A prediction system and method for pressure- and temperature-controlled hydrophobic interfaces

Abstract

This invention discloses a prediction system and method for pressure- and temperature-controlled hydrophobic interfaces. The system acquires interface physicochemical parameters and water molecule microscopic state parameters through a parameter acquisition module; a molecular energy state spatial characterization module determines the hydrogen bond energy state, monomer dipole energy state, and gaseous monomer energy state of different ligand structure types based on microscopic parameters, and constructs the bulk ligand distribution; a ligand structure quantity evolution module obtains the evolution data of the ligand structure quantity as a function of interface energy by calling the hydrophobic interface ligand evolution equation; an energy and kinetic coupling determination module determines the energy equation and hydrophobic force equation of the hydrophobic interface based on the above evolution data, energy state parameters, and thermodynamic parameters; and a prediction output module, combined with environmental temperature and pressure parameters, outputs the predicted results of hydrophobic energy, hydrophobic force, and nanobubbles, and generates industrial fluid control commands. This invention achieves cross-scale correlation from microscopic energy state evolution to macroscopic property prediction, improving the accuracy of hydrophobic interface characteristic prediction.

Description

Technical Field

[0001] This invention relates to the fields of interface physical chemistry and computer simulation technology, specifically to a prediction system and method for pressure- and temperature-controlled hydrophobic interfaces. Background Technology

[0002] Interfacial hydrophobicity is a fundamental and crucial issue in interface science and engineering, essentially reflecting the structural rearrangement and energy change behavior of water molecules when approaching a solid or gas interface. Because water molecules form a highly ordered yet dynamically changing network structure through hydrogen bonds, their original hydrogen bond coordination environment is disrupted when water molecules approach a hydrophobic interface, leading to an increase in local free energy. To reduce the system's free energy, phenomena such as water displacement, density reduction, enrichment of gaseous monomers, and even the formation of nanobubbles often occur near the interface; these macroscopic manifestations are collectively referred to as hydrophobic interactions or hydrophobic effects. Hydrophobicity directly affects the wetting behavior of solid surfaces, contact angle size, bubble stability near the interface, and the adhesion probability between particles and bubbles. Therefore, it has significant theoretical and engineering value in fields such as mineral flotation, foam separation, water treatment, emulsion stability control, and functional material surface design.

[0003] In existing technologies, the analysis of hydrophobic interface behavior mainly relies on experimental measurement methods and molecular-scale simulation methods. Regarding experimental methods, changes in environmental pressure or temperature are typically used to measure parameters such as contact angle, interfacial tension, or bubble size distribution to assess changes in the hydrophobic interface. While these methods can reflect trends in interfacial behavior, they are limited by experimental conditions and testing accuracy, making it difficult to directly obtain information on changes in water structure and gaseous monomer formation near the interface at the microscopic scale. Furthermore, the experimental process is costly and complex, making it unsuitable for rapid judgment and parameter optimization during engineering operations.

[0004] In terms of molecular-scale simulation methods, existing techniques construct molecular models to calculate and analyze the arrangement, density changes, and interactions of water molecules near hydrophobic interfaces. While these methods can reflect the trends in water structure changes near interfaces to some extent, they are limited in scale and time, highly sensitive to model parameter settings, and difficult to adapt to the large-scale, multi-condition computational needs of engineering systems. Furthermore, these methods typically analyze pressure or temperature separately, making it difficult to consider the coupling effects of pressure and temperature simultaneously within the same computational flow.

[0005] In practical engineering applications, hydrophobicity is often characterized by parameters such as contact angle, interfacial tension, or empirical correction coefficients. While this approach is convenient for engineering use, it essentially relies on empirical adjustments and lacks the ability to predict changes in the hydrophobic interface state. When pressure and temperature change simultaneously, existing empirical models struggle to accurately reflect the evolution trend of hydrophobic interface properties, particularly in determining the number and average radius of nanobubbles generated near the hydrophobic interface.

[0006] Existing technologies have shown that pressure changes affect the density distribution of water near the interface and interfacial stability, while temperature changes affect the motion and interaction strength of water molecules, thus influencing the behavior of hydrophobic interfaces. However, current technologies mostly remain at the descriptive level of the effect of a single factor, either pressure or temperature, lacking methods that can simultaneously incorporate pressure and temperature into a unified calculation process. This makes it difficult to establish quantitative relationships between these two factors and the strength of hydrophobic interactions and the behavior of nanobubbles. Under actual industrial operating conditions, pressure and temperature often change simultaneously and influence each other, making it impossible for existing technologies to provide a reliable basis for operating condition selection and process control.

[0007] Furthermore, most existing methods for analyzing hydrophobic interfaces lack engineering implementation. While some methods possess a certain degree of computational completeness, their complex calculation processes and the lack of intuitive physical meaning of parameters make them difficult to translate into computational tools that can be directly used by engineering technicians. Consequently, the control of hydrophobic interfaces still relies primarily on empirical judgment and repeated experiments, making it difficult to achieve digital and refined control.

[0008] Therefore, existing technologies generally suffer from the following shortcomings: they lack a method for predicting hydrophobic interfaces that can simultaneously consider the effects of pressure and temperature within a unified computational framework; they are difficult to quantitatively describe changes from the microscopic state of the interface to macroscopic hydrophobic effects and the behavior of nanobubbles; and they lack implementation methods that can directly serve engineering calculations and parameter optimization, thus limiting the application of hydrophobic interface control technology in actual industrial processes. Summary of the Invention

[0009] The technical objective of this invention is to address the lack of existing methods for predicting hydrophobic interfaces that can simultaneously consider the effects of pressure and temperature within a unified computational framework. This makes it difficult to quantitatively describe changes in the microscopic state of the interface, leading to macroscopic hydrophobic interactions and nanobubble behavior. Furthermore, there is a lack of implementation methods that can directly serve engineering calculations and parameter optimization. This invention provides a prediction system for pressure- and temperature-controlled hydrophobic interfaces. By parameterizing the changes in the state of water molecules near the interface and incorporating environmental parameters such as pressure and temperature into a unified computational process, this invention achieves quantitative prediction of interfacial hydrophobic interactions and nanobubble behavior.

[0010] To achieve the above-mentioned technical objectives, the embodiments of the present invention adopt the following technical solutions.

