with a significantly reduced hydrogen bond breaking enthalpy, accompanied by entropy changes, chemical potential changes, spontaneous dipole enhancement, and evaporation enhancement. These microstructural changes not only affect macroscopic physical quantities such as dielectric constant, refractive index, and density, but also induce interfacial behaviors such as microbubble precipitation and vapor bridge formation, thereby affecting flotation foam stability and bubble-mineral adhesion efficiency. Furthermore, hydrophobicity is also regulated by ion activity: changes in the interfacial water structure alter ion activity, charge density, and induced potential, and these parameters further regulate the strength of the hydrophobic force, ultimately affecting the floatability of mineral particles.

[0046] Traditional DLVO treats water as a continuous medium, neglecting the changes in dielectric properties and ion activity caused by the weakening of hydrogen bond networks at hydrophobic interfaces, and failing to integrate "hydrophobic energy" as a fundamental interaction component into the theoretical framework. Furthermore, existing models lack sufficient explanatory power for key interfacial phenomena, such as the quantitative relationship between the formation mechanism of interfacial nanobubbles and local vapor pressure increases, the densification phenomenon at the gas-liquid interface, and the coupling mechanism between ions and hydrophobicity; all lack systematic derivations from microscopic mechanisms to macroscopic properties. Regarding the handling of key physical quantities, current techniques lack a unified definition and calculation method for interfacial hydrophobic energy, and also fail to integrate concepts such as "vapor bridges" and depletion layers with interfacial boundary conditions and chemical potential changes.

[0047] Therefore, based on the above-mentioned disadvantages and problems, this application provides a photovoltaic module frame removal device, which will be described below with reference to specific embodiments.

[0048] This embodiment discloses a method for simulating and calculating interfacial hydrophobicity based on statistical thermodynamics and modified DLVO theory, such as... Figure 1 As shown.

[0049] In this embodiment, it is first demonstrated that, starting from the perspective of ligand structure and energy state evolution, by setting a hydrogen bond structure model with first and second boundary conditions, combined with Boltzmann distribution and a two-level system, a quantitative description of key thermodynamic parameters such as enthalpy, entropy, and chemical potential of the hydrophobic interface can be achieved, thereby revealing the microscopic physicochemical mechanism of hydrophobic interaction. Furthermore, by establishing the correlation between ionic chemical potential and aqueous chemical potential, the ion redistribution law induced by hydrophobic effect is derived, and its influence on surface charge density and potential is quantitatively characterized. Based on this, the double-layer model and van der Waals force expression in DLVO theory are systematically corrected, ultimately achieving a unified calculation of hydrophobic interaction and traditional interfacial forces, completing the simulation of known flotation parameter conditions, such as... Figure 2 As shown, the details are as follows:

[0050] First, we define the energy state structure of water molecules at hydrophobic interfaces and the energy state of hydrogen bonds. Low-energy hydrophobic interfaces are more prone to exhibiting weakened hydrogen-bonded cyclic water molecules and poorly coordinated water molecules. Therefore, the existence forms of water ligands are classified as: monomers, dimers, trimers, tetramers, pentamers, and hexamers. Among these, trimers, tetramers, and pentamers have cyclic structures, while hexamers have a cage-like structure, such as... Figure 3 As shown. Based on different hydrogen bond structures, ligands are classified into monomers with dipole interactions and liquid ligands with hydrogen bonding interactions. The different hydrogen bond configurations of ligands are the dominant reason why water molecules exhibit different macroscopic energy states. The energies and structures of different ligands in water molecules can be obtained using bond sequence-bond length-bond energy theory, Lagrange mechanics characterization of the O:HO hydrogen bond potential, and DFT calculations. The energy states of water molecules include the interfacial hydrogen bond states of ligands, dipole-dipole interaction energies, and gaseous monomer energies.

[0051] Among them, the interfacial hydrogen bond energy state of j ligand The calculation formula is as follows:

[0052] (Equation 1)

[0053] In the formula, =0.24e=0.4×10 -19 C, water molecule dipole moment The angle between the dipole and the hydrogen ion is vacuum permittivity The dielectric constant is .

[0054] Dipole-dipole interaction energy The calculation formula is as follows:

[0055] (Equation 2)

[0056] In the formula, Boltzmann's constant, For temperature, the static dielectric constant of water Vacuum static dielectric constant Incident light frequency water refractive index Vacuum refractive index Planck constant water molecule radius Intermolecular distance .

[0057] Gas Element Energy The calculation formula is as follows:

[0058] ; (Equation 3)

[0059] In the formula, Boltzmann's constant, For temperature.

[0060] The bulk water at the hydrophobic interface is set as the first boundary condition, and the innermost part closest to the hydrophobic interface is set as the second boundary condition. Using the Boltzmann distribution and a two-level system, key thermodynamic parameters such as enthalpy, entropy, and chemical potential at the interface are quantitatively calculated. The specific calculation method is as follows:

[0061] Based on the hydrogen bond structure model under the first boundary condition, the bulk ligand distribution under the first boundary condition is established using the Boltzmann distribution, and the calculation formula is as follows:

[0062] (Equation 4)

[0063] In the formula, The number of ligands in phase j. This represents the total number of water molecule layers in the bulk phase. The average energy of the volumetric phase;

[0064] The volumetric energy is then obtained, and the calculation formula is as follows:

[0065] (Equation 5)

[0066] In the formula, This refers to the total energy of the body phase.

[0067] Combining the hydrogen bond structure model and the contact angle θ parameter of the second boundary condition, the energy of the second boundary condition is calculated as follows:

[0068] (Equation 6)

[0069] In the formula, The cohesive energy of bulk water molecules, The second boundary condition is the cohesive energy of water molecules. It is the adhesion energy of the interaction between liquid molecules and solid surfaces. The surface tension is the second boundary condition.

