Method for dynamically analyzing stability of nanobubbles and predicting service life of nanobubbles

Abstract

The invention relates to the crossing field of nanofluid mechanics and interface chemistry, and particularly discloses a nanobubble stability dynamic analysis and life prediction method, which comprises the following steps: establishing a hyperbolic pressure balance equation considering inter-ring electrostatic repulsion, constructing a concentric ring close packing ion distribution model, and deducing a series expression of surface hydroxyl ion dynamic adsorption; a diffusion layer Prandtt number correction method based on Brownian motion correction is provided, and accurate calculation of dynamic mass transfer parameters is achieved; and establishing a multi-dimensional coupled nanobubble radius change rate equation, and establishing a critical stable radius criterion and life prediction closed solution. According to the method, the plane hypothesis limitation of a traditional Young-Laplace equation is broken through, and the technical problem that the theoretical prediction deviation of an existing nano bubble model is large is solved through multi-physics field coupling modeling and experimental parameter joint debugging.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of nanofluid mechanics and interface chemistry, and particularly relates to a method for dynamically analyzing stability and predicting life of nanobubbles. BACKGROUND

[0002] Nanobubbles have important application value in the fields of energy, environment, and biomedicine due to their unique physical and chemical properties, but their ultra-high surface area to volume ratio leads to instability affected by interface multi-field coupling effects.

[0003] Traditional theories rely on the classical Young-Laplace equation to describe the mechanical equilibrium dominated by surface tension, but do not fully consider two core factors: the contribution of electrostatic repulsion caused by ion adsorption on the bubble surface to the interfacial pressure difference, and the coupling regulation effect of ion dynamic distribution and Brownian motion on gas diffusion in the solution.

[0004] Existing research has significant limitations in key model construction: (1) Electrostatic repulsion modeling: methods based on the planar double-electric-layer or uniform charge assumption can simplify calculations but ignore the curvature effect, resulting in large prediction errors for sub-micron bubble pressure differences. For the hexagonal lattice model with ion dense packing, the ring spacing-charge density quantitative mapping relationship cannot be established due to the lack of ring geometric symmetry and nonlinear coupling mechanism of force balance.

[0005] (2) Adsorption kinetics analysis: the traditional Smoluchowski model can describe dynamic adsorption, but ignores the nonlinear correction of ion potential well on the adsorption rate of high-curvature interface, and does not consider the micro-convection disturbance induced by Brownian motion.

[0006] (3) Stability criterion establishment: the phenomenological model based on gas diffusion flux (such as the dissolution-re-equilibrium theory) does not couple the regulation of surface charge density on the concentration gradient, resulting in a large order of magnitude deviation between the predicted critical radius and experimental data. Life prediction relies more on semi-empirical formulas, and lacks closed analytical solutions for multi-field coupling. SUMMARY

[0007] The present application aims to provide a method for dynamically analyzing stability and predicting life of nanobubbles, to solve the technical problem of insufficient characterization of multi-field coupling and large theoretical prediction deviation caused by simplification assumptions in traditional models in current nanobubble stability analysis.

[0008] To solve the above technical problems, the present application specifically provides the following technical solutions: A method for dynamically analyzing stability and predicting life of nanobubbles, comprising the following steps: Step 100: Based on the assumption that hydroxide ions on the surface of nanobubbles are arranged in a close-packed concentric ring, an explicit relationship model of charge density is constructed. A third-order ring coupling mechanism is introduced into the explicit relationship model to find the normal component of the Coulomb repulsion force between the rings. The equivalent repulsion analytical solution of the hydroxide ion pressure on the surface of nanobubbles is obtained by using Hankel transformation and Debye shielding correction. The equivalent repulsion analytical solution is substituted into the modified Young-Laplace equation to obtain the calculation model of the net pressure difference inside and outside the bubble. Step 200: Based on the Smoluchowski diffusion control model, the Prandtl number coupled with Brownian motion and diffusion is introduced to correct the thickness of the nanobubble boundary layer, and a differential equation for the surface charge density of the nanobubble is constructed to solve the low-coverage approximate analytical solution of the surface charge density of the nanobubble in real time. Step 300: Describe the motion of nanobubbles based on the Langevin equation with neglect of inertia terms, solve for the effective diffusion coefficient of hydroxide ions on the surface of nanobubbles, and use the effective diffusion coefficient to rewrite the modified nanobubble boundary layer thickness, and update the adsorption rate constant of hydroxide ions on the surface of nanobubbles in the low coverage approximate analytical solution. Step 400: By conserving mass, establish the equation for the rate of change of the nanobubble radius with time using the obtained net pressure difference calculation model inside and outside the bubble, solve for the critical stable radius of the nanobubble, and obtain the closed-loop solution for lifetime prediction by integrating the rate of change equation.

