Comsol-based method and device for predicting bubble formation mediated by black phosphorus quantum dots via optical perforation

Abstract

The application discloses a bubble formation prediction method and device based on COMSOL-mediated black phosphorus quantum dot-mediated optical perforation, and the method comprises the following steps: based on COMSOL, a two-dimensional axisymmetric transient model of solid heat transfer and fluid heat transfer is constructed to obtain a solid heat transfer module and a fluid heat transfer module; a coefficient form partial differential equation interface is set to construct a carrier density equation; according to the carrier density equation, intermediate physical parameters are pre-set; according to the intermediate physical parameters, a heat source condition is pre-set, the solid heat transfer module and the fluid heat transfer module are coupled according to the heat source condition, and a target simulation model is obtained; according to the target simulation model, nanobubble generation is predicted to obtain a bubble formation time, a nanobubble area and a threshold laser flux. The application can improve the accuracy of optical perforation nanobubble generation prediction and can be widely applied to the fields of photo-induced perforation technology and nanobubble technology.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of photoporation technology, and in particular to a bubble formation prediction method and device for black phosphorus quantum dot mediated photoporation based on COMSOL. BACKGROUND

[0002] Nanomaterial mediated photoporation is a new intercellular delivery technology, which induces the surrounding liquid medium to form nanobubbles by laser irradiation of photothermal nanoparticles, and uses nanobubbles to create temporary holes on the cell membrane to achieve exogenous material delivery. Black phosphorus is a new material with excellent photothermal properties and biological safety, and is therefore considered an excellent photoporation mediator. However, the current black phosphorus mediated photoporation technology is still in its infancy. Since the relevant theoretical system has not been perfected, many factors that affect the delivery effect still need to rely on a large number of experimental trial and error and condition optimization to accumulate a large amount of reliable data as a reference basis. In addition, the short life and small size of nanobubbles also make it difficult to capture and observe the photoporation phenomenon experimentally, and various factors limit the development of this technology. SUMMARY

[0003] Therefore, the embodiments of the present application mainly aim to provide a bubble formation prediction method and device for black phosphorus quantum dot mediated photoporation based on COMSOL, in order to solve at least one of the problems in the prior art, and the present application can improve the accuracy of photoporation nanobubble generation prediction.

[0004] To achieve the above-mentioned purpose, one aspect of the embodiments of the present application provides a bubble formation prediction method for black phosphorus quantum dot mediated photoporation based on COMSOL, which comprises:

[0005] Based on COMSOL, a two-dimensional axisymmetric transient model of solid heat transfer and fluid heat transfer is constructed to obtain a solid heat transfer module and a fluid heat transfer module;

[0006] A coefficient form partial differential equation interface is set to construct a carrier density equation;

[0007] According to the carrier density equation, intermediate physical parameters are pre-set;

[0008] According to the intermediate physical parameters, a heat source condition is pre-set, the solid heat transfer module and the fluid heat transfer module are coupled according to the heat source condition, and a target simulation model is obtained;

[0009] According to the target simulation model, nanobubble generation is predicted to obtain bubble formation time, nanobubble region and threshold laser flux.

[0010] In some embodiments, the COMSOL-based two-dimensional axisymmetric transient model of solid heat transfer and fluid heat transfer is constructed to obtain a solid heat transfer module and a fluid heat transfer module, including the following steps:

[0011] The solid heat transfer interface and the fluid heat transfer interface are selected by COMSOL;

[0012] The black phosphorus quantum dot geometric region and the water medium geometric region are constructed by COMSOL;

[0013] The domain of the solid heat transfer interface is set as the black phosphorus quantum dot geometric region to obtain the solid heat transfer module;

[0014] The domain of the fluid heat transfer interface is set as the water medium geometric region to obtain the fluid heat transfer module.

[0015] In some embodiments, the coefficient form partial differential equation interface is set to construct a carrier density equation, including the following steps:

[0016] The coefficient form partial differential equation interface is set;

[0017] The domain of the coefficient form partial differential equation interface is set as the black phosphorus quantum dot geometric region to construct the carrier density equation;

[0018] The carrier density equation represents the change of the carrier density of the black phosphorus quantum dot under ultrafast laser.

[0019] In some embodiments, the coefficient form partial differential equation interface is set to construct a carrier density equation, and the formula used includes:

[0020]

[0021] Wherein, N e represents the carrier density; t represents time; represents the change of the carrier density with time; a0 represents the linear absorption coefficient; I represents the Gaussian pulse laser; E represents the absorbed photon energy when a single photo-generated carrier is generated; a nL represents the nonlinear absorption coefficient; A represents the recombination center recombination coefficient; B represents the radiation recombination coefficient; C represents the Auger recombination coefficient.

[0022] In some embodiments, the intermediate physical parameters are pre-set according to the carrier density equation, including the following steps:

[0023] According to the regulation relationship of the black phosphorus quantum dot thermal physical quantity with the carrier density in the carrier density equation, the carrier heat capacity, the lattice heat capacity, and the carrier-lattice coupling coefficient are set;

[0024] setting the carrier thermal capacity and the lattice thermal capacity in the solid properties of the solid heat transfer module;

[0025] applying the thermophysical properties of water medium in the material library of COMSOL to the fluid heat transfer module;

[0026] setting the initial temperature value of the solid heat transfer module and the initial temperature value of the fluid heat transfer module;

[0027] setting a Gaussian pulse laser according to the laser flux, the pulse width and the pulse peak time.