[0070] The energy difference between the second boundary condition and the first boundary condition is the main reason driving the evolution of the interface structure. The energy calculation formula for the second boundary condition is as follows:

[0071] (Equation 7)

[0072] The energy difference between the second boundary condition and the first boundary condition is:

[0073] (Equation 8)

[0074] In the formula, The difference between the water molecule structure energies under the first and second boundary conditions is given.

[0075] A ligand evolution dynamics model is constructed by first calculating the ligand transformation model over time, as shown in the following formula:

[0076] (Equation 9)

[0077] In the formula, The number of water molecules with ligand j at the hydrophobic interface. Let f be the energy difference for the evolution of ligand j into other ligands, and f be other ligands besides ligand j.

[0078] By applying boundary conditions and the inverse ligand transformation process, a ligand spatial evolution model is formed, in which the calculation formula for the inverse ligand transformation process is as follows:

[0079] (Equation 10)

[0080] Boundary condition constraints include the energy difference between the first and second boundary conditions and the cutoff energy, where the energy difference is shown in Equation 8, and the energy cutoff is calculated as follows:

[0081] (Equation 11)

[0082] In the formula, The second boundary condition is the water molecule structure energy. The second boundary condition is the number of ligands in water molecule j. The number of gaseous water molecules is the second boundary condition.

[0083] The thermodynamic parameters at the interface can be calculated using a two-level system. The calculation formula for a two-level system is as follows:

[0084] (Equation 12)

[0085] In the formula, For the first Water molecules in the layer relative to the layer above ( The number of water molecules added to the bulk phase energy of the layer. The number of water molecules in the innermost layer;

[0086] Thermodynamic parameters at the interface include, but are not limited to, parameters such as hydrogen bond energy, entropy, chemical potential, density potential, and evaporation. The formula for calculating the interface energy is as follows:

[0087] (Equation 13)

[0088] The formula for calculating hydrogen bond energy is as follows:

[0089] (Equation 14)

[0090] The formula for calculating the entropy at the interface is as follows:

[0091] (Equation 15)

[0092] In the formula, For the first Water molecules ligand number, For the first The number of gaseous water molecules transformed from water molecules in the layer. Bulk water molecular layer ligand number, This represents the number of gaseous water molecules that transform from bulk water molecules. The ideal gas constant is 8.314 J / (K mol). Let j be the thermodynamic concentration of ligand j;

[0093] The chemical potential at the interface is calculated as follows:

[0094] (Equation 16)

[0095] In the formula, The standard chemical potential for the conversion of j-ligand into a gaseous monomer;

[0096] (Equation 17)

[0097] In the formula, The standard chemical potential of the gaseous monomer;

[0098] The formula for calculating the density potential at the interface is as follows:

[0099] (Equation 18)

[0100] In the formula, Let be the water density of the i-th layer at the hydrophobic interface. The density of bulk water is taken as 1 g / cm3;

[0101] The above thermodynamic parameters can reveal the microscopic physicochemical origin of hydrophobic interactions.

[0102] To achieve cross-scale prediction from microscopic mechanisms to macroscopic properties, the macroscopic physical property parameters of the interface are calculated based on the evolved interface ligand distribution and hydrogen bond vibrational frequencies. The formula for calculating the evolved interface ligand distribution is as follows:

[0103] (Equation 19)

[0104] In the formula, The total number of water molecules in the i-th layer. For the first The number of liquid monomers in the water layer;

[0105] (Equation 20)

[0106] In the formula, The constant value determines the number of ligands for ligand j under the second boundary condition (i.e., the cutoff point of hydrophobic energy after entropy compensation). Let x be the rate constant for the transformation of ligand j into other ligands, and let x be the distance in the evolution of the number of interfacial ligand structures, in nanometers. This represents the number of other ligands in the evolution of ligand j. The hexamer, representing the highest hydrogen bond energy state, is used as the evolution endpoint to constrain the evolution of the number of interface ligand structures.

[0107] Based on the distribution of ligands at the interface, the macroscopic physical properties of the interface can be calculated, including the vibration frequency, as shown in the following formula:

[0108] (Equation 21)

[0109] In the formula, Let be the average vibration frequency of the i-th layer. Let j be the vibrational frequency of the ligand.

[0110] The formula for calculating the dielectric constant of the i-th layer ligand is as follows:

[0111] ; (Equation 22)

[0112] In the formula, Let be the dielectric constant of the i-th layer of water molecules. The dielectric constant of the j-ligand;

[0113] The formula for calculating refractive index is as follows:

[0114] ; (Equation 23)

[0115] In the formula, For the refraction of the i-th layer of water molecules, The refractive index of ligand j;

[0116] The formula for calculating the dielectric constant of j-ligand is as follows:

[0117] (Equation 24)

[0118] In the formula, The vibrational frequency of the O:H moiety of the hydrogen bond in the j-ligand of the water molecule is . Let be the vibrational frequency of the covalent bond in the j-ligand of the water molecule. Let be the spatial density of water molecules, e be the electron charge, and m be the mass of a water molecule. The vacuum permittivity is 8.854 × 10⁻⁶. -12 F / m, The incident light frequency;

[0119] The formula for calculating the hydrophobicity of the interface is as follows:

[0120] (Equation 25)

[0121] In the formula, For the depletion layer case, hydrophobic interaction energy, The difference between the water molecule structure energy of the i-th layer and the first boundary condition;

[0122] As can be seen from the above, the technical solution disclosed in this embodiment can calculate the dielectric constant of the hydrophobic interface. The dielectric constant of the hydrophobic interface is different from that of the bulk phase. AFM and simulation studies have both found that the dielectric constant of water molecules at the hydrophobic interface is significantly reduced. Figure 4 As shown, the dielectric constant of the hydrophobic interface calculated in this application matches the existing experimental measurement results.

