Experimental method for stability mechanism of carbon dioxide nanobubbles

Abstract

The invention discloses an experimental method for a stability mechanism of carbon dioxide nanobubbles, which comprises the following steps: respectively placing carbon dioxide nanobubbles with different nanobubble diameters in simulation boxes, and evaluating the relationship between the diameters of the carbon dioxide nanobubbles and the sphericity of the nanobubbles; performing a molecular dynamics test on the carbon dioxide nanobubbles, and evaluating the relationship between the system stability of the simulation box and the diameter of the nanobubbles; evaluating the relationship between the stability of the carbon dioxide nanobubbles and the diameter of the nanobubbles; dividing the carbon dioxide nanobubbles corresponding to each bubble diameter into a plurality of concentric spherical shells with different radiuses, and evaluating the relationship between the bubble shell layer and the nanobubble diameter; evaluating the diameter of the carbon dioxide nanobubbles with stability by combining nanobubble sphericity, system stability, stability of the carbon dioxide nanobubbles and bubble shell restraint; when the size of the nanobubbles is large, gas exchange is in a dynamic balance state, and stability is kept.

Description

Technical Field

[0001] The present invention relates to the technical field of nanobubble technology, and particularly relates to an experimental method for the stability mechanism of carbon dioxide nanobubbles. Background Art

[0002] Enhanced oil recovery technology (EOR) effectively addresses the challenges of the rapidly growing global energy demand by increasing the oil recovery rate, extending the production cycle of oilfields, and optimizing the utilization efficiency of energy resources. Therefore, the development of new, efficient, and environmentally friendly oil displacement technologies has become a current research hotspot. Currently, the theoretical and experimental research on nanobubbles in the oil displacement process is still in its infancy, but preliminary experimental results have shown their significant potential and attractiveness.

[0003] The most remarkable feature of nanobubbles is their extremely long existence time. To explain the stability of nanobubbles, many theories have been proposed in recent years. The main hypotheses include the electrostatic repulsion principle, the hydrogen bond model, and the dynamic equilibrium model. The electrostatic repulsion principle holds that the surface of nanobubbles in pure water is negatively charged, and a double electric layer is formed around them. The external electrostatic pressure generated on the surface of the charged nanobubbles balances the Laplace pressure, so the nanobubbles exhibit strong stability. The hydrogen bond model believes that the special hydrogen bond structure at the gas-liquid interface reduces the diffusivity of nanobubbles, thereby making them stable. The dynamic equilibrium model believes that part of the surface of nanobubbles is coated with hydrophobic substances, so the nanobubble surface repels water and thus obtains stability.

[0004] The stability of microbubbles decreases as their size increases, and they can only exist for a few seconds before bursting and disappearing. However, there is currently no research on the relationship between the stability of nanobubbles and their size. Summary of the Invention

[0005] The purpose of the present invention is to provide an experimental method for the stability mechanism of carbon dioxide nanobubbles to solve the technical problem that there is no research on the relationship between the stability of nanobubbles and their size in the prior art.

[0006] To solve the above technical problem, the present invention specifically provides the following technical solutions:

[0007] An experimental method for the stability mechanism of carbon dioxide nanobubbles, comprising the following steps:

[0008] Step 100: Place carbon dioxide nanobubbles with different nanobubble diameters in a simulation box respectively, wherein periodic boundary conditions are adopted in three directions of the simulation box, and evaluate the relationship between the diameter of the carbon dioxide nanobubbles and the sphericity of the nanobubbles;

[0009] Step 200: Conduct molecular dynamics experiments on the carbon dioxide nanobubbles to determine the fitting curves between carbon dioxide nanobubbles with different bubble diameters and multiple reference indicators of the molecular dynamics experiments, and evaluate the relationship between the system stability of the simulation box and the nanobubble diameter;

[0010] Step 300: Evaluate the relationship between the stability of the carbon dioxide nanobubbles and the nanobubble diameter by using three kinetic criteria: mean square displacement, diffusion coefficient, and gas exchange rate;

[0011] Step 400: Regarding the centroid of the carbon dioxide nanobubbles as the center of the sphere, divide the carbon dioxide nanobubbles corresponding to each bubble diameter into several concentric spherical shells with different radii, analyze the number of gas molecules and water molecules and the internal pressure distribution in each spherical shell of the carbon dioxide nanobubbles corresponding to each bubble diameter, and evaluate the relationship between the bubble shell layer and the nanobubble diameter;

[0012] Step 500: Combine the nanobubble sphericity, system stability, stability of the carbon dioxide nanobubbles, and bubble shell layer constraint to evaluate the diameter of the carbon dioxide nanobubbles with stability.