[0028] In some embodiments, the pre-setting of the heat source condition according to the intermediate physical parameters, the coupling of the solid heat transfer module and the fluid heat transfer module according to the heat source condition, and the obtaining of the target simulation model, comprise the following steps:

[0029] obtaining a first volume heat source term according to the linear absorption coefficient, the nonlinear absorption coefficient, the Gaussian pulse laser, the absorbed photon energy when a single photo-generated carrier is generated, and the band gap;

[0030] obtaining a second volume heat source term and a third volume heat source term according to the carrier-lattice coupling coefficient, the carrier temperature and the lattice temperature;

[0031] obtaining a first boundary heat source term and a second boundary heat source term according to the interface thermal conductivity, the lattice temperature and the water medium temperature;

[0032] coupling the solid heat transfer module and the fluid heat transfer module according to the first volume heat source term, the second volume heat source term, the third volume heat source term, the first boundary heat source term and the second boundary heat source term, and obtaining a target simulation model.

[0033] In some embodiments, before the predicting of the nanobubble generation according to the target simulation model, and the obtaining of the bubble formation time and the threshold laser flux, the method further comprises the following steps:

[0034] dividing the black phosphorus quantum dot geometric region and the water medium geometric region in the target simulation model into grids.

[0035] In some embodiments, the predicting of the nanobubble generation according to the target simulation model, and the obtaining of the bubble formation time, the nanobubble region and the threshold laser flux, comprise the following steps:

[0036] obtaining the carrier-lattice temperature change curve of the black phosphorus quantum dot, the lattice-water medium temperature change curve and the water medium temperature distribution graph under the action of the ultrafast laser according to the target simulation model through simulation operation;

[0037] judging the nanobubble generation according to the water medium temperature in the water medium temperature distribution map, when the water medium temperature at the boundary is greater than or equal to the critical temperature of water, taking the moment when the water medium temperature at the boundary is greater than the first preset temperature as the bubble formation time;

[0038] taking the laser flux when the highest water medium temperature at the boundary is equal to the critical temperature of water as the threshold laser flux;

[0039] taking the region where the water medium temperature in the water medium temperature distribution map is greater than the second preset temperature as the nanobubble region.

[0040] To achieve the above object, another aspect of the embodiment of the present application provides a bubble formation prediction device for black phosphorus quantum dot mediated optical perforation based on COMSOL, the device comprising:

[0041] The first module is configured to construct a two-dimensional axisymmetric transient model of solid heat transfer and fluid heat transfer based on COMSOL, to obtain a solid heat transfer module and a fluid heat transfer module;

[0042] The second module is configured to set a coefficient form partial differential equation interface and construct a carrier density equation;

[0043] The third module is configured to pre-set intermediate physical parameters according to the carrier density equation;

[0044] The fourth module is configured to pre-set heat source conditions according to the intermediate physical parameters, and to couple the solid heat transfer module and the fluid heat transfer module according to the heat source conditions, to obtain a target simulation model;

[0045] The fifth module is configured to predict nanobubble generation according to the target simulation model, to obtain a bubble formation time, a nanobubble region and a threshold laser flux.

[0046] To achieve the above object, another aspect of the embodiment of the present application provides an electronic device, which comprises a memory and a processor, the memory stores a computer program, and the processor implements the above-mentioned bubble formation prediction method for black phosphorus quantum dot mediated optical perforation based on COMSOL when executing the computer program.

[0047] To achieve the above object, another aspect of the embodiment of the present application provides a computer readable storage medium, which stores a computer program, and the computer program implements the above-mentioned bubble formation prediction method for black phosphorus quantum dot mediated optical perforation based on COMSOL when executed by a processor.

[0048] To achieve the above object, another aspect of the embodiment of the present application provides a computer program product or computer program, which comprises computer instructions stored in a computer readable storage medium. The processor of the computer device can read the computer instructions from the computer readable storage medium, and the processor executes the computer instructions to make the computer device execute the aforementioned COMSOL-based bubble formation prediction method for black phosphorus quantum dot-mediated photoporation.

[0049] The embodiment of the present application at least has the following beneficial effects: the present application provides a COMSOL-based bubble formation prediction method for black phosphorus quantum dot-mediated photoporation, and the scheme constructs a two-dimensional axisymmetric transient model of solid heat transfer and fluid heat transfer based on COMSOL to obtain a solid heat transfer module and a fluid heat transfer module; a coefficient form partial differential equation interface is set to construct a carrier density equation; intermediate physical parameters are pre-set according to the carrier density equation; heat source conditions are pre-set according to the intermediate physical parameters, the solid heat transfer module and the fluid heat transfer module are coupled according to the heat source conditions to obtain a target simulation model; and nanobubble generation is predicted according to the target simulation model to obtain bubble formation time, a nanobubble region and a threshold laser flux, which can improve the accuracy of photoporation nanobubble generation prediction. BRIEF DESCRIPTION OF DRAWINGS

[0050] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0051] Figure 1 is a flowchart of the COMSOL-based bubble formation prediction method for black phosphorus quantum dot-mediated photoporation provided by the embodiment of the present application;