[0009] In a preferred embodiment of the present invention, in step 100, it is assumed that the surface hydroxide ions are arranged in a close-packed concentric ring configuration. Ring radius Satisfying the tangential spacing ; An explicit relationship for charge density is established by minimizing the total potential energy and solving for the base ring spacing. The calculation formula is as follows: ; ; in, Indicates the base ring spacing; Indicate charge density; This indicates the charge carried by hydroxide ions on the surface of nanobubbles; Indicates the dielectric constant; Represents the Boltzmann constant; Represents thermodynamic temperature; Ring density parameter; Indicates the first The relevant radius of the ring.

[0010] As a preferred embodiment of the present invention, the low-coverage approximate analytical solution of the surface charge density of nanobubbles obtained in real time is substituted into the explicit relationship of charge density, thereby correcting the calculation model of the net pressure difference inside and outside the bubble.

[0011] As a preferred embodiment of the present invention, a three-level ring coupling mechanism is introduced into the explicit relational model, and the method for calculating the normal component of the Coulomb repulsion force between rings specifically includes: Based on the single-loop interaction model, the calculation of the first... Normal pressure contribution of the ring to the center point The calculation formula is: ; Introducing a three-ring coupling mechanism, considering the total hydroxide ion pressure on the surface of nanobubbles coupled with adjacent three rings. for: ; The Debye shielding effect is then introduced to correct the inter-ring interaction potential. : ; Debye shield length : ; in, Line charge density ( ); Represents the coordinate variable in the vertical direction; Represents an angle variable, used to describe the spatial angle distribution during integration; Indicates the distance between ring-shaped structural units; This represents the Debye shielding parameter, which describes the degree of shielding between charge interactions; This indicates the concentration of ions in the bulk phase.

[0012] As a preferred embodiment of the present invention, based on the Smoluchowski diffusion control model, and simultaneously introducing the Prandtl number coupled with Brownian motion and diffusion, it is necessary to construct the time-varying evolution conditions of the charge density on the surface of nanobubbles, quantifying the change in charge density during dynamic adsorption, specifically including: Weak electric field conditions, surface potential , which satisfies the linearized Poisson-Boltzmann equation; Symmetrical electrolytes, in which the positive and negative ions in the solution are in a 1:1 ratio; In the quasi-steady-state diffusion layer, the convection effect is ignored, and the electric double layer is in dynamic equilibrium.

[0013] As a preferred embodiment of the present invention, in step 300, a Smoluchowski diffusion control model is constructed, and the Planck number coupled with Brownian motion and diffusion is introduced to correct the assumptions regarding the thickness of the nanobubble boundary layer. Specifically, this includes: Low Reynolds number condition, Ignore the fluid motion inertia term; Homogeneous fluid, solution viscosity The diffusion coefficient D is independent of spatial location; The statistical average approximation is used, and the Brownian motion velocity field is treated using an ensemble average method. The fluctuation term is linearly correlated with the concentration gradient.

[0014] As a preferred embodiment of the present invention, an equation for the rate of change of bubble radius is established using the mass conservation equation, and the critical stable radius is solved. The calculation formula is: ; By integrating the mass conservation equation, the closed-form solution for lifetime prediction is obtained. The calculation formula is: ,when ; Lifetime prediction closed-loop solution Degenerate into: ; in, Indicates the gas diffusion coefficient; Indicates the initial radius; Represents the gas constant; Represents the Henry coefficient; Represents the vacuum permittivity; Surface tension is a physical quantity that describes the interaction between hydrogen and oxygen ions on the surface of nanobubbles, causing the surface to tend to contract.

[0015] As a preferred embodiment of the present invention, the lifetime prediction closure solution is corrected by an error correction method. The corrections include: After the experiment time exceeds the set time, a time function is introduced. ; And / or, in the presence of multi-bubble interference, introduce an empirical correction factor. , This represents the number of bubbles per unit volume.

[0016] As a preferred embodiment of the present invention, the dynamic diffusion equation describing the motion of nanobubbles based on the Langevin equation that ignores the inertial term is modified based on the convection effect of Brownian motion to obtain the ion concentration evolution equation. After statistical averaging, the effective diffusion equation is obtained, and then the effective diffusion coefficient is obtained. Based on the simultaneous relationship between the time-series and scale-scale characteristics of diffusion and momentum, and combined with the stability condition, a method is derived to rewrite the modified nanobubble boundary layer thickness using the effective diffusion coefficient. for: .

[0017] As a preferred embodiment of the present invention, the adsorption rate constant of hydroxide ions on the surface of the updated nanobubbles is... for: ; Among them, the effective diffusion coefficient ; This represents the Prandtl number.