[0013] As a preferred embodiment of the present invention, in the step 100, the carbon dioxide nanobubbles are composed of bulk water and gas nanobubbles, and the bubble diameters of the carbon dioxide nanobubbles are 3nm, 5nm, 7nm, and 10nm respectively;

[0014] Take snapshots of the carbon dioxide nanobubbles with bubble diameters of 3nm, 5nm, 7nm, and 10nm at 0 - 5ns, distinguish and identify the distribution of carbon dioxide molecules and water molecules, and determine the relationship between the diameter of the carbon dioxide nanobubbles and the nanobubble sphericity.

[0015] As a preferred embodiment of the present invention, in the step 200, the multiple index parameters corresponding to the carbon dioxide nanobubbles include: simulation system electric potential, simulation system pressure, simulation system temperature, carbon atom - oxygen atom radial distribution function, carbon atom - carbon atom radial distribution function, and water molecule and carbon dioxide molecule number density profiles.

[0016] As a preferred embodiment of the present invention, the simulation system electric potential, simulation system pressure, and simulation system temperature refer to the macroscopic electric potential, temperature, and pressure inside the simulation box;

[0017] The specific experimental process for obtaining the simulation system electric potential, simulation system pressure, and simulation system temperature is as follows:

[0018] First, establish a simulation system with periodic boundaries;

[0019] Secondly, physical property parameters are assigned to each particle in the box through force field parameters. The physical property parameters of the particle are specifically: mass, charge, and intra- and intermolecular interaction parameters;

[0020] Then, energy minimization is performed to make the system configuration tend to be reasonable;

[0021] Finally, molecular dynamics simulations of the NVT and NPT ensembles are performed to obtain the temperature and pressure of the simulation system, respectively.

[0022] As a preferred embodiment of the present invention, the calculation formula for the temperature of the simulation system is:

[0023]

[0024] where T is the instantaneous temperature of the system; N is the number of particles; k B is the Boltzmann constant; m i is the mass of the i-th particle; v i is the velocity of the i-th particle;

[0025] The calculation formula for the pressure of the simulation system is:

[0026]

[0027] where P is the instantaneous pressure of the system; V is the volume of the system; r ij = r i - r j is the particle spacing vector; F ij is the intermolecular force; the first term on the right side is the contribution of the ideal gas, and the second term is the virial contribution (calculated through intermolecular forces);

[0028] The calculation formula for the electric potential of the simulation system is:

[0029] U total = U Coulomb + U LJ ;

[0030]

[0031] where U total is the total potential energy of the simulation system; U Coulomb is the total electrostatic potential energy of the simulation system; U LJ is the total van der Waals potential energy of the simulation system; ε0 is the vacuum permittivity; q i , q j are the electric charges of particles i and j; r ij is the particle spacing; ∈ and σ are Lennard-Jones parameters.

[0032] As a preferred embodiment of the present invention, the calculation formulas for the carbon atom-oxygen atom radial distribution function and the carbon atom-carbon atom radial distribution function are specifically as follows:

[0033]

[0034] In the formula, A is the reference particle and B is the particle to be statistically analyzed;

[0035] NA and NB represent the numbers of A and B particles in the system;

[0036] Vs is the volume of the simulation box, and niB(r) represents the number of B particles within the range of radius r - r + Δr of the i-th A particle;

[0037] gAB(r) is the radial distribution function between A particles and B particles.

[0038] As a preferred embodiment of the present invention, in the step 300, the mean square displacement MSD is a measure of the deviation of the particle position relative to the reference position over time, and the MSD at time t is defined as:

[0039]

[0040] where MSD represents the mean square displacement of the particle during the simulation time, R i (t) is the position of particle i at time t, and R i (t0) is the reference position of particle i, N is the total number of particles, and the trend of the mean square displacement MSD over time is used to determine whether the particles are slowly transported due to diffusion.

[0041] As a preferred embodiment of the present invention, according to the Einstein equation, the self-diffusion coefficient of the particle can be calculated from the MSD curve:

[0042]

[0043] In the formula, D is the diffusion coefficient, and the self-diffusion coefficient is 1 / 6 of the slope of the MSD curve. The larger the slope of the curve, the larger the self-diffusion coefficient and the more intense the particle movement.

[0044] As a preferred embodiment of the present invention, the calculation formula for the gas exchange rate is specifically as follows:

[0045]

[0046] In the formula, n o (t) represents the number of gas molecules leaving the carbon dioxide nanobubble at time t, n i (t) represents the number of gas molecules entering the carbon dioxide nanobubble at time t, and n b (t) is the total number of gas molecules in the carbon dioxide nanobubble at time t;

[0047] R e The gas exchange rate of carbon dioxide nanobubbles at time t is R(t), where e The closer R(t) is to 0, the lower the gas exchange rate and the more stable the bubbles are.