[0123] The technical solution disclosed in this embodiment can describe the steam bridge force and quantify the geometric parameters of the steam bridge and the force it generates. The steam bridge force includes the three-phase contact line tension and the Laplace pressure, wherein the calculation formula for the three-phase contact line tension is as follows:

[0124] (Equation 26)

[0125] In the formula, The contact radius of the vapor bridge on the solid surface;

[0126] The formula for calculating Laplace pressure is as follows:

[0127] (Equation 27)

[0128] In the formula, The first principal radius of the steam bridge; This is the second principal radius of the steam bridge; and Representative dimensions are as follows Figure 5 As shown, Figure 5 This is a schematic diagram of a vapor bridge at a hydrophobic interface.

[0129] The formulas for calculating the relevant geometric parameters in the case of a steam bridge are as follows:

[0130] (Equation 28)

[0131] In the formula, V is the gas volume at the hydrophobic interface, and H is the distance between two identical plates in the case of a vapor bridge.

[0132] AFM and SFA experiments show that between two strongly hydrophobic interfaces, a vapor bridge forms a long-range hydrophobic force with a step-like force curve, known as the "jump in" phenomenon. To describe strong hydrophobicity, the interface must possess the following characteristics: (1) large hydrophobic interaction; (2) interface homogeneity and rigidity; (3) large interface area. A larger interface area results in a larger hydrophobic interaction because area interactions lead to more hydrogen bond breakage. For example... Figure 6 and Figure 7 As shown, where Figure 6 For hydrophobic interfaces with small contact angles, the vapor bridging force is represented by a repulsive force at the solid-liquid-gas three-phase contact line when the distance between the phases is small. As the interfacial distance increases, the repulsive force weakens, while the surface tension of the gas-liquid interface increases. Overall, the force is initially repulsive and then attractive. Figure 7 The steam bridge force is the force at a hydrophobic interface with a large contact angle. The force of the solid-liquid-gas three-phase contact line at the large contact angle interface and the surface tension of the gas-liquid interface are both expressed as attractive forces. The steam bridge force calculated in this application can match the existing experimental measurement results.

[0133] Furthermore, it can explain the densification effect at the gas-liquid interface. Specifically, a monomer escape and local densification model is constructed to explain the densification effect at the gas-liquid interface. Low coordination at the gas-liquid interface promotes hydrogen bond breaking and evaporation, and the generated gaseous monomer water molecules directly escape into the gas phase. Therefore, compared with the condensed state interface, the gas-liquid interface no longer contains gaseous monomers. The calculation formula for the monomer escape and local densification model is as follows:

[0134] (Equation 29)

[0135] ; (Equation 30)

[0136] The number of ligands at the gas-liquid interface is calculated using the formula above. Compared to condensed matter interfaces, the gaseous monomers at the gas-liquid interface lead to localized densification. Water molecules, predominantly present under boundary condition 2, are liquid monomers and dimers, a finding supported by the VSFG spectral differences between condensed-water and gas-water interfaces regarding suspended hydrogen bonds. Due to this localized densification, the gas-liquid interface exhibits a larger dielectric constant than the condensed-water hydrophobic interface, a point strongly supported by previous experimental results demonstrating how changes in water structure lead to variations in flow and dielectric response. However, this densification is only relative to the condensed-water hydrophobic interface; experiments show that the gas-liquid interface cannot produce an ice-like surface.

[0137] Compared to the depletion layer scenario, gaseous monomers at the gas-liquid interface escape into the air. In this case, the influence of gaseous monomers can be disregarded when calculating the water molecule structure distribution and hydrophobic energy at the interface. The escape of gaseous monomers leads to an enhanced liquid water molecule structure, manifesting as localized densification of the interface. The calculation formula is as follows:

[0138] (Equation 31)

[0139] The density chemical potential based on the change in the number of liquid ligands can be expressed as follows:

[0140] ; (Equation 32)

[0141] Mixed entropy:

[0142] ; (Equation 33)

[0143] The hydrophobic energy of the i-th layer at the gas-liquid interface can be calculated using the above formula. Local densification weakens the chemical potential of the inner layer of water at the gas-liquid interface and enhances the mixing entropy, causing the hydrophobic effect at the gas-liquid interface to form an energy valley. Bubbles tend to aggregate together, but will not directly merge.

[0144] Furthermore, the correlation between the formation mechanism of interfacial nanobubbles and the structure and vapor pressure of water molecules can be described, as shown in the following calculation formula:

[0145] First, we establish the dynamic equilibrium of the amount of gas absorbed by the water surface and the amount of gaseous monomers escaping into the air under saturation conditions:

[0146] ; (Equation 34)

[0147] In the formula, This is the pressure relative to standard atmospheric pressure. This represents the probability that gaseous water molecules collide with the water surface and are absorbed. The change in the number of j-ligands under pressure;

[0148] The radius R of the nanobubbles formed by the gaseous monomer is calculated using the Laplace equation, as follows:

[0149] ; (Equation 35)

[0150] In the formula, Standard atmospheric pressure This is the pressure relative to standard atmospheric pressure. The gas pressure inside the surface-deposited bubbles. It is the saturated vapor pressure;

[0151] ; (Equation 36)

[0152] In the formula, It is half the average energy of the hydrogen bonds in the i-th layer;

[0153] (Equation 37)

[0154] In the formula, The average number of hydrogen bonds in a water molecule for ligand j;

[0155] By combining the volume of air dissolved in the water, the total gas volume V at the hydrophobic interface can be obtained, and the calculation formula is as follows:

[0156] (Equation 38)

[0157] In the formula, For the volume of an ideal gas molecule, To predict the average radius of nanobubbles, Let N be the solubility of gas l, and N be the total number of water molecules in the i-th layer of the interface.