[0018] Compared with the prior art, the present invention has the following advantages: This invention constructs a "concentric ring close-packed" ion arrangement model for the surface of nanobubbles. Combining the measured ring spacing parameters from AFM, it derives the series solution of the Coulomb repulsion force between the rings, achieving accurate calculation of the electrostatic pressure component. By combining dynamic adsorption kinetics and the Debye shielding effect, it establishes an implicit differential equation for surface charge density. It introduces a Brownian motion-diffusion coupled Prandtl number to correct the mass transfer boundary layer. Through solving the electro-chemical-mechanical coupling equations simultaneously, it derives the critical stability criterion and lifetime analytical solution. This effectively solves the problems in current nanobubble stability analysis, such as insufficient characterization of multi-field coupling effects and large theoretical prediction deviations caused by the simplification assumptions of traditional models. Attached Figure Description

[0019] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0020] Figure 1 This is a schematic diagram of a method for dynamic analysis of nanobubble stability and lifetime prediction according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the nanobubble interface structure and concentric ring ion distribution in an embodiment of the present invention. Figure 3 This is a schematic diagram showing the details of the ring structure in an embodiment of the present invention; Figure 4 This is a vector decomposition diagram of the calculation of electrostatic repulsion between rings according to an embodiment of the present invention; Figure 5 This is a dynamic adsorption evolution curve of surface charge density in an embodiment of the present invention; Figure 6 This is a schematic diagram of the Brownian motion-diffusion coupling effect and diffusion layer correction in an embodiment of the present invention; Figure 7 This is the critical stability radius-charge density phase diagram of an embodiment of the present invention; Figure 8 This is a verification diagram of the initial radius-lifetime prediction model in an embodiment of the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] like Figures 1 to 8 As shown, this invention provides a method for dynamic analysis of nanobubble stability and lifetime prediction. Specifically, it aims to realize a nanobubble stability analysis method based on electro-chemical-mechanical multi-field coupling, comprising the following steps: Step S1: Constructing the electrostatic equilibrium equation Step S1.1: Theoretical Framework Construction To address the stability issue of nanobubbles, a modified electrostatic equilibrium equation is established by combining the classical Young-Laplace equation with the inter-ring electrostatic coupling effect. The steps are as follows: (1) Establishment of the modified equation: A ring electrostatic repulsion correction term is introduced into the surface tension dominant equation to construct a hyperbolic pressure balance relationship; (2) Ion distribution modeling: Based on the close-packed arrangement of concentric rings, a radial-tangential distribution model of surface hydroxide ions is established; (3) Calculation of inter-ring interaction: Derive the Coulomb repulsion tensor of a single ring on neighboring rings and project it onto the normal pressure component; (4) Multi-ring coupling analysis: Combine ring spacing, ring radius, and charge density to construct The series expression.

[0023] Preferably, step S1.1 includes: (1) Equation correction logic Define the radial-tangential double equilibrium condition: ① Normal pressure balance: The pressure difference between the inside and outside of the bubble needs to offset the normal component of the surface tension and the electrostatic repulsion between the rings.

[0024] ② Tangential self-balancing: The tangential components of the repulsive forces between the rings cancel each other out due to symmetry.

[0025] (2) Equilibrium equations of infinitesimal elements For ring-shaped infinitesimal elements The resultant normal forces are in equilibrium and satisfy the following conditions: (1) in, For the first The angle between the circumferential force and the normal, in rad; For the first The electrostatic repulsion force of the ring on the infinitesimal element, N; This represents the angle of the toroidal element.

[0026] (3) Global Integral Equation Integrating along the bubble surface yields the corrected equation: (2) in, Indicates the internal pressure of the bubble; This indicates the external pressure (environmental pressure) of the nanobubbles. This indicates the surface tension of nanobubbles; Indicates the radius of the nanobubble; The physical meaning of this equation is that the integration of the repulsive force between rings along the normal direction produces an equivalent negative pressure gradient. This equation introduces the circumferential integral effect of the repulsive force between rings, breaking through the traditional planar assumption.

[0027] Step S1.2: Construction of concentric ring ion model Preferably, the model is established as follows: (1) Assumptions: ① Geometric arrangement Hydroxide ions are distributed along concentric rings, the first Ring radius ( (base ring spacing); Number of ions per ring It satisfies the tangential close packing condition.

[0028] ② Energy optimization Total potential energy of the system When taking the minimum value, the solution is: (3) in, For ring density parameters, ; Indicates the base ring spacing (the spacing between concentric rings of surface ions), in meters (m). It represents the elementary charge (the amount of electron charge). This represents the dielectric constant of the solution, expressed in F / m. Represents the Boltzmann constant; Represents thermodynamic temperature; Indicates the first The relevant radius of the ring.

[0029] (2) Calculation of geometric parameters: Surface charge density (charge per unit area): (4) Step S1.3: Calculation of inter-ring repulsion and equivalent pressure Preferably, the calculation process includes: (1) Single-ring action model ① No. Normal pressure component of the ring about the center point : (5) In the formula, Line charge density ( ), C / m.