[0052] Figure 2 is a schematic diagram of a geometric model and mesh division of the target simulation model provided by the embodiment of the present application;

[0053] Figure 3 is a schematic diagram of the change of the lattice temperature of the black phosphorus quantum dot and the water medium temperature with time provided by the embodiment of the present application;

[0054] Figure 4 is a schematic diagram of the water medium temperature and bubble distribution provided by the embodiment of the present application;

[0055] Figure 5 is a whole flowchart of the COMSOL-based bubble formation prediction method for black phosphorus quantum dot-mediated photoporation provided by the embodiment of the present application;

[0056] Figure 6 Figure 1 is a schematic diagram of a hardware structure of an electronic device according to an embodiment of the present application. DETAILED DESCRIPTION

[0057] In order to make the objects, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and should not be used to limit the present application. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present application. They are only examples of devices and methods consistent with some aspects of the present application as described in the appended claims.

[0058] It should be noted that although the functional modules are divided in the system schematic diagram, and the logical order is shown in the flowchart, in some cases, the steps shown or described can be performed in a manner different from the module division in the system or the order in the flowchart. The terms "first / S100", "second / S200" in the specification and claims and the above drawings can be used herein to describe various concepts, but unless specifically stated, these concepts are not limited by these terms. These terms are only used to distinguish one concept from another. For example, the first information can also be referred to as the second information, and similarly, the second information can also be referred to as the first information, without departing from the scope of the present application. Depending on the context, the word "if" as used herein can be interpreted as "when" or "upon" or "in response to determining".

[0059] The terms "at least one", "multiple", "each", "any" and the like used in the present application include one, two or more than two, multiple includes two or more than two, each refers to each of the corresponding multiple, and any refers to any one of the multiple.

[0060] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present application belongs. The terms used herein are only for the purpose of describing the embodiments of the present application and are not intended to limit the present application.

[0061] Before the embodiments of the present application are described in detail, first, some nouns and terms involved in the embodiments of the present application are described, and the nouns and terms involved in the embodiments of the present application are applicable to the following explanations.

[0062] Ultrafast laser refers to laser with extremely short pulse width, usually in picoseconds (10 -12 seconds) or femtoseconds (10 -15On the order of seconds, or even shorter. Its core feature is to provide high energy output in a very short time, while avoiding excessive thermal effects on the material.

[0063] Photo-generated carrier refers to the electron and hole pair generated by photon excitation in a semiconductor material. When the energy of a photon is equal to or greater than the band gap of a semiconductor, an electron in the valence band absorbs the photon and transitions to the conduction band to form an electron-hole pair. These carriers are called photo-generated carriers.

[0064] Intracellular substance delivery is a hot topic in the field of biomedicine. Techniques such as gene editing and cell therapy require the delivery of exogenous substances to living cells in vivo to exert their effects. However, due to the selective permeability of the cell membrane, most exogenous substances cannot effectively enter the cell, so how to break through the barrier of the cell membrane has become a major problem in this field. In order to solve this problem, delivery strategies based on biological, chemical, and physical methods such as viral vector delivery, chemical agent permeation of the cell membrane, gene gun, and electroporation have emerged. However, these traditional intercellular delivery methods cannot be widely applied due to their respective drawbacks, and the industry still needs to seek safer and more efficient delivery strategies.

[0065] Nanomaterial-mediated photoporation is a new intercellular delivery technology that induces the formation of nanobubbles around the photothermal nanoparticles by laser irradiation, and uses the nanobubbles to create temporary pores on the cell membrane to achieve exogenous substance delivery. Black phosphorus is a new material with excellent photothermal properties and biological safety, and is therefore considered an excellent photoporation mediator. However, the photoporation technology based on black phosphorus is still in its infancy. Since the related theoretical system is not yet perfect, many factors that affect the delivery effect still need to rely on a large number of experimental trial and error and condition optimization to accumulate a large amount of reliable data as a reference basis. In addition, the short lifespan and small size of nanobubbles make it difficult to capture and observe the photoporation phenomenon experimentally, and various factors limit the development of this technology.

[0066] Therefore, as shown in the Figure 1 The present application provides a COMSOL-based black phosphorus quantum dot-mediated photoporation bubble formation prediction method, which can include but is not limited to steps S100 to S500:

[0067] Step S100, based on COMSOL, a two-dimensional axisymmetric transient model of solid heat transfer and fluid heat transfer is constructed to obtain a solid heat transfer module and a fluid heat transfer module;

[0068] Step S200, set up the coefficient form partial differential equation interface to build the carrier density equation;

[0069] Step S300, according to the carrier density equation, pre-setting intermediate physical parameters;

[0070] Step S400, according to the intermediate physical parameters, pre-setting heat source conditions, according to the heat source conditions, coupling the solid heat transfer module and the fluid heat transfer module to obtain a target simulation model;

[0071] Step S500, according to the target simulation model, predicting the generation of nano-bubbles to obtain bubble formation time, nano-bubble area and threshold laser flux.

[0072] Based on COMSOL physical field simulation software, the photo-thermal conversion process of black phosphorus quantum dots under femtosecond laser and the heat exchange with the surrounding water medium are simulated, the generation of photo-perforation nano-bubbles is predicted, and information such as bubble formation threshold flux and bubble formation time is provided, which can be used for laser effectiveness evaluation of black phosphorus quantum dot mediated photo-perforation and provide valuable theoretical guidance and experimental optimization strategy for further research of this technology.