[0011] In a first aspect, embodiments of the present invention provide a system for predicting hydrophobic interfaces controlled by pressure and temperature, comprising:

[0012] The parameter acquisition module is used to acquire the interfacial physicochemical parameters and the microscopic state parameters of water molecules at the hydrophobic interface to be tested; the interfacial physicochemical parameters include interface type and contact angle. Surface tension The ambient temperature T and ambient pressure P; the microscopic state parameters include the coordination number of water molecules, hydrogen bond length, covalent bond length and the average bulk bond length at the corresponding ambient temperature;

[0013] The molecular energy state spatial characterization module is used to determine the hydrogen bond energy states of water molecules with different ligand structures in water based on the coordination number, hydrogen bond length, and covalent bond length of the water molecules. Single water molecule dipole energy state Gaseous monomer energy state And the bulk ligand distribution is constructed by combining the Boltzmann distribution with the first boundary condition;

[0014] The ligand structure quantity evolution module is used to calculate the energy under the second boundary condition based on the interface type, contact angle, and surface tension. And combined with the average energy of the body phase Determine boundary constants By calling a pre-constructed hydrophobic interface ligand evolution equation, the evolution data of the number of ligand structures at the hydrophobic interface as a function of interface energy are obtained. and ;

[0015] The energy and kinetic coupling determination module is used to determine the energy equation and hydrophobic force equation of the hydrophobic interface based on the evolution data of the number of ligand structures at the hydrophobic interface as a function of interface energy, the hydrogen bond energy state of water ligands, the dipole energy state of monomeric water molecules, the energy state of gaseous monomers, the bulk ligand distribution, and the thermodynamic parameters at the interface.

[0016] The prediction output module is used to output the hydrophobic energy and hydrophobic force at the corresponding ambient temperature and pressure, based on the evolution data of the number of ligand structures at the hydrophobic interface as a function of interfacial energy, the energy equation of the hydrophobic interface, and the hydrophobic force equation. It combines the collected ambient temperature, ambient pressure, the average bond length of the bulk phase at the corresponding ambient temperature, and the reaction rate constant. It uses the Laplace equation combined with the interfacial bubble pressure, saturated vapor pressure, and ambient pressure to predict the average radius R of the nanobubbles. Based on the average hydrogen bond energy, it corrects the interfacial gas solubility, and combines the total volume of the evolved gaseous monomers and the average radius of the nanobubbles to finally calculate the number of nanobubbles at the corresponding ambient temperature and pressure. The hydrophobic energy, hydrophobic force, and the number of nanobubbles at the corresponding ambient temperature and pressure are converted into industrial fluid control commands and output to the controlled equipment.

[0017] Secondly, embodiments of the present invention also provide a method for predicting hydrophobic interfaces controlled by pressure and temperature, comprising:

[0018] Obtain the interfacial physicochemical parameters and the microscopic state parameters of water molecules at the hydrophobic interface to be tested; the interfacial physicochemical parameters include interface type and contact angle. Surface tension The ambient temperature T and ambient pressure P; the microscopic state parameters include the coordination number of water molecules, hydrogen bond length, covalent bond length and the average bulk bond length at the corresponding ambient temperature;

[0019] Based on the coordination number, hydrogen bond length, and covalent bond length of the water molecules, the hydrogen bond energy states of water molecules with different ligand structures in water were determined. Single water molecule dipole energy state Gaseous monomer energy state And the bulk ligand distribution is constructed by combining the Boltzmann distribution with the first boundary condition;

[0020] Calculate the energy under the second boundary condition based on the interface type, contact angle, and surface tension. And combined with the average energy of the body phase Determine boundary constants By calling a pre-constructed hydrophobic interface ligand evolution equation, the evolution data of the number of ligand structures at the hydrophobic interface as a function of interface energy are obtained. and ;

[0021] Based on the evolution data of the number of ligand structures at the hydrophobic interface as a function of interface energy, the hydrogen bond energy state of water ligands, the dipole energy state of monomeric water molecules, the energy state of gaseous monomers, the bulk ligand distribution, and the thermodynamic parameters at the interface, the energy equation and hydrophobic force equation of the hydrophobic interface are determined.

[0022] Based on the evolution data of the number of ligand structures at the hydrophobic interface as a function of interfacial energy, the energy equation and hydrophobic force equation of the hydrophobic interface, combined with the collected ambient temperature, ambient pressure, average bulk bond length at the corresponding ambient temperature, and reaction rate constant, the hydrophobic energy and hydrophobic force at the corresponding ambient temperature and pressure are output. The average radius R of the nanobubbles is predicted by using the Laplace equation combined with the interfacial bubble pressure, saturated vapor pressure and ambient pressure. The solubility of the interfacial gas is corrected based on the average hydrogen bond energy. Combined with the total volume of gaseous monomers generated by the evolution and the average radius of the nanobubbles, the number of nanobubbles at the corresponding ambient temperature and pressure is finally calculated. The hydrophobic energy, hydrophobic force and the number of nanobubbles at the corresponding ambient temperature and pressure are converted into industrial fluid control commands and output to the controlled equipment.

[0023] It should be understood that the summary section is not intended to identify key or essential features of the embodiments of this disclosure, nor is it intended to limit the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description.

[0024] Compared with existing technologies, the pressure and temperature-controlled hydrophobic interface prediction system provided by this invention achieves the following beneficial technical effects: Real-time acquisition of interface physicochemical parameters and water molecule microstate parameters; establishment of a complete energy system including ligand hydrogen bonds, dipole energies, and gaseous monomer energies using a water molecule energy state determination module, fundamentally solving the technical problem of inaccurate energy characterization of hydrophobic interfaces from a microscopic physical perspective; Dynamic tracking of water molecule configuration transformation using a preset evolution equation in conjunction with a ligand structure quantity evolution module, enabling the system to lock the ligand quantity evolution law at the interface in real time; Precise quantification of hydrophobic interface energy changes and direct output of hydrophobic force values ​​by coupling microscopic evolution data with thermodynamic parameters, providing core data support for cross-scale mechanical prediction; Finally, the nanobubble average radius and quantity prediction module, combined with environmental temperature and pressure parameters and bulk average bond length, achieves quantitative monitoring and accurate prediction of the nucleation state of nanobubbles at hydrophobic interfaces, significantly improving the perception dimension and control accuracy of hydrophobic properties in complex industrial environments.

[0025] The method for predicting hydrophobic interfaces controlled by pressure and temperature provided in this invention has the same beneficial technical effects, and will not be elaborated further. Attached Figure Description

[0026] The accompanying drawings described herein are for illustrative purposes only and are not intended to limit the scope of the invention in any way. Furthermore, the shapes and proportions of the components in the drawings are merely illustrative to aid in understanding the invention and are not intended to specifically limit the shapes and proportions of the components. Those skilled in the art, guided by the teachings of this invention, can select various possible shapes and proportions to implement the invention according to specific circumstances. In the drawings:

[0027] Figure 1 A schematic diagram of a pressure and temperature-controlled hydrophobic interface prediction system provided for an embodiment;

[0028] Figure 2 This is a schematic diagram illustrating the relationship between the change in the number of gaseous monomers at the hydrophobic interface and the pressure in the embodiment.