[0158] solubility of gas l in the interface for:

[0159] (Equation 38)

[0160] In the formula The solubility of the gas in the bulk phase. It is half of the average hydrogen bond energy in the bulk phase;

[0161] Based on the average radius of the nanobubbles and the total gas volume at the hydrophobic interface, the total number of nanobubbles at the hydrophobic interface can be obtained. The calculation formula is as follows:

[0162] (Equation 39)

[0163] In the verification experiment, the total number of nanobubbles at the water interface calculated matched the actual experimental verification quantity. The image of the nanobubbles at the interface is shown in the figure below. Figure 8 As shown.

[0164] Furthermore, in this embodiment, the separation pressure between hydrophobic interfaces is obtained through the Derjaguin approximation, and the calculation formula is as follows:

[0165] The hydrophobicity calculation formula for the depletion layer case is as follows:

[0166] (Formula 40)

[0167] In the formula, R is the bubble radius. The hydrophobic interaction energy is for the depletion layer condition;

[0168] The steam bridge case includes both hydrophobic forces and steam bridge forces, calculated as follows:

[0169] (Equation 41)

[0170] In the formula, For the tension of the three-phase contact wire; For Laplace pressure;

[0171] The formula for calculating the gas-liquid interface is as follows:

[0172] (Equation 42)

[0173] In the formula, R is the bubble radius. Hydrophobic interaction energy at the gas-liquid interface;

[0174] By providing reasonable explanations for interfacial phenomena such as gas-liquid interface densification, nanobubble formation, and vapor bridge effect, a theoretical basis for interfacial hydrophobicity based on statistical thermodynamics was established, and the effectiveness of the simulation calculation method for interfacial hydrophobicity was verified.

[0175] In this embodiment, ions are present in the liquid during mineral flotation. Therefore, the aforementioned statistical thermodynamics-based interfacial hydrophobicity theory cannot fully meet the requirements. Thus, it is necessary to deeply integrate interfacial hydrophobicity with the DLVO theory, constructing a complete interfacial hydrophobicity-DLVO theory for simulating the flotation effect during mineral flotation. The specific steps are as follows:

[0176] First, the ion-induced theory is established, which derives the inductive effect of hydrophobic interactions on ion distribution based on changes in the interfacial water chemical potential. The hydration energy between ions and water molecules is then calculated. The calculation formula is as follows:

[0177] (Equation 43)

[0178] In the formula, Let r be the ionic valence state and r be the distance between the ion and the water molecule. The hydrogen bond energy of water molecules in the ion hydration layer;

[0179] Due to the difference in energy states, low-coordinated water molecules are more likely to hydrate with ions. Hydrophobic interactions disrupt the interfacial hydrogen bond structure, lowering the hydrogen bond energy state of water molecules, leading to the enrichment of interfacial ions and reducing the number of hydrated water molecules. The calculation formula is as follows:

[0180] (Equation 44)

[0181] Further calculations were performed to determine the induction of ion enrichment by hydrophobic interactions. First, the interfacial hydrochemical potential was calculated based on the hydrogen bond structure of water molecules. The calculation formula is as follows:

[0182] (Equation 45)

[0183] In the formula, The number of water molecules used for hydration formed by the j-th ligand in the i-th layer. Let be the number of water molecules used for hydration formed by the i-th layer of gaseous monomers. The standard chemical potential of the gaseous monomer, The standard chemical potential of the liquid ligand;

[0184] Further calculation of the number of induced ions The calculation formula is as follows:

[0185] (Equation 46)

[0186] In the formula, For the interfacial water chemical potential, The hydration energy of the nearest neighbor water molecule and ion. The coordination number of water molecules involved in the hydration of ions. This refers to the number of bulk ions A.

[0187] Based on the change in ion activity, the interfacial induced charge density generated by hydrophobic interactions is calculated using the following formula:

[0188] (Equation 47)

[0189] In the formula, The surface charge density of hydrophobic induced ions. To induce the number of anions / cations through hydrophobicity, Hydrophobic induction of anion / cation valence states;

[0190] Due to the differences between the hydration energy state and the hydrogen bond energy state of different ions, the specific adsorption of ions by hydrophobic interactions can be obtained through Boltzmann distribution. The formula for calculating the ion distribution is as follows:

[0191] (Equation 48)

[0192] In the formula, represents the partition function of the hydration energies of different ions. The difference in hydration energy between different ions;

[0193] The hydration energy state of anions is close to that of hydrogen bonds, so the ions induced at the hydrophobic interface are dominated by anions, which is the same as the natural negative charge property of hydrophobic surfaces.

[0194] Hydrophobic interfaces disrupt the interfacial hydrogen bond structure, leading to changes in thermodynamic parameters such as hydrogen bond structure energy, chemical potential, and mixing entropy, as well as physical parameters such as density, dielectric constant, and refractive index. The interfacial water chemical potential induces ion enrichment, which in turn feeds back into the hydrophobic interaction, affecting the interfacial contact angle and hydrophobic interaction energy.