[0030] ② Consider the coupling of adjacent three rings Total pressure: (6) (2) Thermal disturbance correction: Introducing the Debye shielding effect to correct the inter-ring interaction potential : (7) in, in, Line charge density ( ); Represents the coordinate variable in the vertical direction; Represents an angle variable, used to describe the spatial angle distribution during integration; Indicates the distance between ring-shaped structural units; This represents the Debye shielding parameter, which describes the degree of shielding between charge interactions; Indicates the bulk ion concentration; , , Indicates the first , , The normal pressure component of the ring.

[0031] (3) Analytical solution of equivalent pressure: The series solution is obtained through the Hankel transformation: (8) In the formula, This is a modified Bessel function of the second type. , These represent the first and second values ​​of the modified Bessel function of the second kind, respectively, describing the damped oscillation characteristics. This represents a dimensionless parameter, the ratio of the Debye length to the ring spacing.

[0032] Step S1.4: Calibration and Verification of Experimental Parameters Preferably, the calibration process includes: (1) Parameter acquisition ① The surface ion arrangement was scanned using atomic force microscopy (AFM) to obtain the inter-ring spacing. (Accuracy ±0.2 nm); ② Debye length calculation: Input the ion concentration of the solution Calculate the shielding parameters: .

[0033] (2) Verification by example: ① Input parameters: nm (AFM measured). , , .

[0034] ② Calculation steps: 1. From equation (8), we get 2. Regarding Bubbles, pressure correction: 3. The error is reduced by 42% compared with the traditional model.

[0035] (3) Verification rules: ① Applicable conditions: When The time-loop model degenerates into a planar approximation; ② Switching threshold: When Enable the shielding effect correction item at this time.

[0036] Step S1.5: Process Implementation Specifications Technical features and operating requirements: (1) Equipment requirements: High-speed atomic force microscope (HS-AFM) shall be used to realize dynamic monitoring of ring spacing; (2) Formula application range: when the radius of curvature of the bubble surface is... And the ionic strength of the solution This model is activated at that time; (3) Real-time iteration: Establish a feedback adjustment algorithm for the ring spacing d and the Zeta potential.

[0037] Step S2: Ion adsorption kinetics analysis and surface charge density calculation Step S2.1: Model Construction Background and Assumptions Objective: To establish surface charge density The time-varying evolution equation quantifies the change in charge density during dynamic adsorption.

[0038] Assumptions: ① Weak electric field condition: surface potential It satisfies the linearized Poisson-Boltzmann equation.

[0039] ② Symmetrical electrolytes: The ratio of positive to negative ions in the electrolyte solution is 1:1 (e.g., NaCl or NaOH solution), and the bulk concentration is... .

[0040] ③ Quasi-steady-state diffusion layer: Ignoring the influence of convection, the electric double layer is in dynamic equilibrium.

[0041] Step S2.2: Debye-Hückel approximation derivation and parameter coupling Preferably, the derivation process includes: (1) Potential distribution model: ① Linearized Poisson-Boltzmann equation: (9) in, It is the reciprocal of the length of Debye; Indicates distance from surface The potential at the point; Laplace operator (describes the spatial variation of electric potential); This represents the Debye parameter.

[0042] ② Boundary conditions: when (Surface) ;when .

[0043] ③ Analytical solution: (10) in, This represents the surface potential of the bubble, i.e. The potential at that point, This indicates the distance from the surface.

[0044] ④ Expression for surface charge density (Gauss's law): (11) (2) Surface ion concentration correction: ① Correction of hydroxide ion surface concentration (12) ② Solve the equations (10) and (11) simultaneously, and eliminate the... have to: (13) in, This indicates the ion concentration on the surface of the bubble.

[0045] Step S2.3: Establishment of the differential equation for adsorption kinetics Preferably, the equation construction process is as follows: Dynamic equilibrium condition: The rate of change of surface charge density is determined by the difference between adsorption and desorption rates. (14) In the formula, The maximum surface charge density, C / m 2 ; m is the adsorption rate constant. 3 / (mol·s); S is the desorption rate constant. -1 .

[0046] Substituting into the expression for surface ion concentration, we get: (15) Step S2.4: Calculation of adsorption rate dominated by Brownian motion Preferably, the calculation is based on the Smoluchowski diffusion control model: (1) Adsorption rate constant: (16) in, The diffusion coefficient (Stokes-Einstein equation). (17) In the formula, The viscosity of the solution. The effective radius of the ion is given.

[0047] Diffusion boundary layer thickness under non-convection conditions for: = (18) (2) The adsorption rate constant can be obtained. The final expression: (19) in, Indicates the effective radius of the ion.

[0048] Step S2.5: Steady-state analytical solution of the dynamic equation Preferably, the steady-state solution is derived as follows: steady state conditions The equation simplifies to: (20) Introducing dimensionless parameters: (twenty one) (Dimensionless parameter) (22) (Dimensionless parameter) (23) Implicit equation transformation: (twenty four) Low-coverage approximate solution : (25) in, Represents the dimensionless surface charge density. This represents the actual charge density.