[0029] Figure 3 This is a schematic diagram of the density at the interface in the embodiment;

[0030] Figure 4 This is a schematic diagram illustrating the relationship between hydrophobic energy and pressure in the embodiment;

[0031] Figure 5This is a schematic diagram illustrating the relationship between the number of air molecules and pressure in the embodiment;

[0032] Figure 6 This is a schematic diagram showing the bubble radius under different pressures in the embodiment;

[0033] Figure 7 This is a schematic diagram illustrating the relationship between hydrophobic energy and temperature in the embodiments.

[0034] Figure 8 This is a schematic diagram showing the effect of temperature on bubble radius in the example. Detailed Implementation

[0035] To enable those skilled in the art to better understand the technical solutions of this invention, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this invention.

[0036] Example 1: A predictive system for hydrophobic interfaces regulated by pressure and temperature, such as... Figure 1 As shown, it includes a parameter acquisition module, a molecular energy state spatial characterization module, a ligand structure quantity evolution module, an energy and dynamics coupling determination module, and a prediction output module.

[0037] The parameter acquisition module is used to acquire the interfacial physicochemical parameters and the microscopic state parameters of water molecules at the hydrophobic interface to be tested; the interfacial physicochemical parameters include interface type and contact angle. Surface tension The ambient temperature T and ambient pressure P; the microscopic state parameters include the coordination number of water molecules, hydrogen bond length, covalent bond length and the average bulk bond length at the corresponding ambient temperature.

[0038] The molecular energy state spatial characterization module is used to determine the hydrogen bond energy states of water molecules with different ligand structures based on the coordination number, hydrogen bond length, and covalent bond length of water molecules. Single water molecule dipole energy state Gaseous monomer energy state And through the Boltzmann distribution, combined with the first boundary condition, the bulk phase ligand distribution is constructed (corresponding to formulas 1-4).

[0039] The ligand structure number evolution module is used to calculate the energy under the second boundary condition based on the interface type, contact angle, and surface tension. And combined with the average energy of the body phase Determine boundary constants By calling a pre-constructed hydrophobic interface ligand evolution equation, the evolution data of the number of ligand structures at the hydrophobic interface as a function of interface energy are obtained. and (Corresponding formula 5-14).

[0040] The energy and kinetic coupling determination module is used to determine the energy equation and hydrophobic force equation (corresponding to formulas 8-11 and 25) of the hydrophobic interface based on the evolution data of the number of ligand structures at the hydrophobic interface as a function of interface energy, hydrogen bond energy states of water ligands, dipole energy states of monomeric water molecules, energy states of gaseous monomers, bulk ligand distribution, and thermodynamic parameters at the interface.

[0041] The prediction output module is used to calculate the number of ligand structures at the hydrophobic interface based on the evolution data of the number of ligand structures at the hydrophobic interface as a function of the interfacial energy, the energy equation of the hydrophobic interface, and the hydrophobic force equation. It combines the collected ambient temperature, ambient pressure, the average bond length of the bulk phase at the corresponding ambient temperature, and the reaction rate constant to output the hydrophobic energy and hydrophobic force at the corresponding ambient temperature and pressure. It uses the Laplace equation combined with the interfacial bubble pressure, saturated vapor pressure, and ambient pressure to predict the average radius R of the nanobubbles (corresponding to formulas 15-21). Based on the average hydrogen bond energy, it corrects the interfacial gas solubility and combines the total volume of the evolved gaseous monomers and the average radius of the nanobubbles to finally calculate the number of nanobubbles at the corresponding ambient temperature and pressure (corresponding to formulas 22-24). The hydrophobic energy, hydrophobic force, and the number of nanobubbles at the corresponding ambient temperature and pressure are converted into industrial fluid control commands and output to the controlled equipment.

[0042] Example 2: Based on the same inventive concept as the pressure and temperature-controlled hydrophobic interface prediction system provided in the above examples, this embodiment of the invention also provides a method for predicting pressure and temperature-controlled hydrophobic interfaces, including:

[0043] Obtain the interfacial physicochemical parameters and the microscopic state parameters of water molecules at the hydrophobic interface to be tested; the interfacial physicochemical parameters include interface type and contact angle. Surface tension Ambient temperature T and ambient pressure P; microscopic state parameters include water molecule coordination number, hydrogen bond length, covalent bond length and the average bulk bond length at the corresponding ambient temperature;

[0044] Based on the coordination number, hydrogen bond length, and covalent bond length of water molecules, the hydrogen bond energy states of water ligands with different ligand structures in water were determined. Single water molecule dipole energy state Gaseous monomer energy state And through the Boltzmann distribution, combined with the first boundary condition, the bulk phase ligand distribution is constructed (corresponding to formulas 1-4).

[0045] Calculate the energy under the second boundary condition based on the interface type, contact angle, and surface tension. And combined with the average energy of the body phase Determine boundary constants By calling a pre-constructed hydrophobic interface ligand evolution equation, the evolution data of the number of ligand structures at the hydrophobic interface as a function of interface energy are obtained. and (Corresponding formula 5-14);

[0046] Based on the evolution data of the number of ligand structures at the hydrophobic interface as a function of interface energy, the hydrogen bond energy state of water ligands, the dipole energy state of monomeric water molecules, the energy state of gaseous monomers, the bulk ligand distribution, and the thermodynamic parameters at the interface, the energy equation and hydrophobic force equation of the hydrophobic interface are determined (corresponding to formulas 8-11 and 25).

[0047] Based on the evolution data of the number of ligand structures at the hydrophobic interface as a function of interfacial energy, the energy equation of the hydrophobic interface, and the hydrophobic force equation, combined with the collected ambient temperature, ambient pressure, average bulk bond length at the corresponding ambient temperature, and reaction rate constant, the hydrophobic energy and hydrophobic force at the corresponding ambient temperature and pressure are output. The average radius R of the nanobubbles is predicted using the Laplace equation combined with the interfacial bubble pressure, saturated vapor pressure, and ambient pressure (corresponding to formulas 15-21). Based on the average hydrogen bond energy to correct the interfacial gas solubility, combined with the total volume of gaseous monomers generated and the average radius of the nanobubbles, the number of nanobubbles at the corresponding ambient temperature and pressure is finally calculated (corresponding to formulas 22-24). The hydrophobic energy, hydrophobic force, and the number of nanobubbles at the corresponding ambient temperature and pressure are converted into industrial fluid control commands and output to the controlled equipment.