[0195] The innermost interface ligand contact angle parameter and interfacial potential are corrected due to changes caused by ion adsorption. The corrected calculation of the ligand contact angle parameter is as follows:

[0196] First, considering the inductive effect of the hydrophobic interface, the difference in water molecule structure energy between the first and second boundary conditions under the hydrophobic induction effect is: The calculation formula is as follows:

[0197] (Equation 49)

[0198] At this point, the contact angle relationship after the addition of ions is as follows:

[0199] (Equation 50)

[0200] The difference in water molecule structure energy between the first and second boundary conditions under the combined effects of hydrophobic induction and total surface potential adsorption is: The calculation formula is as follows:

[0201] (Equation 51)

[0202] At this point, the corresponding contact angle relationship is:

[0203] (Equation 52)

[0204] The formula for calculating the interface potential is as follows:

[0205] (Equation 53)

[0206] In the formula, The potential caused by the hydrophobic-induced change in the ion density of the i-th layer;

[0207] The ion partition function is used to quantitatively correlate bulk phase pH, ion activity, and interfacial induced charge. The interfacial induced charge density can be calculated using Equation 47 above. The interfacial potential is calculated as follows:

[0208] (Equation 54)

[0209] In the formula, For Debye length, They are Greek letters. The potential is caused by the ion density of the i-th layer due to adsorption on the original surface.

[0210] Furthermore, the ion-induced theory is used to correct the surface potential and double-layer structure of the hydrophobic interface, thus accurately reflecting the non-uniform distribution of ions at the hydrophobic interface. The calculation formula is as follows:

[0211] ; (Equation 55)

[0212] In the formula, denoted as the number of bulk ions, and k as the Boltzmann constant.

[0213] Furthermore, the Hamaker constant can be corrected by using Equations 46, 47 and 54 above to calculate the dielectric constant and refractive index parameters after hydrophobic correction, so that the van der Waals force calculation is more in line with the actual interface situation.

[0214] Furthermore, this embodiment also integrates the feedback effect of ion hydration to correct the hydrophobic energy, and the bulk structure energy after adding ions is: The calculation formula is as follows:

[0215] (Equation 56)

[0216] In the formula, M is the ion hydration number. This represents the number of ions in the bulk phase. The number of water molecules j-ligands that have not undergone ion hydration in the bulk phase;

[0217] Considering only the inductive effect of the hydrophobic interface, the total interfacial energy of the i-th layer is:

[0218] (Equation 57)

[0219] In the formula, The first under hydrophobic induction The difference in structural energy between the layer and the first boundary condition water molecules;

[0220] (Equation 58)

[0221] In the formula, The number of water molecules in the j-ligand that did not undergo hydration;

[0222] The difference between the ion hydration energy induced at the hydrophobic interface of condensed matter and that of the bulk phase is calculated as follows:

[0223] (Equation 59)

[0224] In the formula, The first under hydrophobic induction The chemical potential of liquid water molecules in a layer of water. The first under hydrophobic induction The chemical potential of gaseous water molecules in the water layer. For the first Chemical potential of changes in the number of ions in the layer;

[0225] Combined with the adsorption of intrinsic surface potential at the hydrophobic interface, hydrophobic energy The calculation formula is as follows:

[0226] (Equation 60)

[0227] In the formula, The first under the total surface potential adsorption and hydrophobic induction effect The chemical potential of liquid water molecules in a layer of water. The first under the total surface potential adsorption and hydrophobic induction effect The chemical potential of gaseous water molecules in the water layer. The first under the total surface potential adsorption and hydrophobic induction effect Chemical potential due to changes in the number of ions in the layer. The first under the influence of hydrophobic induction and total surface potential adsorption The difference between the water molecule structural energy of the layer and the first boundary condition is calculated as follows:

[0228] (Equation 61)

[0229] The total surface potential is the difference between the adsorbed ion hydration energy at the interface and the bulk phase, calculated as follows: (Equation 62)

[0230] In the formula, M is the ion hydration number. This represents the number of hydrophobically induced ions. This represents the number of ions in the bulk phase. This represents the number of adsorbed ions;

[0231] Furthermore, in this embodiment, the modified hydrophobic interactions can be superimposed and integrated with van der Waals forces and electrostatic forces to form a comprehensive interfacial force calculation result covering the depletion layer, vapor bridge, and gas-liquid interface interactions. The comprehensive interfacial force calculation result obtained by this model can directly map the adhesion and bonding characteristics between bubbles and target mineral particles in the flotation system, providing microscopic quantitative support for the macroscopic separation effect of flotation: the larger the comprehensive interfacial force value, the tighter the adhesion and bonding between bubbles and mineral particles, the stronger the structural stability of the mineral particle-bubble aggregate, and the less likely it is to detach and dissociate under the shearing and disturbance effects of the flotation flow field, which can effectively improve the flotation efficiency of the aggregate; the better the adaptability of the comprehensive interfacial force value (matching the contribution of different interface types such as depletion layer and vapor bridge), the more accurately the bubbles can adhere according to the rigidity / flexibility characteristics of the mineral interface, greatly reducing ineffective adhesion and improving the targeting of flotation. Meanwhile, the model's quantitative results on the subdivided effects of depletion layer, steam bridge, and gas-liquid interface bubble surface clearly define the contribution ratio of each force to bubble-mineral particle adhesion under different interface types, providing targeted guidance for flotation process control: for example, for minerals with flexible hydrophobic interfaces, the depletion layer effect can be strengthened through process optimization to improve overall adhesion; for minerals with rigid hydrophobic interfaces, the initial adhesion efficiency between bubbles and mineral particles can be enhanced by regulating the pulp environment to promote steam bridge formation. In summary, the comprehensive interface force calculation results of this embodiment can intuitively reflect the bubble-mineral particle adhesion effect and aggregate stability under different hydrophobic interface types. It can predict the collection efficiency and flotation recovery rate of target minerals during flotation, and also provide precise micro-quantitative basis for flotation reagent selection, pulp environment control, and process parameter optimization. This achieves directional guidance from the calculation of micro-interface forces to the macro-separation effect of flotation, ensuring the accuracy, stability, and efficiency of flotation separation. Taking the particle-interface interaction of the same type of hydrophobic interface as an example, its interaction force is:

[0232] (Equation 63)

[0233] In the formula, A is the corrected Hamark constant.