[0048] As a preferred embodiment of the present invention, the specific calculation formula for the internal pressure distribution of each spherical shell is:

[0049]

[0050] In the formula, Ω represents the local space volume, p i represents the particle momentum, m i represents the particle mass. Λi is 1 when the particle is located in the local space and 0 otherwise;

[0051] r ij represents the vector between particles i and j, f ij represents the particle force, l ij represents r ij in the proportion within the local space, where 0 < l ij < 1.

[0052] The present invention has the following beneficial effects compared with the prior art:

[0053] Through the relationships between the sphericity of nanobubbles, the system stability, the stability of carbon dioxide nanobubbles, and the bubble shell layer and the diameter of nanobubbles, the present invention obtains that when the size of nanobubbles is large, the gas exchange is in a dynamic equilibrium state and maintains stability, while when the size of nanobubbles is small, the molecules in the bubbles are in a negative exchange state, resulting in weak stability.

[0054] Since large-sized nanobubbles all have a complete layered structure, including a high-density core with a radius of 2 nm and strong stability, while small-sized nanobubbles only have a transition layer and a diffusion layer. Due to water intrusion, the morphology of small-sized nanobubbles is easily variable and the diffusion is intense, with a high exchange rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only exemplary, and for those of ordinary skill in the art, without creative efforts, other implementation drawings can also be obtained based on the provided drawings.

[0056] Figure 1 It is a schematic flow chart of the experimental method of the embodiment of the present invention;

[0057] Figure 2 Snapshot of 3 - 10nm carbon dioxide nanobubbles at 0 - 5ns according to an embodiment of the present invention;

[0058] Figure 3 Graph showing the relationship between the system stability and the nanobubble diameter according to an embodiment of the present invention;

[0059] Figure 4 Graph showing the relationship between the stability of carbon dioxide nanobubbles and the nanobubble diameter according to an embodiment of the present invention;

[0060] Figure 5 Graph showing the relationship between the parameters of the bubble shell layer and the nanobubble diameter according to an embodiment of the present invention. Detailed implementation manners

[0061] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0062] As Figure 1 shown, the present invention provides an experimental method for the stability mechanism of carbon dioxide nanobubbles, including the following steps:

[0063] Step 100: Place carbon dioxide nanobubbles with different nanobubble diameters in a simulation box respectively, where periodic boundary conditions are adopted in three directions of the simulation box, and evaluate the relationship between the diameter of the carbon dioxide nanobubbles and the sphericity of the nanobubbles;

[0064] Step 200: Conduct molecular dynamics experiments on the carbon dioxide nanobubbles, determine the fitting curves between the carbon dioxide nanobubbles with different bubble diameters and multiple reference indicators of the molecular dynamics experiments, and evaluate the relationship between the system stability of the simulation box and the nanobubble diameter;

[0065] Step 300: Use three kinetic criteria, namely mean square displacement, diffusion coefficient, and gas exchange rate, to evaluate the relationship between the stability of the carbon dioxide nanobubbles and the nanobubble diameter;

[0066] Step 400: Regarding the centroid of the carbon dioxide nanobubbles as the center of the sphere, divide the carbon dioxide nanobubbles corresponding to each bubble diameter into several concentric spherical shells with different radii and a thickness of 0.1nm, analyze the number of gas molecules and water molecules and the internal pressure distribution in each spherical shell of the carbon dioxide nanobubbles corresponding to each bubble diameter, and evaluate the relationship between the bubble shell layer and the nanobubble diameter;

[0067] Step 500: Evaluate the diameter of stable carbon dioxide nanobubbles by combining the sphericity of nanobubbles, system stability, the stability of carbon dioxide nanobubbles, and the confinement of the bubble shell.

[0068] In this embodiment, CO2 gas is selected as the research object, and molecular dynamics simulation is used to study the kinetic properties of carbon dioxide nanobubbles, such as mean square displacement, diffusion coefficient, and gas molecule exchange rate, at diameters of 3 nm, 5 nm, 7 nm, and 10 nm, and to analyze the relationship between the stability of carbon dioxide nanobubbles and their size.

[0069] Furthermore, this embodiment further explores the significant layered structure of carbon dioxide nanobubbles at different sizes, and clarifies the microscopic mechanism and principle of the good stability of nanobubbles. By dividing the nanobubble into several spherical shells with a thickness of 0.1 nm, the gas density and the number of molecules in different shells of the bubble are analyzed to study the changes in gas density, the number of molecules, and the internal pressure corresponding to different bubble diameters.