[0048] Low-energy hydrophobic interfaces are more prone to the formation of weakened hydrogen-bonded cyclic water molecules and poorly coordinated water molecules. Therefore, in some embodiments, the existence forms of water molecule ligands (i.e., ligand structure types, such as six ligand structure types) are classified as: monomer, dimer, trimer, tetramer, pentamer, and hexamer, among which the trimer, tetramer, and pentamer are cyclic structures, and the hexamer is a cage-like structure.

[0049] In this embodiment, the molecular energy state spatial characterization module is configured to perform the following specific steps when determining the hydrogen bond energy state of the water molecule ligand: acquiring the microscopic charge, dipole moment, hydrogen bond angle, and dielectric constant of the water molecule; establishing an energy state contribution function for the hydrogen bond length based on the interaction law between the charge and the dipole in the electric field; substituting the real-time acquired microscopic state parameters into the energy state contribution function (e.g., Equation 1), and obtaining the hydrogen bond energy state of ligand j by calculating the electrostatic interaction energy between the charge center and the dipole moment under a specific orientation. :

[0050] (Equation 1);

[0051] in, The microscopic charge of a water molecule. =0.24e=0.4×10 -19 (Unit: C), water molecule dipole moment =5×10 -30 (Unit: C·m), hydrogen bond angle dielectric constant , For hydrogen bond length, is the vacuum permittivity.

[0052] In this embodiment, the molecular energy state spatial characterization module calculates the dipole interaction based on the dipole moment and covalent bond length of the monomeric water molecule to determine the dipole energy state of the monomeric water molecule, as expressed by:

[0053] (Equation 2);

[0054] in, The static dielectric constant of water is the dipole energy state of a single water molecule. Vacuum static dielectric constant Incident light frequency water refractive index Vacuum refractive index water molecule radius h is Planck's constant, and the intermolecular distance is... , where k is the Boltzmann constant and T is the temperature.

[0055] The molecular energy state spatial characterization module calculates the energy states of gaseous monomers based on the Boltzmann constant, using the following formula:

[0056] (Equation 3);

[0057] In the formula, η is the translational kinetic energy of the gas, which is the energy state of a gaseous single unit; k is the Boltzmann constant, and T is the temperature.

[0058] The molecular energy state spatial characterization module calculates the average energy state of water molecules based on different water molecule ligand structures and the average hydrogen bond length in the bulk phase. Based on the Boltzmann distribution and combined with the first boundary condition, it obtains the bulk phase ligand distribution.

[0059] In this embodiment, 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, key thermodynamic parameters such as enthalpy, entropy, and chemical potential at the interface are quantitatively calculated.

[0060] The molecular energy state spatial characterization module establishes the bulk ligand distribution of the first boundary condition through the Boltzmann distribution, and the calculation formula is as follows:

[0061] (Equation 4);

[0062] in, For the hydrogen bond energy state of ligand j, This represents the total number of water molecule layers in the bulk phase. Let n be the average energy of the bulk phase, n be the coordination number of water molecules, k be the Boltzmann constant, and T be the temperature. The number of ligands in the bulk water molecule layer j.

[0063] In some embodiments, the ligand structure number evolution module is also configured to perform the following steps: acquire the interface physicochemical parameters output by the parameter acquisition module, combine them with the second boundary condition, determine the energy of the second boundary condition, and determine the energy difference between the first boundary condition and the second boundary condition, so as to construct an energy distribution gradient that varies with the number of water molecule layers i at the interface, i.e., the interface distance x (corresponding to the following formulas 1-11).

[0064] The hydrogen bond energy state of ligand j output by calling the molecular energy state space characterization module and gaseous monomer energy state By combining the ambient temperature T and energy distribution gradient, the conversion probability and conversion rate constant between different ligand configurations are determined (corresponding to Equation 18 below); based on the second boundary condition energy, the cutoff point of the hydrophobic energy after entropy compensation is identified, and the boundary constants in the hydrophobic interface ligand evolution equation are calculated accordingly. (Corresponding to Formula 6 below).

[0065] In the embodiment, the conversion rate constant and the boundary constant are substituted into the hydrophobic interface ligand evolution equation, and the energy difference is used as the spatial evolution driving force. An integral operation is performed along the interface normal direction to solve the evolution data of the number of ligand structures at the hydrophobic interface as a function of the interface energy (i.e., the number of ligands after evolution at each level of the interface, corresponding to the following formula 14).

[0066] In this embodiment, the ligand structure number evolution module obtains the interface physicochemical parameters output by the parameter acquisition module, and combines them with the second boundary condition to determine the energy of the second boundary condition using formula (5). The calculation formula is as follows:

[0067] (Equation 5);

[0068] In the formula, The cohesive energy of bulk water molecules, The cohesive energy of water molecules under the second boundary condition. It is the adhesion energy of the interaction between liquid molecules and solid surfaces. The surface tension is the second boundary condition.

[0069] Energy difference between the first boundary condition and the second boundary condition for: (Equation 6);

[0070] in, ; For total interface energy The preset maximum value, The volume average energy; in the embodiments, it can be based on... Determine boundary constants .

[0071] Thermodynamic parameters at the interface include, but are not limited to, parameters such as hydrogen bond energy, entropy, chemical potential, density, and evaporation.

[0072] The energy equations for the hydrophobic interface (used for calculating the interface energy) determined by the energy and dynamics coupling determination module are as follows: Equations 7 to 12:

[0073] (Equation 7);

[0074] in, For the total interface energy, For hydrogen bond energy, For the chemical potential of liquid ligands, For the chemical potential of gaseous monomers, The entropy at the interface. The energy difference is for gaseous monomers.

[0075] In this embodiment, the method for determining the hydrogen bond energy is as follows:

[0076] (Equation 8);

[0077] in, For the first The number of gaseous water molecules transformed from water molecules in the layer. For the first Water molecules ligand number, for Ligand hydrogen bond energy state.

[0078] Entropy at the interface The calculation formula is as follows:

[0079] (Equation 9);

[0080] 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. for Ligand thermodynamic concentration; This represents the entropy change at the interface. This represents the thermodynamic concentration of gaseous monomers in the bulk phase. For the interface Water molecules ligands, For the interface Thermodynamic concentration of gaseous monomers. In the body phase Thermodynamic concentration of ligands.

[0081] The chemical potential of the liquid ligand at the interface is calculated as follows (Equations 8-11 below are supplements to Equation 7):

[0082] (Equation 10);

[0083] In the formula, For the interface In the layer Chemical potential of ligands.

[0084] for Standard chemical potential of ligands;

[0085] (Equation 11);

[0086] In the formula, The standard chemical potential of the gaseous monomer; Let be the chemical potential of the gaseous monomer in the i-th layer of the hydrophobic interface.