[0073] In some embodiments, step S100 can include but is not limited to steps S110 to S140:

[0074] Step S110, selecting a solid heat transfer interface and a fluid heat transfer interface through COMSOL;

[0075] Step S120, constructing a black phosphorus quantum dot geometric region and a water medium geometric region through COMSOL;

[0076] Step S130, setting the domain of the solid heat transfer interface as the black phosphorus quantum dot geometric region to obtain the solid heat transfer module;

[0077] Step S140, setting the domain of the fluid heat transfer interface as the water medium geometric region to obtain the fluid heat transfer module.

[0078] In step S100 of some embodiments, a two-dimensional axisymmetric transient model is established in COMSOL, a simulation region is set, and a solid heat transfer module and a fluid heat transfer module are added, which lay a foundation for subsequent establishment of a double-temperature equation describing the change of the carrier temperature and the lattice temperature of the black phosphorus quantum dot under the action of the ultrafast laser and establishment of a heat conduction equation describing the heat exchange between the carrier temperature of the black phosphorus quantum dot and the surrounding water medium. Among them, the solid heat transfer interface is set in the simulated black phosphorus quantum dot geometric region, and the fluid heat transfer interface is set in the simulated water medium geometric region. Exemplarily, first, open the COMSOL simulation software, select "two-dimensional axisymmetric model" in the model wizard, and select the "fluid heat transfer" physical interface and two "solid heat transfer" physical interfaces in the selection of physical field interface. Then, after selecting "transient" research in the selection research interface, enter the main interface, and construct the circular geometric region of the black phosphorus quantum dot and the water medium under the "geometry" module, so as to obtain the black phosphorus quantum dot geometric region and the water medium geometric region, which are used to simulate the spherical symmetric simulation model of the black phosphorus quantum dot heating the surrounding water medium. Finally, the two "solid heat transfer" physical interfaces are renamed as "carrier heat transfer" and "lattice heat transfer" respectively, and the dependent variables are changed to carrier temperature T e and lattice temperature T l , respectively. In the domain setting, the black phosphorus quantum dot geometric region is selected; the "fluid heat transfer" physical interface is renamed as "water medium heat transfer", and the dependent variable is changed to water medium temperature T w , and the water medium geometric region is selected in the domain setting.

[0079] In some embodiments, step S200 can include but is not limited to steps S210 to S220:

[0080] Step S210, setting the coefficient form partial differential equation interface;

[0081] Step S220, setting the domain of the coefficient form partial differential equation interface as the black phosphorus quantum dot geometric region, and constructing the carrier density equation;

[0082] Wherein, the carrier density equation represents the change of the carrier density of the black phosphorus quantum dot under the ultrafast laser.

[0083] In step S200 of some embodiments, a coefficient form partial differential equation interface is added in COMSOL and set in the simulated black phosphorus quantum dot geometric region, so as to establish a carrier density equation describing the change of the carrier of the black phosphorus quantum dot under the action of the ultrafast laser. Exemplarily, a physical field interface selection partial differential equation interface-coefficient form partial differential equation is added in COMSOL, which is renamed as "carrier density", and the dependent variable is changed to carrier density N e , the dependent variable physical quantity customization unit is 1 / m 3 , and the source term physical quantity customization unit is 1 / m3 • s, domain selection as black phosphorus quantum dot geometric region, initial value set to 10 12 [1 / cm 3 ]. Finally, by adjusting the diffusion coefficient, absorption coefficient, source term, mass coefficient, damping coefficient and other coefficient form partial differential equation parameters, meet the following equation form, so as to realize the description of the change of black phosphorus quantum dot carrier density under ultrafast laser action, then there is the following equation form:

[0084]

[0085] Where, N e represents the carrier density; t represents time; represents the change of carrier density with time; α0 represents the linear absorption coefficient; I represents the Gaussian pulse laser; α nL represents the nonlinear absorption coefficient; A represents the recombination center recombination coefficient; B represents the radiation recombination coefficient; C represents the Auger recombination coefficient; E represents the photon energy absorbed when a single photo-generated carrier is generated, which is the photon energy absorbed when single photon absorption is hv, and the photon energy absorbed when two-photon absorption is 2hv; h represents the Planck constant; v represents the frequency of the laser.

[0086] In some embodiments, step S300 can include but is not limited to steps S310 to S350:

[0087] Step S310, according to the regulation relationship of black phosphorus quantum dot thermophysical quantity by the carrier density in the carrier density equation, set the carrier heat capacity, lattice heat capacity and carrier-lattice coupling coefficient;

[0088] Step S320, set the carrier heat capacity and lattice heat capacity in the solid properties of the solid heat transfer module;

[0089] Step S330, apply the thermophysical properties of water medium in the material library of COMSOL to the fluid heat transfer module;

[0090] Step S340, set the initial temperature value of the solid heat transfer module and the initial temperature value of the fluid heat transfer module;

[0091] Step S350, set the Gaussian pulse laser according to the laser flux, pulse width and pulse peak time.