[0234] (Equation 64)

[0235] The dielectric constant of the hydrophobic surface, Let be the dielectric constant of the i-th layer of the hydrophobic interface. The refractive index of the hydrophobic surface, Let be the refractive index of the i-th layer of the hydrophobic interface, and h be Planck's constant. The incident light frequency;

[0236] In the formula, Z is the corrected double-layer interaction constant.

[0237] (Equation 65)

[0238] The effect of hydrophobicity on dielectric constant and refractive index corrects the corresponding parameters of DLVO.

[0239] For the gas-liquid interface, considering the local compaction of the gas-liquid interface, the chemical potential correction is obtained based on the change in the amount of hydrated water in the next nearest neighbor:

[0240] ; (Equation 66)

[0241] In the formula, is the standard chemical potential of the ion;

[0242] Induced ion activity:

[0243] (Equation 67)

[0244] The induction effect causes anions to accumulate at the interface, resulting in a natural negative charge at the gas-liquid interface, and the surface potential decreases as the ion activity increases.

[0245] Energy of the i-th layer at the gas-liquid interface and the bulk phase The difference is as follows:

[0246] (Equation 68)

[0247] Among them: gas-liquid interface structural energy difference The calculation formula is as follows:

[0248] (Equation 69)

[0249] Difference in ion hydration energy at the gas-liquid interface The calculation formula is as follows:

[0250] (Equation 70)

[0251] The formula for the interaction force between bubbles is:

[0252] (Equation 71)

[0253] For the separation pressure between two interfaces with different properties, a sparse horizontal plane with a spacing of D and a sphere with a radius of R are selected (the contact angles of the two interfaces are respectively...). The separation pressure caused by the corrected hydrophobicity can be categorized into two scenarios. Scenario 1: When the spacing D is large, then... The hydrophobic effect formed at the interface under boundary condition 2 is greater than The hydrophobic effect formed at this interface includes:

[0254] (Equation 72)

[0255] The effective distances between the two interfaces are as follows:

[0256] (Equation 73)

[0257] (Equation 74)

[0258] Scenario 2: When the spacing D is small, at this time The hydrophobic effect formed at the interface under boundary condition 2 is less than The hydrophobic effect formed at this interface includes:

[0259] (Equation 75)

[0260] Similarly, the weakening of hydrophobicity caused by hydrophobic-induced ions is as follows: Case 1:

[0261] (Equation 76)

[0262] Scenario 2:

[0263] (Equation 77)

[0264] Take the contact angle of the plate as The ball is Double-layer force:

[0265] (Equation 78)

[0266] Different types of hydrophobic interfaces exhibit synergistic effects of hydrophobic forces, van der Waals forces, and double-layer forces. This multi-force coupled interfacial interaction effect can effectively improve the interfacial adhesion efficiency between target minerals and bubbles in the flotation system, enhance the stability of mineral particle-bubble aggregates, reduce the interfacial adhesion energy barrier, and thus achieve efficient collection and separation of target minerals during the flotation process, optimizing the accuracy and recovery rate of flotation separation.

[0267] In summary, this simulation method for interfacial hydrophobicity based on statistical thermodynamics and modified DLVO theory first constructs a microscopic theoretical model of interfacial hydrophobic interactions. By defining the hydrogen bond structure of the bulk water and the innermost layer of the interface, and utilizing Boltzmann distribution and a two-level system, key thermodynamic parameters such as enthalpy, entropy, and chemical potential at the interface are quantitatively calculated. Furthermore, macroscopic physical quantities such as the interfacial dielectric constant and refractive index are derived through changes in hydrogen bond vibration frequencies, achieving cross-scale predictions from microscopic mechanisms to macroscopic properties. This method can provide reasonable explanations for interfacial phenomena such as gas-liquid interface densification, nanobubble formation, and vapor bridge effects. Further, in the simulation of mineral flotation effects, when ions are always present in the liquid, an ion-induced theory is established to quantitatively describe the influence of hydrophobic interactions on ion distribution, surface charge density, and potential. This allows for systematic correction of the double-layer model, van der Waals forces, and surface potential in traditional DLVO theory, enabling accurate simulation and dynamic prediction of the forces acting at different interfaces, providing reliable data support for optimizing mineral flotation processes.

[0268] This embodiment also discloses a simulation calculation system for interface hydrophobicity based on statistical thermodynamics and modified DLVO theory, such as... Figure 9 As shown, it specifically includes:

[0269] The parameter input module is configured to take flotation environment parameters, ion concentration, and ligand contact angle parameters as input.

[0270] The calculation module is configured to define the structure and energy state of water molecule ligands at the hydrophobic interface; the bulk phase of the hydrophobic interface is set as the first boundary condition, and the innermost side of the hydrophobic interface is set as the second boundary condition. Combined with the hydration of ions and water molecules, the ion distribution is calculated, the contact angle parameters of the innermost interface ligands and the interface potential that change due to ion adsorption are corrected, and the hydrophobic surface potential and double layer structure are corrected according to the ion-induced theory. Then, the macroscopic physical property parameters of the interface after hydrophobic correction are calculated.

[0271] The output module is configured to visualize and output the macroscopic physical property parameters of the hydrophobic reaction interface, reflecting the flotation effect under the obtained parameter conditions.