[0087] The formula for calculating the density at the interface is as follows:

[0088] (Equation 12);

[0089] In the formula, The total number of water molecules in the i-th layer. Let be the water density of the i-th layer at the hydrophobic interface. The mass of a water molecule. The volume of a water molecule in a gaseous monomer. The volume of a water molecule in the liquid j-ligand. This represents the number of liquid ligands.

[0090] To achieve cross-scale prediction from microscopic mechanisms to macroscopic properties, the macroscopic physical property parameters of the interface are obtained, and the calculation formula for the evolved interface ligand distribution is as follows:

[0091] (Equation 13);

[0092] In the formula, is the total number of water molecules in the i-th layer, which is a constant (the key point of Formula 13 is the distribution of the number of different water molecule structures in the i-th layer on the right side of the formula, while the left side is only the total number of water molecules in the i-th layer of the interface, which is a fixed value). For the first The number of liquid monomers in the water layer;

[0093] The pre-constructed evolution equation for hydrophobic interface ligands is as follows:

[0094] (Equation 14);

[0095] In the formula, Let j be the number of ligands in the i-th layer of water molecules. The boundary constant 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 be the conversion rate constant for the transformation of ligand j to other ligands. denoted as , representing the conversion rate constant from other ligands to ligand j; x represents the distance in the evolution of the interfacial ligand structure, in nanometers; as the hydrophobic interface moves further away, the destructive effect of hydrophobic interactions on the hydrogen bond structure weakens, and the interfacial hydrogen bond structure gradually strengthens as it moves further away from the hydrophobic interface, generating an energy gradient. The number of interfacial water molecule layers i corresponding to the corresponding hydrogen bond structure increases, i.e., the interfacial distance changes. x and i can be interconverted, such as the distance corresponding to the number of water molecule layers multiplied by the layer thickness, which are different manifestations of the same parameter. 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.

[0096] In the study of pressure dependence, this invention establishes a quantitative relationship between pressure and the concentration of gaseous monomers at the interface by deriving an accurate gas-liquid equilibrium equation. The dynamic equilibrium equation for gaseous monomers is as follows:

[0097] (Equation 15);

[0098] , (Formula 16;

[0099] (Equation 17);

[0100] In the formula, This represents the probability that gaseous water molecules collide with the water surface and are absorbed. Standard atmospheric pressure The mass of a water molecule. This represents the number of gaseous water molecules after a pressure change. This represents the number of ligands in water molecules j after a pressure change. The number of water molecules that are transformed between gaseous and liquid monomers. This refers to the number of gaseous monomers. The difference in the number of gaseous water molecules caused by the pressure change; They are different; the former refers to the number of gaseous monomers affected by pressure, while the latter refers to the gaseous monomers generated by hydrophobic interactions. This refers to the number of liquid ligands. This represents the energy difference of interfacial water molecules caused by changes in ambient pressure. This set of dynamic equilibrium equations for gaseous monomers calculates the effect of pressure on the number of interfacial ligands; all formulas related to ligand number in this paper can be applied to this equation.

[0101] In the study of temperature dependence, this invention innovatively reconstructs the ligand energy distribution and conversion probability model for boundary conditions and transition regions. Based on the Boltzmann distribution of hydrogen bond energy states in the bulk ligand structure, thermodynamic analysis shows that increasing temperature significantly reduces the cohesive energy of water molecules, while the reaction rate constant remains constant.

[0102] (Equation 18);

[0103] In the formula, The energy difference before and after the reaction is obtained from the energy difference of the hydrogen bond between the two ligands. The combined effect of these two competing factors ultimately leads to the overall weakening of the hydrophobic effect.

[0104] The prediction output module is based on the theory of interfacial gas monomer formation. This module uses the Laplace equation to determine the average bubble radius R, as shown in the following formula:

[0105] (Equation 19);

[0106] (Equation 20);

[0107] (Equation 21);

[0108] In the formula, The gas pressure inside the surface-deposited bubbles. It is the saturated vapor pressure. The surface tension of the water at the interface; It is half of the average hydrogen bond energy of the i-th layer. The average number of hydrogen bonds in a water molecule for ligand j; Standard atmospheric pressure.

[0109] Calculated gas volume:

[0110] (Equation 22);

[0111] In the formula, For an ideal gas volume, For the gas in the interface, Gas in the interface The solubility of , R is the predicted average radius of the nanobubbles, and N is the total number of water molecules in the i-th layer of the interface.

[0112] Gas in the interface solubility for:

[0113] (Equation 23);

[0114] 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.

[0115] By combining gas volume and bubble radius, the predicted number of interfacial nanobubbles can be obtained. :

[0116] (Equation 24);

[0117] In the formula, Let R be the volume of an ideal gas molecule, and R be the average radius of the nanobubble. R can be the radius of the collected particles or the radius of the nanobubble calculated using Equation 19.

[0118] The hydrophobic equation of the interface is: (Equation 25);

[0119] This invention can directly obtain the predicted average radius and number of nanobubbles near hydrophobic interfaces under given pressure and temperature conditions. Compared with existing technologies that mainly rely on experimental observation or empirical estimation, this invention incorporates the effects of pressure and temperature on the interface state into the calculation through a unified calculation process, enabling quantitative characterization of the generation and size changes of nanobubbles, thereby significantly improving the accuracy and consistency of the predicted average radius and number of nanobubbles.

[0120] Secondly, this invention can simultaneously obtain the calculated results of the hydrophobic interface interaction strength, thereby enabling the prediction of the magnitude and trend of hydrophobic force. In existing technologies, hydrophobic force is usually obtained indirectly through experiments, which is sensitive to test conditions, has poor repeatability, and is difficult to quickly compare and predict under different operating conditions. This invention unifies the processing of changes in the hydrophobic interface state and changes in interface energy, so that the determination of hydrophobic force no longer depends on the results of a single experiment, but is jointly determined by environmental parameters and interface state, thereby improving the stability and comparability of hydrophobic force results under different pressure and temperature conditions.

[0121] Furthermore, the reason why this invention obtains more accurate nanobubble characteristic parameters and hydrophobicity results is that its technical solution does not correct a single interface parameter, but considers the influence of pressure and temperature on the interface state. This avoids the error amplification problem caused by step-by-step correction, empirical superposition, or parameter fragmentation in the prior art, making the final calculation results closer to the interface behavior under actual working conditions.

[0122] Furthermore, in engineering applications, the method of this invention can quickly output key interface parameters such as the average radius, number, and hydrophobicity of nanobubbles by inputting pressure and temperature parameters that can be directly obtained in the industrial process. This reduces the reliance on repeated experimental debugging, improves the efficiency of process parameter optimization, and reduces engineering operating costs. It has the advantages of being easy to operate and having a wide range of applications.