[0049] Step S2.6: Experimental parameter calibration and verification procedure Preferably, the calibration process includes: (1) Example of input parameters: ① Solution conditions: NaOH solution, , ② Physical property parameters: , nm ③ Calculated value: , (2) Step-by-step verification: ① Calculate the adsorption rate : ② Back-calculation of desorption rate Assume the experiment measures a steady state. Substituting into the formula, we get .

[0050] ③ Verify the surface potential: Substitute Calculated , compared with the measured Zeta potential range error .

[0051] Step S2.7: Implementation Specifications and Verification Standards Technical features and operating requirements: (1) Parameter measurement requirements: ① Ionic strength: Measured using a conductivity meter ,calculate value; ② Surface morphology: Atomic force microscopy (AFM) calibration of effective ion radius ; ③ Dynamic data: In , 10, 100s measurement Verify the dynamic model.

[0052] (2) Exception handling rules: ① Determination of out-of-tolerance: When the deviation between theoretical prediction and experimental value is >15%, recalibration is required. Or check for surface contamination; ② Balance time verification: If the time constant If the reaction time is not between 10 and 100 seconds, the solution stirring conditions need to be adjusted.

[0053] Step S3: Brownian motion-diffusion coupling effect and Prandtl number correction of the diffusion layer Step S3.1: Model Background and Basic Assumptions Objective: To establish a coupled dynamic model of Brownian motion and diffusion mass transfer, and to modify the boundary layer thickness to accurately describe the adsorption rate on the surface of nanobubbles.

[0054] Assumptions: (1) Low Reynolds number condition: Ignoring the fluid motion inertia term, the Stokes drag formula applies; (2) Homogeneous fluid: solution viscosity The diffusion coefficient D is independent of spatial location; (3) Statistical average approximation: The Brownian motion velocity field is treated with ensemble averaging, and the fluctuation term is linearly related to the concentration gradient.

[0055] Step S3.2: Constructing the Langevin equations while neglecting inertia terms Preferably, the equation construction process is as follows: (1) Simplification of equations of motion Langevin's equations describe the motion of nanobubbles: (26) Ignoring the inertia term ( The equation degenerates into: (27) in, Indicates the instantaneous velocity of the bubble; Indicates the damping coefficient ( ).

[0056] Statistical properties: average speed ; velocity autocorrelation function .

[0057] (2) Derivation of diffusion coefficient (Einstein's relation): (28) in, Where is the bubble radius.

[0058] Step S3.3: Brownian motion-diffusion mass transfer coupling equation Preferably, the coupling equation is constructed as follows: By modifying the dynamic diffusion equation and considering the Brownian convection effect, the ion concentration evolution equation becomes: (29) After statistical averaging, the effective diffusion equation is obtained: in, Represents the statistical average of ion concentrations; (30) Effective diffusion coefficient : (31) Step S3.4: Prandtl number correction for diffusion layer thickness Preferably, the correction process includes: (1) Definition of Prandtl number: The ratio of diffusion capacity to momentum transport capacity: (32) in, Kinematic viscosity, The fluid density is given.

[0059] (2) Derivation of the boundary layer thickness correction formula: Based on dimensional analysis and boundary layer analogy, the corrected thickness is: (33) Derivation logic: ① Momentum-diffusion feature time matching: ; ② By combining scale correlations and steady-state conditions, the final formula is derived.

[0060] Step S3.5: Update adsorption kinetic parameters Preferably, the parameter update includes: (1) Correction of adsorption rate constant: The original diffusion layer thickness is replaced with a corrected value, and the adsorption rate is updated as follows: (34) (2) Update of the surface charge density kinetic equation: Substitute the corrected ,have to: (35) in, This represents the rate of change of surface charge density over time. Indicates the ion diffusion coefficient; Indicates the Brownian diffusion coefficient; Represents Avogadro's constant; Represent Prandtl numbers; Indicates the bulk concentration of ions in the solution; Represents the vacuum permittivity; Maximum surface charge density (charge density at saturation adsorption); This represents the desorption rate constant.

[0061] Step S3.6: Parameter calibration and implementation verification (1) Preferably, the calibration and verification process includes: ① Measurement of key parameters: Fluid properties: kinematic viscosity Ion diffusion coefficient determined by rotational rheometer. Calibration is performed using electrochemical impedance spectroscopy or dynamic light scattering techniques.

[0062] Nanobubble parameters: radius Measured by atomic force microscopy (AFM) or dynamic light scattering (DLS).

[0063] ② Model validation steps: Theoretical calculation: Calculated according to the formula , , Then substitute into the formula to find .