[0092] In step S300 of some embodiments, the required intermediate physical quantities for simulation are defined in the COMSOL global definition to confirm the related physical parameters required for simulation. Among them, the black phosphorus quantum dot material physical parameters can include but are not limited to black phosphorus density ρ BP , carrier heat capacity coefficient γ e , Fermi energy εF Fermi energy density of states D(ε) F Debye Energy E D Carrier-lattice coupling constant λ e-ph Effective mass m * Reduced Planck constant Boltzmann constant k B A. Recombination coefficient of recombination center; B. Radiative recombination coefficient; C. Auger recombination coefficient; D. Black phosphorus quantum dot size r; E. Band gap g Linear absorption coefficient α0, nonlinear absorption coefficient α NL By utilizing the material's physical parameters, the changes in carrier density and other thermophysical properties of black phosphorus quantum dots (SPQDs) under ultrafast laser irradiation can be accurately described. Based on the relationship between carrier density and the thermophysical quantities of SPQDs, the carrier heat capacity, lattice heat capacity, and carrier-lattice coupling coefficient required for the two-temperature equation are defined to accurately describe the photothermal conversion process of SPQDs under ultrafast laser irradiation. Next, the thermophysical properties of water from the COMSOL material library are used to describe the heat conduction process of water under the influence of a high-temperature boundary heat source. Finally, femtosecond laser parameters, including pulsed laser flux and pulse width, are defined to establish a Gaussian ultrafast laser model.

[0093] For example, based on the relationship between the thermophysical quantities of black phosphorus quantum dots and the carrier density, the carrier heat capacity C required for the two-temperature equation is defined. e lattice heat capacity C l The carrier-lattice coupling coefficient g is used to accurately describe the photothermal conversion process of black phosphorus quantum dots under ultrafast laser irradiation. The parameters of the black phosphorus material used are shown in Table 1. These parameters are set in the COMSOL global definition, and the carrier heat capacity C is also set. e lattice heat capacity C l The solid properties are set in the "Carrier Heat Transfer" and "Lattice Heat Transfer" sub-modules of the solid heat transfer module, respectively. In COMSOL, the material parameters for the water medium can be obtained by adding "H2O(water)[liquid]" from the material library. After adding, apply this material property to the geometric region of the water medium in the geometry selection. Next, in the fluid heat transfer module, i.e., the "Water Medium Heat Transfer" module, set both the fluid type and thermal conductivity to "From Material" (i.e., the previously added material), set the velocity field to zero, and set the initial temperature value of each thermophysical field module (including the "Carrier Heat Transfer", "Lattice Heat Transfer", and "Water Medium Heat Transfer" modules) to 300K. Optionally, the laser used in the simulation is a Gaussian pulsed laser, and its relevant settings are as follows:

[0094]

[0095] Where I represents the Gaussian pulsed laser; F represents the laser flux; t p t is the pulse width; t0 is the pulse peak time. For the black phosphorus quantum dot-mediated optical perforation studied, its laser radiation range is much larger than the size of the black phosphorus quantum dots themselves, so there is no need to consider the radial distribution of the Gaussian laser.

[0096] Table 1

[0097]

[0098]

[0099] Where, m e The electron mass has a value of 9.11 × 10⁻⁶. -31 (kg).

[0100] In some embodiments, step S400 may include, but is not limited to, steps S410 to S440:

[0101] Step S410: Based on the linear absorption coefficient, nonlinear absorption coefficient, Gaussian pulse laser, photon energy absorbed when generating a single photogenerated carrier, and band gap, the first bulk heat source term is obtained.

[0102] Step S420: Based on the carrier-lattice coupling coefficient, carrier temperature, and lattice temperature, the second body heat source term and the third body heat source term are obtained.

[0103] Step S430: Based on the interfacial thermal conductivity, lattice temperature and water medium temperature, the first boundary heat source term and the second boundary heat source term are obtained;

[0104] Step S440: Based on the first body heat source term, the second body heat source term, the third body heat source term, the first boundary heat source term, and the second boundary heat source term, couple the solid heat transfer module and the fluid heat transfer module to obtain the target simulation model.

[0105] In step S400 of some embodiments, the following heat source terms are added to the solid heat transfer module describing carrier temperature and lattice temperature, and the fluid heat transfer module describing water medium temperature changes: a laser heat source term, a carrier-lattice coupling term, and a black phosphorus quantum dot-water medium interface heat transfer term. Specifically, the laser source term may include a first bulk heat source term Q1, the carrier-lattice coupling term may include a second bulk heat source term Q2 and a third bulk heat source term Q3, and the black phosphorus quantum dot-water medium interface heat transfer term may include a first boundary heat source term Q. b1 Second boundary heat source term Q b2 This enables physical field coupling of the described carrier temperature, lattice temperature, and water medium temperature changes. In addition, an isothermal region is set in the solid heat transfer module.

[0106] For example, a first volume heat source term Q1 and a second volume heat source term Q2 are added to the "Carrier Heat Transfer" module to describe the energy absorbed by the carriers after being irradiated by laser and the interaction between the carriers and the crystal lattice, which has the following form:

[0107]

[0108] Q2=-g(T e -T l )

[0109] In the formula, Q1 represents the first-body heat source term; Q2 represents the second-body heat source term; α0 represents the linear absorption coefficient; α nL I represents the nonlinear absorption coefficient; E represents the Gaussian pulse laser; E represents the energy of the absorbed photon when generating a single photogenerated carrier. g Indicates the band gap; g represents the carrier-lattice coupling coefficient; T e T represents carrier temperature; l This indicates the lattice temperature.