[0123] In summary, this invention achieves accurate prediction of the average radius, number, and hydrophobic force of nanobubbles at hydrophobic interfaces through its technical solution. It overcomes the problems of difficulty in determining relevant parameters, large dispersion of results, and insufficient engineering applicability in existing technologies, and can meet the requirements of accuracy, stability, and predictability in actual industrial processes.

[0124] In this embodiment of the invention, the initial parameters collected are: an interface contact angle of 180°, a temperature of 25°C, an atmospheric pressure of 1 atm, and a water molecule layer with a molecular number of 10. 10 The default pH value of the solution is 7, and the default model is the interaction between a 100nm radius sphere and a hydrophobic interface. The software parameters and the interaction model can be adjusted according to actual needs.

[0125] like Figures 2-6As shown, hydrophobic interactions weaken the interfacial ligand structure, resulting in a large number of gaseous monomers. This quantity increases with increasing interfacial contact angle (i.e., enhanced hydrophobicity). Compared to the more stable liquid water ligands, gaseous monomers are more sensitive to pressure changes. Based on this, this invention explores the effect of increased pressure on the reduction of gaseous monomer quantity and further predicts that the interconversion between gaseous monomers and liquid ligands leads to enhanced interfacial ligand structure and weakened interfacial hydrophobicity. This also results in a reduction in the size of interfacial nanobubbles due to the constraint of enhanced interfacial hydrogen bond energy. Figure 7 , Figure 8 As shown, increasing temperature reduces the ligand structure of liquid water, increases the reaction rate constant, and accelerates the evolution of interfacial ligands. The range of hydrophobic interfacial ligand evolution decreases accordingly. The reduction in the size of interfacial nanobubbles due to increased temperature is reflected in the decreased constraint of the weakened hydrogen bond energy states, leading to an increase in bubble radius. In summary, this invention systematically elucidates the mechanism by which pressure and temperature regulate the stability of interfacial nanobubbles from the perspective of interfacial molecular structure evolution.

[0126] In some embodiments, the pressure and temperature-controlled hydrophobic interface prediction system provided by the present invention is implemented by a computer program. The computer program runs on a conventional computer device, which includes at least a processor, a memory, and input / output devices. The processor is used to execute computer program instructions stored in the memory, the memory is used to store parameters required by the theoretical model, intermediate calculation results, and final calculation results, and the parameter acquisition module and prediction output module are used to realize user parameter input and display and save calculation results.

[0127] This invention does not rely on special modifications to the computer hardware structure, but rather achieves the modeling and calculation of the hydrophobic behavior of complex interfaces through software.

[0128] In this embodiment, the user first initiates the pressure and temperature-controlled hydrophobic interface prediction system via a graphical user interface. After system startup, an initial interface is displayed, guiding the user through the parameter input process. At this stage, the user selects the interface type to be analyzed, such as a solid-liquid interface, a bubble-liquid interface, or a particle-bubble interface. Different interface types correspond to different boundary condition settings, but all are processed based on the unified statistical thermodynamic theoretical framework of this invention.

[0129] After selecting the interface type, the system enters the parameter acquisition module (parameter acquisition interface), where the user inputs or confirms the required environmental and model parameters.

[0130] In a preferred embodiment, the environmental parameters include temperature, pressure, and chemical environmental parameters of the solution. Temperature can be expressed in degrees Celsius or Kelvin, and pressure can be expressed in standard atmospheric pressure. Model parameters include parameters describing the water molecule layer near the interface, estimates of the bulk water molecule distribution, and feature size parameters for interface geometry modeling.

[0131] In some implementations, to facilitate demonstration and verification of the model's rationality, the interface contact angle is selected as 180 degrees, the ambient temperature as 25 degrees Celsius, the ambient pressure as one standard atmosphere, and the total number of water molecule layers as being on the order of ten to the power of ten. It is also assumed that the interface is an ideal hydrophobic surface with a certain radius of curvature. The above parameters are merely examples; users can adjust the parameters according to actual research or engineering needs.

[0132] After parameter input and confirmation, the system enters the calculation execution phase. At this point, the program first calculates the occupancy probability of bulk water molecules in different ligand energy states using the Boltzmann distribution based on the input ambient temperature parameters, thus obtaining the initial distribution of the number of various ligand structures within the bulk region. Subsequently, based on the selected interface type and interface boundary conditions, the program constructs a ligand evolution model from the bulk phase to the interface region. By deriving the interface ligand evolution equation, it calculates the change in the number of water molecules transforming from high-coordination structures to low-coordination structures in different spatial layers. This process achieves a quantitative description of the degree of weakening of water molecule structures near the interface.

[0133] After completing the interfacial ligand evolution calculations, the program further incorporates a pressure-based model. Based on the input environmental pressure parameters, the program utilizes the dynamic equilibrium equation between gaseous monomers and liquid ligands to calculate the amount of gaseous monomers generated near the interface and the corresponding changes in liquid ligands under the current pressure conditions. Through this calculation process, quantitative results can be obtained regarding the change of interfacial gaseous monomers with pressure, thus reflecting the influence of pressure changes on interfacial hydrophobicity. This step is one of the key features that distinguishes this invention from traditional empirical models, ensuring that hydrophobicity is no longer a single empirical parameter but is determined by calculable thermodynamic quantities.

[0134] After the pressure response calculation is completed, the program further incorporates the effect of temperature into the overall model. Based on the input ambient temperature parameters, the program recalculates the ligand reaction rate constant, thereby correcting the number of bulk and interfacial ligand structures. By simultaneously considering the influence of temperature on hydrogen bond energy and entropy contributions, the program can reflect the dual effect of increased temperature leading to weakened hydrophobic interactions but increased gaseous monomer formation within the same calculation flow. This process provides fundamental data for subsequent predictions of hydrophobic energy and nanobubble behavior.

[0135] After completing the calculations of the aforementioned fundamental physical quantities, the program proceeds to the hydrophobic interaction energy calculation stage. Based on the hydrophobic free energy model constructed according to this invention, the program comprehensively calculates multiple contributing factors, including structural energy difference, chemical potential, mixing entropy, and translational entropy, to obtain numerical results of the interfacial hydrophobic energy under the current environmental pressure and temperature conditions. This hydrophobic interaction energy can be directly used to analyze interfacial stability and can also serve as an important basis for further calculations of contact angle variation trends.

[0136] In a preferred embodiment, the program further predicts the trend of the interfacial contact angle based on the calculated interfacial hydrophobic interaction energy and interfacial structural parameters. By combining the hydrophobic energy with the interfacial tension relationship, a quantitative trend of the contact angle changing with ambient pressure and temperature can be obtained. This prediction result can be directly compared with experimental measurement results to verify the rationality of the model.