[0070] Specifically, in step 100, the carbon dioxide nanobubble is composed of bulk water and gas nanobubbles, and the bubble diameters of the carbon dioxide nanobubbles are 3 nm, 5 nm, 7 nm, and 10 nm, respectively.

[0071] Take snapshots of carbon dioxide nanobubbles with bubble diameters of 3 nm, 5 nm, 7 nm, and 10 nm at 0 - 5 ns, distinguish and identify the distribution of carbon dioxide molecules and water molecules, and determine the relationship between the diameter of the carbon dioxide nanobubble and the sphericity of the nanobubble.

[0072] As Figure 2 shown, take snapshots of carbon dioxide nanobubbles with diameters of 3 - 10 nm at 0 - 5 ns. Among them, blue represents CO2 molecules and red represents water molecules. At the initial stage of the simulation, part of the CO2 molecules dissolve in water, but as the simulation progresses, the CO2 bubble tends to be stable and the bubble size does not change significantly. See the horizontal comparison in Figure 2 of Figure 2 (a), Figure 2 (b), Figure 2 (c).

[0073] In addition, as the diameter of the carbon dioxide nanobubble increases, the sphericity of the nanobubble is higher. See the vertical comparison in Figure 2 of Figure 2 (a), Figure 2 (d), Figure 2 (g), Figure 2 (j).

[0074] To further determine the equilibrium of the simulation system, the relationship between the diameter of the nanobubble and the temperature, pressure, and potential energy of the system is determined by further simulating the temperature, pressure, and potential energy of the system. In step 200, the corresponding relationship between the diameter of the carbon dioxide nanobubble, the carbon atom-oxygen atom radial distribution function, the carbon atom-carbon atom radial distribution function, and the number density profiles of water molecules and carbon dioxide molecules is further determined.

[0075] Among them, the electric potential, pressure, and temperature of the simulation system refer to the macroscopic electric potential, temperature, and pressure inside the simulation box;

[0076] The specific experimental process for obtaining the electric potential, pressure, and temperature of the simulation system is as follows:

[0077] First, a simulation system with periodic boundaries is established;

[0078] Secondly, physical property parameters are assigned to each particle in the box through force field parameters. The specific physical property parameters of the particle are: mass, charge, intra-molecular and inter-molecular interaction parameters;

[0079] Then, energy minimization is performed to make the system configuration more reasonable;

[0080] Finally, molecular dynamics simulations of the NVT and NPT ensembles are performed to obtain the temperature and pressure of the simulation system, respectively.

[0081] The calculation formula for the temperature of the simulation system is:

[0082]

[0083] In the formula, T is the instantaneous temperature of the system; N is the number of particles; k B is the Boltzmann constant; m i is the mass of the i-th particle; v i is the velocity of the i-th particle;

[0084] The calculation formula for the pressure of the simulation system is:

[0085]

[0086] In the formula, P is the instantaneous pressure of the system; V is the volume of the system; r ij = r i - r j is the particle spacing vector; F ij is the intermolecular force; the first term on the right side is the contribution of the ideal gas, and the second term is the virial contribution (calculated through intermolecular forces);

[0087] The calculation formula for the electric potential of the simulation system is:

[0088] U total = U Coulomb + U LJ ;

[0089]

[0090] wherein, U total is the total potential energy of the simulation system; U Coulomb is the total electrostatic potential energy of the simulation system; U LJ is the total van der Waals potential energy of the simulation system; ε0 is the vacuum permittivity; q i , q j are the electric charges of particles i and j; r ij is the particle spacing; ∈ and σ are Lennard-Jones parameters.

[0091] Among them, the relationship between the diameter of the nanobubble, the system electric potential, the temperature and the pressure of the system is as Figure 3 (a), Figure 3 (b), Figure 3 (c) shown. It can be seen that as the diameter of the nanobubble increases, the temperature and pressure fluctuations become smaller, and the system potential energy becomes lower, indicating that the increase in diameter makes the system more stable. In addition, the potential energies of all simulations tend to be unchanged, indicating that the system has reached an equilibrium state, and the CO2 gas molecules dissolved in the aqueous phase are saturated. At this time, the calculation of kinetic parameters and the results of statistical sampling are both reliable.

[0092] Figure 3 (d) and 2(e) show the radial distribution function RDF of carbon dioxide and water molecules. The RDF reflects the ratio of the regional density to the global density in a periodic system. Among them, Figure 3 (d) shows the RDFg C-C between the carbon atoms C in the carbon dioxide molecule, Figure 3 (e) shows the RDFg C-o between the carbon atom C in the carbon dioxide molecule and the oxygen atom O in the water molecule. For nanobubble systems with different diameters, the maximum sampling radius of the reference particle is half of the size of the system simulation box, and the maximum distance of the radial distribution function RDF can be regarded as infinity in the periodic system.