[0110] In the "lattice heat transfer" module, a third-body heat source term Q3 and a first-boundary heat source term Q are set. b1 To describe the thermalization process of the crystal lattice under carrier-lattice interaction and the heat transfer process between high-temperature black phosphorus quantum dots and the surrounding water medium, it has the following form:

[0111] Q3=g(T e -T l )

[0112] Q b1 =-G(T) l -T w )

[0113] In the formula, Q3 represents the third-body heat source term; Q b1 The term represents the first boundary heat source; G represents the interfacial thermal conductivity; T represents the first boundary heat source term; G represents the interfacial thermal conductivity; T represents the first boundary heat source term; G represents the first boundary heat source term ... w This indicates the temperature of the water medium.

[0114] Set a second boundary heat source term Q for the "Water Medium Heat Transfer" module. b2 This describes the process by which water gains heat from high-temperature black phosphorus quantum dots, causing it to heat up. It has the following forms:

[0115] Q b2 =G(T) l -T w )

[0116] In the formula, Q b2 This represents the second boundary heat source term.

[0117] Finally, isothermal settings were added to the "Carrier Heat Transfer" and "Lattice Heat Transfer" modules in the solid-state heat transfer module. The final simulation model satisfies the following expression:

[0118]

[0119] Specifically, the expression is as follows:

[0120]

[0121] Among them, C w ρ represents the heat capacity of the water medium; w k represents the density of the water medium. w This indicates the thermal conductivity of the water medium.

[0122] Before step S500 in some embodiments, the method further includes: meshing based on the geometric model in the target simulation model, namely the geometric region of black phosphorus quantum dots and the geometric region of the water medium. For example, meshing is performed on the simulated geometric regions of black phosphorus quantum dots and the water medium, respectively, wherein an additional boundary layer mesh setting and local refinement are performed at the boundaries to effectively describe the high temperature gradient appearing at the interface. Optionally, a boundary layer mesh with 5 layers, 4 iterations, a maximum cell depth of 6, and a smooth transition to the inner mesh is set at the interface between the black phosphorus quantum dots and the water medium to effectively describe the high temperature gradient appearing at the interface, resulting in... Figure 2 The geometric model and mesh division diagram shown are illustrated.

[0123] In some embodiments, step S500 may include, but is not limited to, steps S510 to S540:

[0124] Step S510: Based on the target simulation model, through simulation calculation, obtain the carrier-lattice temperature change curve, the lattice-water medium temperature change curve, and the water medium temperature distribution map of black phosphorus quantum dots under ultrafast laser action.

[0125] Step S520: Determine the generation of nanobubbles based on the water medium temperature in the water medium temperature distribution diagram. When the water medium temperature at the boundary is greater than or equal to the critical temperature of water, the moment when the water medium temperature at the boundary is greater than the first preset temperature is taken as the bubble formation time.

[0126] Step S530: The laser flux at the boundary when the highest water medium temperature is equal to the critical temperature of water is taken as the threshold laser flux.

[0127] Step S540: The region in the water medium temperature distribution map where the water medium temperature is greater than the second preset temperature is designated as the nanobubble region.

[0128] Before running the simulation, a suitable time step was selected in the COMSOL transient solver, and the tolerance term was set to user-defined with a relative error. Then, the simulation was run to obtain the water medium temperature change, and whether the water medium temperature exceeded a first preset temperature was set as the criterion for nanobubble prediction, thus achieving nanobubble prediction under black phosphorus quantum dot-mediated optical perforation. For example, a suitable time step and simulation time range were set, the tolerance term was set to user-defined, and the relative error was set to 0.001. After simulation, the following results can be obtained: Figure 3 The diagram shows the lattice temperature and water medium temperature of black phosphorus quantum dots changing over time. It also shows the carrier-lattice temperature variation curves and lattice-water medium temperature variation curves of black phosphorus quantum dots under ultrafast laser irradiation, as well as... Figure 4 The diagram shows the temperature distribution of the water medium. Next, the formation of nanobubbles can be determined by the temperature of the water medium; if the temperature of the water medium at the boundary exceeds the critical temperature T of water... c (T c =647K), then it can be considered that under the laser radiation of flux F, nanobubbles were generated around the black phosphorus quantum dots. The bubble generation time corresponds to the moment when the water medium temperature at the boundary exceeds 647K (i.e., the first preset temperature). At this time, the temperature in the water medium temperature distribution diagram is at 550K (approximately equal to 85% of T). c The region above the second preset temperature can be considered a nanobubble region, such as... Figure 4 As shown. Furthermore, based on this temperature criterion, the minimum laser flux required to generate nanobubbles from black phosphorus quantum dots, i.e., the threshold laser flux, was explored. The criterion is that at a threshold laser flux F... thr Under laser radiation, the highest temperature of the water medium at the boundary just exceeds 647K, which can be referenced. Figure 3 .

[0129] In summary, the overall processing flow of the COMSOL-based black phosphorus quantum dot-mediated photoporation bubble formation prediction method of this invention is as follows: Figure 5 As shown:

[0130] Step 1: Construct a two-dimensional axisymmetric transient model of solid-fluid heat transfer based on COMSOL.