[0064] Experimental control: in different Lower measurement steady state ,verify The fitting error of the model to the σ(t) curve before and after correction must be compared, and the relative error must be ≤10%.

[0065] Step S3.7: Implementing Standards and Handling Anomalies Technical features and operating requirements: (1) Parameter verification order: First measure , , ,calculate and , then calculate and .

[0066] (2) Model validation threshold: like It is necessary to check whether the low Reynolds number assumption has failed.

[0067] If calculation It needs to be checked again. The measurement accuracy.

[0068] (3) Exception handling rules: Adsorption rate is abnormally high: Check Are there any omissions in the calculation? . contributions.

[0069] The diffusion layer thickness is too small ( ): Remeasure ionic strength and recalculate .

[0070] Step S4: Stability Criteria and Lifetime Prediction of Nanobubbles Step S4.1: Establishment of the equation for the rate of change of radius and definition of parameters Preferably, the equation construction process is as follows: (1) Construction of the mass conservation equation: ① Relationship between bubble volume change rate and gas diffusion flux: (36) Indicates the concentration of dissolved gas; bubble surface ( The gas concentration gradient.

[0071] Simplifying, we get the rate of change of bubble radius over time. equation: (37) Parameter description: , representing the gas concentration inside the bubble, where (including environmental static pressure) (and Laplace pressure); Dissolved gas diffusion coefficient, calibrated through gas permeation experiments.

[0072] (2) Setting gas diffusion boundary conditions: Surface concentration expression: (38) Far-field boundary conditions: Indicates the surface of the bubble ( The gas concentration of ) Indicates the gas concentration in a bulk solution; measures Dissolved oxygen meter or infrared spectroscopy may be required.

[0073] Step S4.2: Derivation of the steady-state analytical solution of the diffusion field Preferably, the solution process includes: (1) Simplification of governing equations: The diffusion equation for dissolved gases is: (39) Its general solution is in the form of: (40) , This represents the integration constant, which is determined by the boundary conditions.

[0074] (2) Substitute the boundary conditions: Solving for constants and .

[0075] Thus, the interfacial concentration gradient is obtained: (41) Step S4.3: Derivation of the radius dynamic equation Preferably, the equation is derived as follows: Substituting the concentration gradient into the equation for the rate of change of radius, we get: (42) Key parameter calibration: ① Static pressure The system uses a pressure sensor to record the ambient static water pressure in real time, with the required accuracy being... .

[0076] ② Surface tension Temperature was measured using the pendant drop method or a surface tension meter, and the temperature was controlled within ±0.5℃.

[0077] Step S4.4: Determination of stability criterion Preferably, the criterion is constructed as follows: (1) Analytical solution for critical radius: make The value equals zero, so the critical radius corresponding to the stability condition is obtained: (43) (2) Verification method ① Measurement of different Value of actual stable radius of bubble Verify whether it is satisfied .

[0078] ② If there is a deviation Inspection required The measurement method (e.g., replacing it with electrophoresis for retesting).

[0079] Step S4.5: Integral Implementation of the Lifetime Prediction Equation Preferably, the integration process includes: (1) Dimensionless treatment: Ignore the static pressure term Lifetime integral Simplified to: (44) (2) Derivation of the closed-loop solution: (45) (3) Simplified formula applicable conditions: when... At that time, it degenerates into: (46) Indicates the initial radius of the bubble; This represents the diffusion coefficient of the dissolved gas.

[0080] Step S4.6: Experimental Verification and Parameter Calibration Procedure Preferably, the verification process includes: (1) Experimental data collection: ① Initial radius determination: using an atomic force microscope (AFM) Statistical analysis of nanobubble imaging distributed.

[0081] ② Lifetime measurement: In a temperature-controlled cell (temperature control accuracy ±0.1℃), the bubble disappearance time Texp is recorded using a high-speed camera.

[0082] ③ Parameter synchronization recording: Parameters need to be recorded synchronously for each batch of experiments. (Zeta potentiometer) and (Microelectrode method using an electrochemical workstation).

[0083] (2) Error correction algorithm: ① Surface charge decay correction: If the experiment lasts longer than 5 minutes, a time function needs to be introduced. The lifespan formula was revised.

[0084] ② Handling of multi-bubble interference: When the bubble density Add an experience correction factor. (n is the number of bubbles per unit volume).

[0085] Step S4.7: Implementation Case (1) Case conditions: ① Fluid parameters: 25℃ deionized water, dissolved oxygen , ; ② Bubble parameters: , , .

[0086] (2) Calculation process: ① Calculation of critical radius: ② Simplified lifespan calculation formula: ③ Actual measurement verification: The measured lifespan Texp = 8.9 days, with a relative error of 6.7%, meets the acceptance criteria. ).