[0093] The specific calculation formulas for the carbon atom-oxygen atom radial distribution function and the carbon atom-carbon atom radial distribution function are as follows:

[0094]

[0095] wherein, A is the reference particle (such as an oxygen atom or a carbon atom), and B is the particle to be statistically analyzed (carbon atom);

[0096] NA and NB represent the numbers of A particles and B particles in the simulation system;

[0097] Vs is the volume of the simulation box, and niB(r) represents the number of B particles within the range of the radius r - r + Δr of the i-th A particle;

[0098] gAB(r) is the radial distribution function between A particles and B particles.

[0099] From Figure 3 (d) and 2(e), it can be seen that the distal radial distribution functions RDF of each system are equal, so the comparison of the peaks is valid. In Figure 3 it can be seen from (d) that the number density of carbon dioxide molecules around the carbon dioxide molecules in the large-diameter nanobubble system is higher, while Figure 3 it can be seen from (e) that the number density of water molecules around carbon dioxide in the small-diameter nanobubble system is higher. In addition, since the positions where the RDF peaks of the nanobubble systems with different diameters appear are the same, it indicates that different diameters do not affect the distribution characteristics of carbon dioxide in the bubbles and the gas-liquid distribution characteristics in the aqueous phase.

[0100] Figure 3 (f) shows the density profiles of gas molecules and water molecules in the CO2 bubble systems with diameters of 3 nm, 5 nm, 7 nm, and 10 nm. The closer the CO2 number density is to the bubble center, the greater the gas density. On the contrary, the closer the density profile of water molecules is to the center, the smaller the number density. It can be obtained that there is high-density CO2 gas in the central part of each size of nanobubble. The farther away from the center, the more water molecules there are in the nanobubble, the closer to the bubble-water interface, the bubble density, and the closer to the bulk water, where the existence state of gas molecules is closer to that of dissolved gas molecules.

[0101] During the simulation process, the gas molecules in the simulation system are constantly moving. When the gas molecules move out of the bubble, it is not conducive to the stable existence of the bubble. In order to judge the stability of the bubble, this embodiment uses three kinetic criteria, namely, the mean square displacement, the diffusion coefficient, and the gas exchange rate, to evaluate the relationship between the stability of the nanobubble and its diameter.

[0102] In step 300, the mean square displacement MSD is a measure of the deviation of the particle position from the reference position over time. The MSD at time t is defined as:

[0103]

[0104] where MSD represents the mean square displacement of the particles during the simulation time, R i (t) is the position of particle i at time t, R i (t0) is the reference position of particle i, and N is the total number of particles. The trend of the mean square displacement MSD over time is used to determine whether the particles are slowly transferred due to diffusion.

[0105] According to Einstein's equation, the self-diffusion coefficient of particles can be calculated from the MSD curve:

[0106]

[0107] where D is the diffusion coefficient, and the self-diffusion coefficient is 1 / 6 of the slope of the MSD curve. As shown in Figure 4 (b), the relationship diagram between the three-dimensional diffusion coefficient of gas molecules and the diameter of nanobubbles. The greater the slope of the curve, the greater the self-diffusion coefficient and the more intense the particle movement. Therefore, obviously, the smaller the diameter of the nanobubble, the greater the slope of the curve and the more intense the particle movement. The larger the diameter of the nanobubble, the smaller the slope of the curve and the smoother the particle movement.

[0108] Figure 4 (a) shows the mean square displacement of gas molecules in the four-size nanobubble system within 5 ns. It can be seen that as the diameter of the carbon dioxide nanobubble increases, the mean square displacement MSD of the carbon dioxide gas molecules decreases. Thus, it can be obtained that the diffusion coefficient of gas molecules in larger-diameter nanobubbles is lower (see Figure 4 (b)), that is, the mobility of gas molecules is poorer. For nanobubbles with diffusion coefficients of 3 nm and 5 nm, the possibility of gas molecules diffusing away from the bubble is higher.

[0109] To further measure the stability of nanobubbles, the specific calculation formula for the gas exchange rate is:

[0110]

[0111] where n o (t) represents the number of gas molecules leaving the carbon dioxide nanobubble at time t, and n i (t) represents the number of gas molecules entering the carbon dioxide nanobubble at time t, and n b (t) is the total number of gas molecules in the carbon dioxide nanobubble at time t;

[0112] R e (t) is the gas exchange rate of the carbon dioxide nanobubble at time t. Among them, the closer R e (t) is to 0, the lower the gas exchange rate and the more stable the bubble.