[0137] After completing the calculations related to hydrophobic energy and contact angle, the program further enters the nanobubble prediction stage. Using the previously calculated amount of gaseous monomers generated at the interface, and combining it with the Laplace equation, the program calculates the average radius and number of nanobubbles near the interface. Through this step, the program can predict the size variation trend of nanobubbles under different ambient temperatures and pressures, thereby explaining the nucleation and stabilization behavior of nanobubbles near the hydrophobic interface.

[0138] After completing the entire calculation process, the prediction output module can output the calculation results to the results display interface. In this module, users can intuitively view the distribution of interface ligand structures, the curve of hydrophobic interaction energy changing with parameters, and the changes in the number and radius of nanobubbles, etc. The results can be displayed in either graphical or numerical table format to meet the needs of different users. Users can also use the software's save function to store the calculation results as image files or data files for subsequent analysis or report writing.

[0139] In some embodiments, the system also includes a data interaction module for uploading the nanobubble prediction results to a remote monitoring platform in real time via a communication link, so that the remote monitoring platform can generate online monitoring reports or early warning information for the hydrophobic interface state.

[0140] In some embodiments, the parameter acquisition module includes: a spectral analysis unit for acquiring the vibrational energy spectrum of water molecules using a Raman spectrometer or an infrared spectrometer, and extracting the coordination number, hydrogen bond length, and covalent bond length of water molecules based on the peak position and full width at half maximum (FWHM); and a physical sensing unit for acquiring ambient pressure and ambient temperature in real time using a pressure sensor and a thermistor, and acquiring the real-time contact angle of the hydrophobic interface using an optical image recognition component.

[0141] In this embodiment, mineral flotation is selected as the application scenario. During flotation, the adhesion behavior between the pulp and bubbles is affected by the hydrophobicity of the interface and the bubble size distribution. The operating pressure and pulp temperature in the flotation cell change with the operating conditions, resulting in unstable bubble behavior.

[0142] In this embodiment, environmental parameters during the operation of the flotation cell are first collected, including the operating pressure inside the flotation cell, the pulp temperature, and the mineral surface parameters. These parameters are then input into the hydrophobic interface prediction method of this invention, and the calculation system automatically completes the interface state calculation.

[0143] Based on the input pressure and temperature parameters, the system outputs predicted results of the average radius and number of nanobubbles near the hydrophobic interface under the current operating conditions. When the prediction results show that the average radius of the nanobubbles is too large or the number is insufficient, the operator optimizes the flotation conditions by adjusting the gas supply pressure or operating temperature. When the prediction results show that the number of bubbles is too large or the interface stability is insufficient, the operating parameters are adjusted accordingly to bring the bubble behavior back to a suitable range. By applying the method of this invention, the size and number of bubbles can be predicted in advance during the flotation process, reducing the number of process adjustments and improving the stability of the flotation process and the mineral recovery efficiency.

[0144] As can be seen from the above embodiments, the interface hydrophobicity modeling and calculation method provided by the present invention can systematically predict the hydrophobic behavior of different interface systems under different temperature and pressure conditions without conducting a large number of experiments. This method not only has clear physical meaning, but also a clear calculation process and controllable parameters. Those skilled in the art can implement the technical solution of the present invention on a computer device based solely on the content disclosed in this specification, without any creative effort.

[0145] In summary, this invention provides a complete technical solution that can quantitatively describe the effects of pressure and temperature on interfacial hydrophobicity by combining statistical thermodynamics theory with computer simulation technology. This not only deepens the understanding of the hydrophobic mechanism in theory, but also provides a reliable technical means for interface control and process optimization in engineering applications.

[0146] The systems, devices, modules, or units described in the above embodiments can be implemented by computer chips or physical entities, or by products with certain functions. A typical implementation device is a computer. Specifically, the computer can be, for example, a personal computer, a laptop computer, or a tablet computer, or any combination of these devices.

[0147] The above provides a detailed description of the prediction system and method for pressure and temperature-controlled hydrophobic interfaces provided by the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The above description of the embodiments is only for the purpose of helping to understand the concept of the present invention and should not be construed as limiting the scope of protection of the present invention.

Claims

1. A system for predicting hydrophobic interfaces controlled by pressure and temperature, characterized in that, include: The parameter acquisition module is used to acquire the interfacial physicochemical parameters and the microscopic state parameters of water molecules of the hydrophobic interface to be tested. The interfacial physicochemical parameters include interface type, contact angle, surface tension, ambient temperature and ambient pressure. The microscopic state parameters include water molecule coordination number, hydrogen bond length, covalent bond length and the average bulk bond length at the corresponding ambient temperature. The molecular energy state spatial characterization module is used to determine the hydrogen bond energy state of water ligands of different ligand structure types in water, the dipole energy state of monomeric water molecules, and the energy state of gaseous monomeric water molecules based on the coordination number, hydrogen bond length, and covalent bond length of the water molecules, and to construct the bulk phase ligand distribution by means of Boltzmann distribution and combined with the first boundary condition. The ligand structure number evolution module is used to calculate the energy under the second boundary condition based on the interface type, contact angle and surface tension, and determine the boundary constant by combining the bulk average energy. It calls the pre-constructed hydrophobic interface ligand evolution equation to obtain the evolution data of the number of ligand structures at the hydrophobic interface as a function of the interface energy. The energy and kinetic coupling determination module is used to determine the energy equation and hydrophobic force equation of the hydrophobic interface based on the evolution data of the number of ligand structures at the hydrophobic interface as a function of interface energy, the hydrogen bond energy state of water ligands, the dipole energy state of monomeric water molecules, the energy state of gaseous monomers, the bulk ligand distribution, and the thermodynamic parameters at the interface. The prediction output module is used to output the hydrophobic energy and hydrophobic force at the corresponding ambient temperature and pressure based on the evolution data of the number of ligand structures at the hydrophobic interface as a function of the interfacial energy, the energy equation of the hydrophobic interface, and the hydrophobic force equation. It combines the collected ambient temperature, ambient pressure, the average bond length of the bulk phase at the corresponding ambient temperature, and the reaction rate constant. It uses the Laplace equation combined with the interfacial bubble pressure, saturated vapor pressure, and ambient pressure to predict the average radius of nanobubbles. Based on the average hydrogen bond energy, it corrects the interfacial gas solubility, combines the total volume of the evolved gaseous monomers and the average radius of the nanobubbles, and finally calculates the number of nanobubbles at the corresponding ambient temperature and pressure. Based on the hydrophobic energy, hydrophobic force, and the number of nanobubbles at the corresponding ambient temperature and pressure, it converts them into industrial fluid control commands and outputs them to the controlled equipment.