[0272] In this embodiment, the calculation module can also be configured to calculate the bulk ligand distribution and bulk energy of the first boundary condition based on the ion distribution and Boltzmann distribution when calculating thermodynamic parameters. Based on the corrected contact angle parameter of the innermost interface ligand, a ligand transformation model over time is constructed to calculate the second boundary condition. Through the inverted ligand transformation process and the application of boundary condition constraints, a ligand spatial evolution model is formed. Combined with the two-level system, the thermodynamic parameters at the interface are calculated. The boundary condition constraints include the energy difference between the first boundary condition and the second boundary condition, the ligand structure, and the energy cutoff.

[0273] In this embodiment, the calculation module can also be configured to calculate the corrected van der Waals force and electrostatic force using the corrected vibration frequency, dielectric constant, and refractive index, and to calculate the superposition of the corrected interface hydrophobic energy with one or more of the corrected van der Waals force and electrostatic force, in order to simulate the interaction forces between different types of hydrophobic interfaces, between interfaces and bubbles, between interfaces and particles, and between bubbles and particles.

[0274] In this embodiment, MATLAB was used to complete the interface and function design, and its input interface is as follows: Figure 7 As shown, the input modules are used to input parameters such as flotation environment parameters, ion concentration, and ligand contact angle. The environment parameters include mineral flotation process environment parameters such as temperature and pressure. The calculation module uses MATLAB to compile the formulas in the above interface hydrophobicity simulation calculation method to calculate the simulation results and achieve the effects that the above method can achieve. The output module is used to visualize the calculation results and simulation process.

[0275] This embodiment discloses a set of verification results. The initial parameters are: interface contact angle of 180°, temperature of 25°C, atmospheric pressure of 1 atm, and the number of water molecules in the layer is 10. 10 The default pH value in the solution is 7, and the model defaults to the interaction between a sphere with a radius of 100 nm and a hydrophobic interface. The pH value is related to the ion concentration. After calculation, multiple data points and visualizations can be obtained, such as the average vibrational frequency of hydrogen bonds at the hydrophobic interface. Figure 11 As shown, the covalent bond frequency is as follows Figure 12 As shown, the refractive index is as Figure 13 As shown, the surface charge density induced by hydrophobic interaction is as follows: Figure 14 As shown, the hydrophobic effect induces the surface potential as follows: Figure 15 As shown, the interfacial hydrophobicity is as follows Figure 16 As shown, the interfacial hydrophobic energy under ion-induced adsorption interface energy is as follows: Figure 17 As shown, etc.

[0276] In summary, this interface hydrophobicity simulation and calculation system based on statistical thermodynamics and modified DLVO theory, using the MATLAB platform, can convert the above theoretical models into mathematical formulas and write corresponding functions, enabling quantitative prediction of the variation of hydrophobic forces with distance, contact angle, ion concentration, and temperature in mineral particle flotation processes.

[0277] It should be noted that the interface hydrophobicity simulation calculation based on statistical thermodynamics and modified DLVO theory in this embodiment is a system corresponding to the interface hydrophobicity simulation calculation method based on statistical thermodynamics and modified DLVO theory described above. The functional modules in the system correspond to the respective steps in the prediction method. The interface hydrophobicity simulation calculation system based on statistical thermodynamics and modified DLVO theory in this embodiment can be implemented in conjunction with the interface hydrophobicity simulation calculation method based on statistical thermodynamics and modified DLVO theory. Accordingly, the relevant technical details mentioned in the interface hydrophobicity simulation calculation system based on statistical thermodynamics and modified DLVO theory in this embodiment can also be applied to the interface hydrophobicity simulation calculation method based on statistical thermodynamics and modified DLVO theory. Furthermore, the aforementioned functional modules can be fully or partially integrated into a single physical entity, or they can be physically separated. These modules can be implemented entirely in software through processing elements; they can be fully implemented in hardware; or some modules can be implemented through processing elements calling software, while others are implemented in hardware. Moreover, these modules can be fully or partially integrated together, or implemented independently. The processing element here can be an integrated circuit with signal processing capabilities. In the implementation process, some or all of the steps of the above method, or the functional modules mentioned above, can be completed by the integrated logic circuits in the hardware of the processor element or by instructions in the form of software.

[0278] This embodiment also discloses a storage medium for a simulation calculation method of interface hydrophobicity based on statistical thermodynamics and modified DLVO theory. The storage medium is used to connect to a processor and memory. The processor is used to provide control and calculation capabilities. The memory stores a computer program. When the computer program is executed by the processor, it implements the simulation calculation method of interface hydrophobicity based on statistical thermodynamics and modified DLVO theory. The storage medium is a non-volatile storage medium. The non-volatile storage medium stores an operating system and a computer program. The memory provides an environment for the operation of the operating system and the computer program.

[0279] In this embodiment, when the processor executes the interface hydrophobicity simulation calculation method based on statistical thermodynamics and modified DLVO theory, it performs the following steps:

[0280] Collect and obtain flotation environment parameters, ion concentration, and ligand contact angle parameters;

[0281] Define the ligand structure and energy state of water molecules at hydrophobic interfaces;

[0282] The bulk phase based on the hydrophobic interface is set as the first boundary condition, and the innermost side closest to the hydrophobic interface is set as the second boundary condition. Combining the hydration of ions and water molecules, the ion distribution is calculated. The contact angle parameters of the innermost interface ligands and the interface potential that change due to ion adsorption are corrected. The hydrophobic surface potential and double layer structure are corrected according to the ion-induced theory. Then, the macroscopic physical property parameters of the interface after hydrophobic correction are calculated.