[0113] Figure 4 (c) shows the gas exchange rates corresponding to different nanobubble diameters. It can be seen that the gas exchange rate of 3-nm nanobubbles is as high as 15%, while the gas exchange rate of 10-nm nanobubbles is as low as 5%. Therefore, the larger the diameter of the nanobubble, the smaller the gas exchange rate, the lower the proportion of gas molecules diffusing out to the bubble itself, and the stronger the stability. And Figure 4(d) shows the relationship between the bubble sphericity and the diameter of nanobubbles. It can be seen that the bubble sphericity of nanobubbles with a diameter of 7 nm - 10 nm is the most stable, and the number of gas molecules diffusing outward is small.

[0114] To further understand the relationship between the stability of nanobubbles and their structure, in this embodiment, the number of gas molecules and water molecules in each spherical layer of nanobubbles is analyzed. Regarding the centroid of the nanobubble as the center of the sphere, the nanobubble is divided into several concentric spherical shells with different radii and a thickness of 0.1 nm.

[0115] From Figure 5 (a) the number of carbon dioxide molecules and water molecules in each spherical shell, it can be seen that as the radius of the nanobubble increases, the number of gas molecules in each spherical layer increases. For 7 nm and 10 nm nanobubbles, there are no water molecules in the spherical shell within 2 nm of the nanobubble, while in 3 nm and 5 nm nanobubbles, the number of water molecules increases with the increase of the spherical shell radius. Therefore, the spherical shell without water molecule infiltration is called the core region. It should be noted that smaller-sized nanobubbles do not have a core layer.

[0116] Figure 5 (b) shows the radial density distribution of gas molecules in nanobubbles of each size. It can be seen from the figure that the gas molecules in the core layer of 7 nm and 10 nm nanobubbles have a very high density, approaching the liquid density of CO2. Correspondingly, the gas density in the central region of 3 nm and 5 nm nanobubbles is low and unevenly distributed.

[0117] The gas density in the spherical shell with a radius larger than the core region decreases rapidly with the increase of the radius. The number of water molecules in the spherical shell with a radius larger than the core region increases with the increase of the radius, but the region where the gas density decreases rapidly with the increase of the radius is called the transition layer. This region is the region where the nanobubble develops from the aggregation of high-density gas to a gas-liquid mixture with a higher water content.

[0118] When the radius of the spherical shell approaches the radius of the bubble, the gas molecule density is already close to the density of dissolved gas molecules in the liquid phase. The number of gas molecules in the spherical shell decreases with the increase of the radius, while the number of water molecules increases linearly. This region is called the exchange layer, which is the region where the nanobubble exchanges substances with the liquid-phase water.

[0119] Based on Figure 5 (a) and Figure 5 (b), it can be known that the nanobubble is a composite structure composed of gas molecules and water molecules. Larger-sized nanobubbles with good stability have a high-density core region that smaller-sized nanobubbles do not have. This is the main difference between the two.

[0120] When the nanobubble does not have a core region, its structure consists of a transition region and an exchange region. Therefore, small-sized nanobubbles have a loose structure and contain a large number of water molecules. Their morphology is easily variable and the mass exchange is intense, resulting in the instability of the relatively high exchange rate and high diffusion coefficient as described above.

[0121] In addition, in order to further represent the stability of the nanobubble, the specific calculation formula for the internal pressure distribution of each spherical shell is as follows:

[0122]

[0123] In the formula, Ω represents the local space volume, p i represents the particle momentum, m i represents the particle mass. When the particle is located within the local space, Λi is 1; otherwise, it is 0.

[0124] r ij represents the vector between particles i and j, f ij represents the particle force, l ij represents the proportion of r ij within the local space, where 0 < l ij < 1.

[0125] According to Figure 5 (c) As shown in the internal pressure distribution diagram of each spherical shell, as the radius of the nanobubble increases, the internal pressure of the spherical shell increases. For 7-nm and 10-nm nanobubbles, the internal pressure in the core layer is close to zero, and the internal pressure of the outer shell layer is always greater than that of the inner shell layer. Each spherical shell dispersedly bears a great deal of the internal pressure of the nanobubble and further prevents the diffusion of molecules in the inner shell layer to the outer layer under the concentration gradient.

[0126] In this embodiment, molecular dynamics simulations are used to study the mean square displacement, diffusion coefficient, and kinetic property parameters of the gas exchange rate corresponding to carbon dioxide nanobubbles with diameters of 3 nm, 5 nm, 7 nm, and 10 nm, so as to analyze the relationship between the stability of carbon dioxide nanobubbles and their size.

[0127] Through the simulation experiments, it can be seen that gas molecules in large-sized nanobubbles (such as 7 nm and 10 nm) have a lower diffusion coefficient, and the number of dissolved and precipitated molecules is equal, thus having relatively high stability. In addition, large-sized nanobubbles have a complete three-layer hierarchical structure: the core, the transition layer, and the exchange layer. The diameter of the core is 2 nm, which has an extremely high gas density, and the gas density in the external transition layer decreases with the increase of the radius.