[0087] The technical effects of this invention are reflected in three dimensions: theoretical innovation, technological breakthrough, and industrial value, as detailed below: (1) Theoretical innovation ① Pioneering a theoretical framework for dynamic equilibrium of surface charge Breaking through the traditional planar assumption, this paper for the first time incorporates the electrostatic force dual-domain decomposition (normal pressure balance / tangential self-balance), interring ion migration dynamics and the Debye shielding-Brown motion coupling mechanism into a unified model, achieving full coupling analysis of surface system parameters with a model parameter correlation degree of 95%.

[0088] ② Establish a method for analyzing the distribution of ring ions We propose an analytical algorithm for inter-ring potential energy based on the Bessel function and a three-level ring coupling correction rule (main ring + adjacent rings on both sides), and develop a radial charge density gradient calculation model, which greatly improves the prediction error of diffusion layer thickness.

[0089] (2) Technological advantages ① Breakthrough in precision At pH 4-12, salt concentration Prediction error of nanobubble stability under harsh conditions of 25-180℃ (Traditional model error) Even under extreme conditions (150℃ / 0.5M NaCl), it still maintains a 12% accuracy advantage.

[0090] ② Multi-scenario adaptability Surface charge characterization: analyzable radius of curvature ion distribution on the surface of nano / micro bubbles; Dynamic response analysis: Supported Simulation of dynamic changes in the inter-ring spacing (based on HS-AFM real-time feedback data).

[0091] ③ Cross-scale scalability By introducing a dimensionless ring density parameter To achieve bulk nanobubbles ( ) and surface nanobubbles ( The unified modeling improves the applicability of the model.

[0092] (3) Industrial application value ① Enhancing the efficiency of oil and gas extraction Adjustment by ring spacing Optimizing the electrostatic repulsion-viscosity balance of oil-dispatch nanobubbles in high-temperature, high-salinity oil reservoirs (mineralization) This method improves the recovery rate by 6.2-9.8%, which is 2.3 percentage points higher than the traditional model scheme.

[0093] ② Energy saving in wastewater treatment Based on the Debye shielding effect dynamic compensation algorithm, precise control of the nanobubble lifetime in the air flotation process is achieved: In electroplating wastewater treatment, the bubble persistence time was extended from 4.2 h to 6.8 h; Energy consumption per unit processing capacity decreased by 18.7% (actual measured data: from 2.4 kWh / m³). 3 Reduced to 1.95 kWh / m 3 ).

[0094] ③ Innovation in microelectronics manufacturing By using a ring model to predict the collapse energy threshold of nanobubbles during wafer cleaning, the particle removal rate on silicon wafer surfaces was increased to 99.997% (compared to traditional methods). ).

[0095] The above embodiments are merely exemplary embodiments of this application and are not intended to limit this application. The scope of protection of this application is defined by the claims. Those skilled in the art can make various modifications or equivalent substitutions to this application within its substance and scope of protection, and such modifications or equivalent substitutions should also be considered to fall within the scope of protection of this application.

Claims

1. A method for dynamic analysis of the stability and lifetime prediction of nanobubbles, characterized in that, Includes the following steps: Step 100: Based on the assumption that hydroxide ions on the surface of nanobubbles are arranged in a close-packed concentric ring, an explicit relationship model of charge density is constructed. A third-order ring coupling mechanism is introduced into the explicit relationship model to find the normal component of the Coulomb repulsion force between the rings. The equivalent repulsion analytical solution of the hydroxide ion pressure on the surface of nanobubbles is obtained by using Hankel transformation and Debye shielding correction. The equivalent repulsion analytical solution is substituted into the modified Young-Laplace equation to obtain the calculation model of the net pressure difference inside and outside the bubble. Step 200: Based on the Smoluchowski diffusion control model, the Prandtl number coupled with Brownian motion and diffusion is introduced to correct the thickness of the nanobubble boundary layer, and a differential equation for the surface charge density of the nanobubble is constructed to solve the low-coverage approximate analytical solution of the surface charge density of the nanobubble in real time. Step 300: Describe the motion of nanobubbles based on the Langevin equation with neglect of inertia terms, solve for the effective diffusion coefficient of hydroxide ions on the surface of nanobubbles, and use the effective diffusion coefficient to rewrite the modified nanobubble boundary layer thickness, and update the adsorption rate constant of hydroxide ions on the surface of nanobubbles in the low coverage approximate analytical solution. Step 400: By conserving mass, establish the equation for the rate of change of the nanobubble radius with time using the obtained net pressure difference calculation model inside and outside the bubble, solve for the critical stable radius of the nanobubble, and obtain the closed-loop solution for lifetime prediction by integrating the rate of change equation.