[0283] The flotation effect under parameter conditions is obtained based on the macroscopic physical property parameters of the interface.

[0284] In summary, although the embodiments of this application have been described in detail above, the above embodiments are not intended to limit this application. Those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A method for simulating and calculating interfacial hydrophobicity based on statistical thermodynamics and modified DLVO theory, characterized in that, The steps include the following: Obtain flotation environment parameters, ion concentration, and ligand contact angle parameters; Define the ligand structure and energy state of water molecules at hydrophobic interfaces; The bulk phase based on the hydrophobic interface is set as the first boundary condition, and the innermost side closest to the hydrophobic interface is set as the second boundary condition. Combining the hydration of ions and water molecules, the ion distribution is calculated. The contact angle parameters of the innermost interface ligands and the interface potential that change due to ion adsorption are corrected. The hydrophobic surface potential and double layer structure are corrected according to the ion-induced theory. Then, the macroscopic physical property parameters of the interface after hydrophobic correction are calculated. The flotation effect under parameter conditions is obtained based on the macroscopic physical property parameters of the interface.

2. The method for simulating and calculating interfacial hydrophobicity based on statistical thermodynamics and modified DLVO theory according to claim 1, characterized in that, The water molecule ligand structures at the interface include monomers, dimers, cyclic structures, and cage structures; the energy states of the ligands include the interfacial hydrogen bond states, dipole-dipole interaction energies, and gas monomer energies.

3. The method for simulating and calculating interfacial hydrophobicity based on statistical thermodynamics and modified DLVO theory according to claim 1, characterized in that, The thermodynamic parameters are calculated as follows: based on the ion distribution, the bulk ligand distribution and bulk energy of the first boundary condition are calculated using the Boltzmann distribution. According to the corrected contact angle parameter of the innermost interface ligand, a ligand transformation model over time is constructed to calculate the second boundary condition. Through the inverse ligand transformation process and the application of boundary condition constraints, a ligand spatial evolution model is formed. Combined with the two-level system, the thermodynamic parameters at the interface are calculated. The boundary condition constraints include the energy difference between the first and second boundary conditions, ligand structure, and energy cutoff.

4. The method for simulating and calculating interfacial hydrophobicity based on statistical thermodynamics and modified DLVO theory according to claim 3, characterized in that, The thermodynamic parameters at the interface include hydrogen bond energy, entropy, chemical potential, density potential, and evaporation.

5. The method for simulating and calculating interfacial hydrophobicity based on statistical thermodynamics and modified DLVO theory according to claim 1, characterized in that, The macroscopic physical properties include vibration frequency, dielectric constant, refractive index, and interface hydrophobicity.

6. The method for simulating and calculating interfacial hydrophobicity based on statistical thermodynamics and modified DLVO theory according to claim 5, characterized in that, The corrected van der Waals force and electrostatic force are calculated using the corrected vibration frequency, dielectric constant, and refractive index. The corrected interfacial hydrophobic energy is superimposed with one or more of the corrected van der Waals force and electrostatic force to simulate the interaction forces between different types of hydrophobic interfaces, between interfaces and bubbles, between interfaces and particles, and between bubbles and particles.

7. A simulation and calculation system for interface hydrophobicity based on statistical thermodynamics and modified DLVO theory, characterized in that, include: The parameter input module is configured to take flotation environment parameters, ion concentration, and ligand contact angle parameters as input. The calculation module is configured to define the structure and energy state of water molecule ligands at the hydrophobic interface; the bulk phase of the hydrophobic interface is set as the first boundary condition, and the innermost side of the hydrophobic interface is set as the second boundary condition. Combined with the hydration of ions and water molecules, the ion distribution is calculated, the contact angle parameters of the innermost interface ligands and the interface potential that change due to ion adsorption are corrected, and the hydrophobic surface potential and double layer structure are corrected according to the ion-induced theory. Then, the macroscopic physical property parameters of the interface after hydrophobic correction are calculated. The output module is configured to visualize and output the macroscopic physical property parameters of the hydrophobic reaction interface, reflecting the flotation effect under the obtained parameter conditions.

8. The interface hydrophobicity simulation calculation system based on statistical thermodynamics and modified DLVO theory according to claim 7, characterized in that, The calculation module can also be configured to calculate the bulk ligand distribution and bulk energy of the first boundary condition based on the ion distribution and Boltzmann distribution when calculating thermodynamic parameters. Based on the corrected contact angle parameter of the innermost interface ligand, a ligand transformation model over time is constructed to calculate the second boundary condition. Through the inverted ligand transformation process and the application of boundary condition constraints, a ligand spatial evolution model is formed. Combined with the two-level system, the thermodynamic parameters at the interface are calculated. The boundary condition constraints include the energy difference between the first boundary condition and the second boundary condition, the ligand structure, and the energy cutoff.

9. The interface hydrophobicity simulation calculation system based on statistical thermodynamics and modified DLVO theory according to claim 7, characterized in that, The calculation module can also be configured to calculate the corrected van der Waals force and electrostatic force using the corrected vibration frequency, dielectric constant, and refractive index, and to calculate the corrected interface hydrophobic energy superimposed with one or more of the corrected van der Waals force and electrostatic force, in order to simulate the interaction forces between different types of hydrophobic interfaces, between interfaces and bubbles, between interfaces and particles, and between bubbles and particles.

10. A storage medium based on a simulation calculation method for interfacial hydrophobicity using statistical thermodynamics and modified DLVO theory, characterized in that, The storage medium is used to store computer program instructions capable of implementing the interface hydrophobicity simulation calculation method based on statistical thermodynamics and modified DLVO theory as described in any one of claims 1 to 6.

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