[0128] Small-sized nanobubbles (3 nm, 5 nm) do not have a core, and their structure consists of a transition region and a diffusion region. Small-sized nanobubbles have a loose structure and contain a large number of water molecules. Their morphology is easily variable and the mass exchange is intense, resulting in the instability of the relatively high exchange rate and high diffusion coefficient as described above.

[0129] Since the density of gas molecules in the transition layer corresponding to nanobubbles with a larger radius is low and the density of water molecules is high, and the internal pressure they bear is greater, the internal pressure of the outer shell layer is always greater than that of the inner shell layer. Each spherical shell dispersedly bears the extremely large internal pressure of the nanobubble and further prevents the diffusion of molecules in the inner shell layer to the outer layer under the concentration gradient.

[0130] Therefore, in this embodiment, through the relationships between the sphericity of nanobubbles, the system stability, the stability of carbon dioxide nanobubbles, and the bubble shell layer and the diameter of nanobubbles, it is obtained that when the size of nanobubbles is relatively large, gas exchange is in a dynamic equilibrium state and stability is maintained, while when the size of nanobubbles is relatively small, the molecules in the bubbles are in a negative exchange state, resulting in weak stability.

[0131] By analyzing the gas density and the number of molecules in different shell layers of the bubble, it is found that large-size nanobubbles have a three-layer hierarchical structure: a core layer, a transition layer, and an exchange layer. Among them, there are no water molecules in the bubble core, the radius is about 2 nm, and the density is extremely high (close to the density of liquid CO2); water molecules invade in the transition layer, and the number of water molecules increases with the increase of the radius, and the gas density decreases rapidly; the exchange layer is the shell layer where gas molecules exchange at the interface of the nanobubble, mainly composed of liquid-phase water and dissolved gas molecules.

[0132] Therefore, large-size nanobubbles all have a complete hierarchical structure, including a high-density core with a radius of 2 nm and strong stability, while small-size nanobubbles only have a transition layer and a diffusion layer. Due to the invasion of water, the morphology of small-size nanobubbles is easy to change and the diffusion is intense, with a high exchange rate.

[0133] The above embodiments are only exemplary embodiments of the present application and are not used to limit the present application. The protection scope of the present application is defined by the claims. Those skilled in the art can make various modifications or equivalent replacements within the essence and protection scope of the present application, and such modifications or equivalent replacements should also be regarded as falling within the protection scope of the present application.

Claims

1. An experimental method for the stability mechanism of carbon dioxide nanobubbles, characterized in that: The following steps are involved: Step 100, placing carbon dioxide nanobubbles with different nanobubble diameters in a simulation box respectively, wherein periodic boundary conditions are used in three directions of the simulation box to evaluate the relationship between the diameter of the carbon dioxide nanobubble and the sphericity of the nanobubble; Step 200, performing a molecular dynamics test on the carbon dioxide nanobubbles, determining fitting curves between carbon dioxide nanobubbles with different bubble diameters and multiple reference indicators of the molecular dynamics test, and evaluating the relationship between the system stability of the simulation box and the nanobubble diameter; Step 300, using three kinetic criteria, namely mean square displacement, diffusion coefficient and gas exchange rate, to evaluate the relationship between the stability of the carbon dioxide nanobubbles and the diameter of the nanobubbles; Step 400: taking the mass center of the carbon dioxide nanobubble as the sphere center, dividing the carbon dioxide nanobubble corresponding to each bubble diameter into a plurality of concentric spherical shells with different radii, analyzing the number of gas molecules and water molecules and the internal pressure distribution in each spherical shell of the carbon dioxide nanobubble corresponding to each bubble diameter, and evaluating the relationship between the bubble shell and the nanobubble diameter; Step 500: Evaluate the diameter of stable carbon dioxide nanobubbles by combining the nanobubble sphericity, system stability, stability of carbon dioxide nanobubbles, and bubble shell constraint.

2. An experimental method for the stability mechanism of carbon dioxide nanobubbles according to claim 1, characterized in that: In step 100, the carbon dioxide nanobubbles are composed of bulk water and gas nanobubbles, and the bubble diameters of the carbon dioxide nanobubbles are 3 nm, 5 nm, 7 nm, and 10 nm respectively; Carbon dioxide nanobubbles with bubble diameters of 3nm, 5nm, 7nm, and 10nm were snapshotted at 0-5ns to distinguish and identify the distribution of carbon dioxide molecules and water molecules, and to determine the relationship between the diameter of carbon dioxide nanobubbles and the sphericity of the nanobubbles.