[0131] Step 2: Construct the carrier density equation.

[0132] Step 3: Confirm the relevant physical parameters required for the simulation.

[0133] Step 4: Confirm the heat source settings and complete the coupling of each physical field.

[0134] Step 5: Mesh generation based on the geometric model.

[0135] Step 6: Predict nanobubble generation.

[0136] The formation of nanobubbles can then be determined by the temperature of the water medium. If the temperature of the water medium at the boundary exceeds the critical temperature T of water... c (T c =647K), that is, satisfying T w ≥T c Therefore, it can be assumed that under laser radiation with flux F, nanobubbles are generated around the black phosphorus quantum dots. The bubble generation time corresponds to the moment when the water medium temperature at the boundary exceeds 647K, at which point the temperature in the water medium temperature distribution diagram is around 550K (≈85% T). c The region described above can be considered a nanobubble region. If the temperature of the water medium at the boundary does not exceed the critical temperature of water, i.e., T... w <T c Then return to step 1: Construct a two-dimensional axisymmetric transient model of solid and fluid heat transfer based on COMSOL.

[0137] Furthermore, based on this temperature criterion, the minimum laser flux required to generate nanobubbles from black phosphorus quantum dots can be explored, i.e., the threshold laser flux. The criterion is that at a flux F... thr Under laser radiation, the highest temperature of the water medium at the boundary just exceeds 647K. For example, a preset laser flux is set, and under laser radiation of the preset flux, it is determined whether the highest temperature of the water medium at the boundary just exceeds 647K, i.e., whether the condition T is met. w,max =T c If the conditions are met, the preset laser flux will be output as the threshold laser flux; otherwise, the process will return to the step of setting the preset laser flux.

[0138] This invention also provides a COMSOL-based device for predicting bubble formation in black phosphorus quantum dot-mediated optical perforation, which can realize the above-mentioned COMSOL-based method for predicting bubble formation in black phosphorus quantum dot-mediated optical perforation. The device includes:

[0139] The first module is used to construct a two-dimensional axisymmetric transient model of solid heat transfer and fluid heat transfer based on COMSOL, so as to obtain the solid heat transfer module and the fluid heat transfer module.

[0140] The second module is used to set up the interface for coefficient-form partial differential equations and construct the carrier density equation.

[0141] The third module is used to pre-set intermediate physical parameters according to the carrier density equation;

[0142] The fourth module is used to pre-set heat source conditions based on the intermediate physical parameters, and couple the solid heat transfer module and the fluid heat transfer module according to the heat source conditions to obtain the target simulation model.

[0143] The fifth module is used to predict the generation of nanobubbles based on the target simulation model, and to obtain the bubble formation time, nanobubble region and threshold laser flux.

[0144] It is understood that the content of the above method embodiments is applicable to the present device embodiments. The specific functions implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0145] This invention also provides an electronic device, which includes a processor and a memory. The memory stores a computer program, and when the processor executes the computer program, it implements the aforementioned COMSOL-based method for predicting bubble formation in black phosphorus quantum dot-mediated optical perforation. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc.

[0146] It is understood that the content of the above method embodiments is applicable to this device embodiment. The specific functions implemented by this device embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0147] refer to Figure 6 , Figure 6 The hardware structure of an electronic device according to another embodiment is illustrated. The electronic device includes:

[0148] The processor 601 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of the present invention.

[0149] The memory 602 can be implemented in the form of read-only memory (ROM), static storage device, dynamic storage device, or random access memory (RAM). The memory 602 can store the operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 602 and is called and executed by the processor 601 to execute the bubble formation prediction method for black phosphorus quantum dot-mediated optical perforation based on COMSOL according to the embodiments of the present invention.

[0150] The input / output interface 603 is used to implement information input and output;

[0151] The communication interface 604 is used to enable communication and interaction between this device and other devices. Communication can be achieved through wired means (such as USB, network cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.).

[0152] Bus 605 transmits information between various components of the device (e.g., processor 601, memory 602, input / output interface 603, and communication interface 604);

[0153] The processor 601, memory 602, input / output interface 603, and communication interface 604 are connected to each other within the device via bus 605.

[0154] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned COMSOL-based method for predicting bubble formation in black phosphorus quantum dot-mediated optical perforation.

[0155] It is understood that the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0156] This invention also provides a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions, causing the computer device to perform the aforementioned COMSOL-based black phosphorus quantum dot-mediated bubble formation prediction method.

[0157] In summary, the bubble formation prediction method and apparatus for black phosphorus quantum dot-mediated optical perforation based on COMSOL according to the embodiments of the present invention have the following advantages:

[0158] This invention simulates the photothermal conversion of black phosphorus quantum dots under ultrafast laser irradiation and the thermophysical process by which these dots induce the formation of nanobubbles in the surrounding water medium. Based on this model, the bubble formation threshold flux and nanobubble generation time can be provided for black phosphorus quantum dot-mediated optical perforation technology, offering specific experimental optimization parameters for subsequent nanobubble imaging and capture experiments. This invention provides valuable theoretical guidance for black phosphorus-based optical perforation technology and offers experimental guidance for further exploration of this technology, demonstrating practical application value.