2. The prediction system according to claim 1, characterized in that, The molecular energy state spatial characterization module is configured to perform the following specific steps when determining the hydrogen bond energy state of water molecule ligands: acquiring the microscopic charge, dipole moment, hydrogen bond angle, and dielectric constant of the water molecule; establishing an energy state contribution function regarding the hydrogen bond length based on the interaction law between charge and dipole in an electric field; substituting the real-time acquired microscopic state parameters into the energy state contribution function, and obtaining the hydrogen bond energy state of ligand j by calculating the electrostatic interaction energy between the charge center and the dipole moment under a specific orientation. .

3. The prediction system according to claim 1, characterized in that, The ligand structure quantity evolution module is configured to perform the following steps: The interface physicochemical parameters output by the parameter acquisition module are obtained, and the energy of the second boundary condition is determined in combination with the second boundary condition. The energy difference between the first boundary condition and the second boundary condition is also determined to construct the energy distribution gradient that varies with the interface distance x. The hydrogen bond energy state of ligand j output by the molecular energy state space characterization module and gaseous monomer energy state By combining the ambient temperature T and the energy distribution gradient, the conversion probability and conversion rate constant between different ligand configurations are determined respectively. Based on the energy under the second boundary condition, the cutoff point of hydrophobic energy after entropy compensation is identified, and the boundary constant in the hydrophobic interface ligand evolution equation is calculated accordingly. Substitute the conversion rate constant and boundary constant into the hydrophobic interface ligand evolution equation, use the energy difference as the spatial evolution driving force, perform integral operation along the interface normal direction, and calculate the number of ligands after evolution at each level of the interface.

4. The prediction system according to claim 1, characterized in that, The prediction output module is configured to perform the following operations: The ligand structure quantity evolution module receives the data based on the rate constant. The number of ligands at each level of the interface calculated by the evolution equation By combining the energy under the second boundary condition and the density distribution at ambient temperature T, the total interfacial energy at the interface is calculated. and density ; Through the total interfacial energy The energy change of the hydrophobic interface is determined by dynamic iteration under non-equilibrium conditions, and the total interfacial energy is used. Average energy of the body The difference, combined with the predicted average radius R of the nanobubbles and the density at the interface, According to the formula: Calculate and output the hydrophobic force.

5. The prediction system according to claim 1, characterized in that, The prediction output module is configured to perform the following operations: Based on the mechanical equilibrium state under the hydrophobic force, the average radius R of the nanobubbles is predicted by using the Laplace equation in combination with the interfacial precipitated bubble pressure, saturated vapor pressure and ambient pressure. Based on the average hydrogen bond energy to correct the solubility of the interfacial gas, combined with the total volume of the evolved gaseous monomers and the average radius R of the nanobubbles, the number of nanobubbles under the corresponding ambient temperature and pressure is finally calculated.

6. The prediction system according to claim 1, characterized in that, The system also includes a data interaction module, which is used to upload the number of nanobubbles under the corresponding ambient temperature and ambient pressure to the remote monitoring platform in real time via a communication link, so that the remote monitoring platform can generate online monitoring reports or early warning information for the hydrophobic interface state.

7. The prediction system according to claim 1, characterized in that, The parameter acquisition module includes: Spectral analysis unit: The vibrational energy spectrum of water molecules is obtained using a Raman spectrometer or an infrared spectrometer, and the coordination number, hydrogen bond length and covalent bond length of the water molecules are extracted based on the peak position and full width at half maximum (FWHM). Physical sensing unit: It uses pressure sensors and thermal sensors to acquire ambient pressure and temperature in real time, and uses optical image recognition components to acquire the real-time contact angle of the hydrophobic interface.

8. A method for predicting hydrophobic interfaces controlled by pressure and temperature, characterized in that, include: The interfacial physicochemical parameters and the microscopic state parameters of water molecules of the hydrophobic interface to be tested are obtained. The interfacial physicochemical parameters include interface type, contact angle, surface tension, ambient temperature and ambient pressure. The microscopic state parameters include water molecule coordination number, hydrogen bond length, covalent bond length and the average bulk bond length at the corresponding ambient temperature. Based on the coordination number, hydrogen bond length and covalent bond length of water molecules, the hydrogen bond energy state, monomeric water molecule dipole energy state and gaseous monomer energy state of water molecules with different ligand structure types are determined, and the bulk phase ligand distribution is constructed by Boltzmann distribution and combined with the first boundary condition. Based on the interface type, contact angle, and surface tension, the energy under the second boundary condition is calculated and the boundary constant is determined by combining the bulk average energy. The pre-constructed hydrophobic interface ligand evolution equation is then called to obtain the evolution data of the number of ligand structures at the hydrophobic interface as a function of the interface energy. Based on the evolution data of the number of ligand structures at the hydrophobic interface as a function of interface energy, the hydrogen bond energy state of water ligands, the dipole energy state of monomeric water molecules, the energy state of gaseous monomers, the bulk ligand distribution, and the thermodynamic parameters at the interface, the energy equation and hydrophobic force equation of the hydrophobic interface are determined. Based on the evolution data of the number of ligand structures at the hydrophobic interface as a function of interfacial energy, the energy equation of the hydrophobic interface, and the hydrophobic force equation, combined with the collected ambient temperature, ambient pressure, average bulk bond length at the corresponding ambient temperature, and reaction rate constant, the hydrophobic energy and hydrophobic force at the corresponding ambient temperature and pressure are output. The average radius of the nanobubbles is predicted by using the Laplace equation combined with the interfacial bubble pressure, saturated vapor pressure, and ambient pressure. The solubility of the interfacial gas is corrected based on the average hydrogen bond energy. Combined with the total volume of gaseous monomers generated by the evolution and the average radius of the nanobubbles, the number of nanobubbles at the corresponding ambient temperature and pressure is finally calculated. The hydrophobic energy, hydrophobic force, and the number of nanobubbles at the corresponding ambient temperature and pressure are converted into industrial fluid control commands and output to the controlled equipment.

9. The prediction method according to claim 8, characterized in that, The method further includes uploading the number of nanobubbles under the corresponding ambient temperature and ambient pressure to a remote monitoring platform in real time via a communication link, so that the remote monitoring platform can generate an online monitoring report or early warning information for the hydrophobic interface state.

10. The prediction method according to claim 8, characterized in that, The method further includes: The vibrational energy spectrum of water molecules was obtained using a Raman spectrometer or an infrared spectrometer, and the coordination number, hydrogen bond length, and covalent bond length of the water molecules were extracted based on the peak position and full width at half maximum (FWHM). The system uses pressure and thermal sensors to obtain ambient pressure and temperature in real time, and uses optical image recognition components to obtain the real-time contact angle of the hydrophobic interface.

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