3. An experimental method for the stability mechanism of carbon dioxide nanobubbles according to claim 1, characterized in that: In step 200, the multiple index parameters corresponding to the carbon dioxide nanobubbles include: simulated system potential, simulated system pressure, simulated system temperature, carbon atom-oxygen atom radial distribution function, carbon atom-carbon atom radial distribution function, and water molecule and carbon dioxide molecule number density profiles.

4. An experimental method for the stability mechanism of carbon dioxide nanobubbles according to claim 3, characterized in that: Simulating system potential, simulating system pressure, and simulating system temperature refer to simulating the macroscopic potential, temperature, and pressure inside the box; The specific test process for obtaining the simulated system potential, simulated system pressure, and simulated system temperature is as follows: First, a simulation system with periodic boundaries is established; Secondly, the physical property parameters of each particle in the box are assigned through the force field parameters. The specific physical property parameters of the particles are: mass, charge, intramolecular and intermolecular interaction parameters; Then, energy minimization is performed to make the system configuration reasonable; Finally, molecular dynamics simulations of the NVT and NPT ensembles were performed to obtain the simulated system temperature and simulated system pressure, respectively.

5. An experimental method for the stability mechanism of carbon dioxide nanobubbles according to claim 4, characterized in that: The calculation formula for the simulated system temperature is: Where T is the instantaneous temperature of the system; N is the number of particles; k B is the Boltzmann constant; m i is the mass of the ith particle; v i is the velocity of the ith particle; The calculation formula for the simulated system pressure is: Where P is the instantaneous pressure of the system; V is the volume of the system; r ij =r i -r j is the particle distance vector; F ij is the interaction force between particles; the first term on the right is the contribution of ideal gas, and the second term is the potential contribution (calculated by intermolecular forces); The calculation formula for the simulated system potential is: IN total =U Coulomb +U LJ ; Where U total is the total potential energy of the simulated system; U Coulomb is the total electrostatic potential energy of the simulated system; U LJ is the total van der Waals potential energy of the simulated system; ε0 is the dielectric constant of vacuum; q i ,q j is the charge of particles i and j; r ij is the interparticle distance; ∈ and σ are Lennard-Jones parameters.

6. An experimental method for the stability mechanism of carbon dioxide nanobubbles according to claim 3, characterized in that: The calculation formulas of the carbon atom-oxygen atom radial distribution function and the carbon atom-carbon atom radial distribution function are as follows: In the formula, A is the reference particle and B is the particle being counted; NA and NB represent the number of A and B particles in the system; Vs is the volume of the simulation box, niB(r) represents the number of B particles within the radius r-r+Δr of the i-th A particle; gAB(r) is the radial distribution function between particles A and B.

7. An experimental method for the stability mechanism of carbon dioxide nanobubbles according to claim 1, characterized in that: In step 300, the mean square displacement (MSD) is a measure of the deviation of the particle position relative to the reference position over time. The MSD at time t is defined as: Where MSD represents the mean square displacement of the particle during the simulation time, R i (t) is the position of particle i at time t, R i (t0) is the reference position of particle i, N is the total number of particles, and the mean square displacement (MSD) is trended over time to determine whether the particles are slowly transported due to diffusion.

8. An experimental method for the stability mechanism of carbon dioxide nanobubbles according to claim 7, characterized in that: According to Einstein's equation, the self-diffusion coefficient of the particle can be calculated from the MSD curve: Where D is the diffusion coefficient, the self-diffusion coefficient is 1 / 6 of the slope of the MSD curve. The larger the slope of the curve, the larger the self-diffusion coefficient and the more violent the particle movement.

9. An experimental method for the stability mechanism of carbon dioxide nanobubbles according to claim 1, characterized in that: The calculation formula of the gas exchange rate is specifically: Where n o (t) represents the number of gas molecules leaving the carbon dioxide nanobubble at time t, n i (t) represents the number of gas molecules entering the carbon dioxide nanobubble at time t, n b (t) is the total number of gas molecules in the carbon dioxide nanobubble at time t; R e (t) is the gas exchange rate of carbon dioxide nanobubbles at time t, where R e The closer (t) is to 0, the lower the gas exchange rate is and the more stable the bubbles are.

10. An experimental method for the stability mechanism of carbon dioxide nanobubbles according to claim 1, characterized in that: The calculation formula for the internal pressure distribution of each spherical shell is as follows: In the formula, Ω represents the local space volume, p i represents the particle momentum, m i Represents the mass of the particle. When the particle is located in the local space, Λi is 1, otherwise it is 0; r ij represents the vectors of particles i and j, and f ij represents the particle force, l ij Represents r ij The ratio in the local space, 0 <l ij <1.

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