2. The method for dynamic analysis of nanobubble stability and lifetime prediction according to claim 1, characterized in that, In step 100, it is assumed that the surface hydroxide ions are arranged in a close-packed concentric ring pattern. Ring radius Satisfying the tangential spacing ; An explicit relationship for charge density is established by minimizing the total potential energy and solving for the base ring spacing. The calculation formula is as follows: ； ； in, Indicates the base ring spacing; Indicate charge density; This indicates the charge carried by hydroxide ions on the surface of nanobubbles; Indicates the dielectric constant; Represents the Boltzmann constant; Represents thermodynamic temperature; Ring density parameter; Indicates the first The relevant radius of the ring.

3. The method for dynamic analysis of nanobubble stability and lifetime prediction according to claim 2, characterized in that, By substituting the low-coverage approximate analytical solution of the surface charge density of nanobubbles obtained in real time into the explicit relationship of charge density, the calculation model of net pressure difference inside and outside the bubble is corrected.

4. The method for dynamic analysis of nanobubble stability and lifetime prediction according to claim 2, characterized in that, Introducing a three-level ring coupling mechanism into the explicit relational model, the specific methods for calculating the normal components of the Coulomb repulsion force between rings include: Based on the single-loop interaction model, the calculation of the first... Normal pressure contribution of the ring to the center point The calculation formula is: ； Introducing a three-ring coupling mechanism, considering the total hydroxide ion pressure on the surface of nanobubbles coupled with adjacent three rings. for: ； The Debye shielding effect is then introduced to correct the inter-ring interaction potential. : ； Debye shield length : ； in, Line charge density ( ); Represents the coordinate variable in the vertical direction; Represents an angle variable, used to describe the spatial angle distribution during integration; Indicates the distance between ring-shaped structural units; This represents the Debye shielding parameter, which describes the degree of shielding between charge interactions; This indicates the concentration of ions in the bulk phase.

5. The method for dynamic analysis of nanobubble stability and lifetime prediction according to claim 1, characterized in that, Based on the Smoluchowski diffusion control model, and when simultaneously introducing the Prandtl number coupled with Brownian motion and diffusion, it is necessary to construct the time-varying evolution conditions of the charge density on the nanobubble surface to quantify the change in charge density during dynamic adsorption. Specifically, this includes: Weak electric field conditions, surface potential , which satisfies the linearized Poisson-Boltzmann equation; Symmetrical electrolytes, in which the positive and negative ions in the solution are in a 1:1 ratio; In the quasi-steady-state diffusion layer, the convection effect is ignored, and the electric double layer is in dynamic equilibrium.

6. The method for dynamic analysis of nanobubble stability and lifetime prediction according to claim 1, characterized in that, In step 300, a Smoluchowski diffusion control model is constructed, and the Prandtl number, which couples Brownian motion with diffusion, is introduced to correct the assumptions about the thickness of the nanobubble boundary layer. Specifically, this includes: Low Reynolds number condition, Re 1. Neglect the fluid motion inertia term; Homogeneous fluid, solution viscosity The diffusion coefficient D is independent of spatial location; The statistical average approximation is used, and the Brownian motion velocity field is treated using an ensemble average method. The fluctuation term is linearly correlated with the concentration gradient.

7. The method for dynamic analysis of nanobubble stability and lifetime prediction according to claim 1, characterized in that, An equation for the rate of change of bubble radius is established using the mass conservation equation, and the critical stable radius is then solved. The calculation formula is: ； By integrating the mass conservation equation, the closed-form solution for lifetime prediction is obtained. The calculation formula is: ,when 1; Lifetime prediction closed-loop solution Degenerate into: ； in, Indicates the gas diffusion coefficient; Indicates the initial radius; Represents the gas constant; Represents the Henry coefficient; Represents the vacuum permittivity; Surface tension is a physical quantity that describes the interaction between hydrogen and oxygen ions on the surface of nanobubbles, causing the surface to tend to contract.

8. The method for dynamic analysis of nanobubble stability and lifetime prediction according to claim 1, characterized in that, The lifetime prediction closed-loop solution is obtained through error correction. The corrections include: After the experiment time exceeds the set time, a time function is introduced. ; And / or, in the presence of multi-bubble interference, introduce an empirical correction factor. , This represents the number of bubbles per unit volume.

9. The method for dynamic analysis of nanobubble stability and lifetime prediction according to claim 1, characterized in that, The dynamic diffusion equation describing the motion of nanobubbles based on the Langevin equation, which ignores the inertial term, is modified based on the convection effect of Brownian motion to obtain the ion concentration evolution equation. After statistical averaging, the effective diffusion equation is obtained, and then the effective diffusion coefficient is obtained. Based on the simultaneous relationship between the time-series and scale-scale characteristics of diffusion and momentum, and combined with the stability condition, a method is derived to rewrite the modified nanobubble boundary layer thickness using the effective diffusion coefficient. for: 。 10. The method for dynamic analysis of nanobubble stability and lifetime prediction according to claim 1, characterized in that, The updated adsorption rate constant of hydroxide ions on the surface of nanobubbles for: ； Among them, the effective diffusion coefficient ; This represents the Prandtl number.

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