[0159] In some alternative embodiments, the functions / operations mentioned in the block diagrams may not occur in the order shown in the operation diagrams. For example, depending on the functions / operations involved, two consecutively shown blocks may actually be executed substantially simultaneously, or the blocks may sometimes be executed in reverse order. Furthermore, the embodiments presented and described in the flowcharts of this invention are provided by way of example to provide a more comprehensive understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is altered and sub-operations described as part of a larger operation are executed independently.

[0160] Furthermore, although the invention has been described in the context of functional modules, it should be understood that, unless otherwise stated, one or more of the described functions and / or features may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in a separate physical device or software module. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding the invention. Rather, given the properties, functions, and internal relationships of the various functional modules in the apparatus disclosed herein, the actual implementation of the module will be understood within the scope of conventional skill of an engineer. Therefore, those skilled in the art can implement the invention as set forth in the claims using ordinary techniques without excessive experimentation. It is also understood that the specific concepts disclosed are merely illustrative and not intended to limit the scope of the invention, which is determined by the full scope of the appended claims and their equivalents.

[0161] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0162] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0163] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0164] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0165] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0166] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

[0167] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of the present invention.

Claims

1. A method for predicting bubble formation in black phosphorus quantum dot-mediated optical perforation based on COMSOL, characterized in that, Includes the following steps: Based on COMSOL, a two-dimensional axisymmetric transient model of solid heat transfer and fluid heat transfer is constructed to obtain the solid heat transfer module and the fluid heat transfer module. Set up an interface for coefficient-form partial differential equations to construct carrier density equations; Based on the carrier density equation, intermediate physical parameters are pre-set; Based on the intermediate physical parameters, heat source conditions are preset, and the solid heat transfer module and the fluid heat transfer module are coupled according to the heat source conditions to obtain the target simulation model; Based on the target simulation model, the generation of nanobubbles is predicted, and the bubble formation time, nanobubble region, and threshold laser flux are obtained. The process of constructing a two-dimensional axisymmetric transient model of solid heat transfer and fluid heat transfer based on COMSOL to obtain the solid heat transfer module and the fluid heat transfer module includes the following steps: Select the solid heat transfer interface and the fluid heat transfer interface using COMSOL. Using COMSOL, construct the geometric regions of black phosphorus quantum dots and the geometric regions of water medium; The solid heat transfer module is obtained by setting the domain of the solid heat transfer interface to the geometric region of the black phosphorus quantum dot. The fluid heat transfer interface is set to the geometric region of the water medium to obtain the fluid heat transfer module; The process of setting up a coefficient-form partial differential equation interface to construct the carrier density equation includes the following steps: Configure the interface for the partial differential equation in coefficient form; The domain of the interface of the coefficient form partial differential equation is set as the geometric region of black phosphorus quantum dots to construct the carrier density equation; The carrier density equation characterizes the change in carrier density of black phosphorus quantum dots under ultrafast laser conditions. The interface for setting coefficient-form partial differential equations is used to construct the carrier density equation, and the formulas used include: ； in, Represents carrier density; Indicates time; This represents the change in carrier density over time. Indicates the linear absorption coefficient; Indicates Gaussian pulsed laser; This represents the photon energy absorbed when a single photogenerated carrier is generated. Indicates the nonlinear absorption coefficient; Indicates the composite coefficient of the composite center; Indicates the radiative recombination coefficient; This represents the Auger composite coefficient.

2. The bubble formation prediction method for black phosphorus quantum dot-mediated optical perforation based on COMSOL according to claim 1, characterized in that, The step of pre-setting intermediate physical parameters according to the carrier density equation includes the following steps: Based on the relationship between the thermophysical properties of black phosphorus quantum dots and the carrier density in the carrier density equation, the carrier heat capacity, lattice heat capacity, and carrier-lattice coupling coefficient are set. The charge carrier heat capacity and lattice heat capacity are set in the solid properties of the solid heat transfer module; The thermophysical properties of water media from COMSOL's material library are applied to the fluid heat transfer module; Set the initial temperature value of the solid heat transfer module and the initial temperature value of the fluid heat transfer module; The Gaussian pulse laser is set based on the laser flux, pulse width, and pulse peak time.

3. The bubble formation prediction method for black phosphorus quantum dot-mediated optical perforation based on COMSOL according to claim 1, characterized in that, The process of pre-setting heat source conditions based on the intermediate physical parameters, and coupling the solid heat transfer module and the fluid heat transfer module according to the heat source conditions to obtain the target simulation model includes the following steps: Based on the linear absorption coefficient, nonlinear absorption coefficient, Gaussian pulse laser, the photon energy absorbed when generating a single photogenerated carrier, and the band gap, the first volume heat source term is obtained. Based on the carrier-lattice coupling coefficient, carrier temperature, and lattice temperature, the second-body heat source term and the third-body heat source term are obtained; Based on the interfacial thermal conductivity, lattice temperature, and water medium temperature, the first boundary heat source term and the second boundary heat source term are obtained; Based on the first body heat source term, the second body heat source term, the third body heat source term, the first boundary heat source term, and the second boundary heat source term, the solid heat transfer module and the fluid heat transfer module are coupled to obtain the target simulation model.

4. The bubble formation prediction method for black phosphorus quantum dot-mediated optical perforation based on COMSOL according to claim 1, characterized in that, Before predicting nanobubble generation and obtaining bubble formation time and threshold laser flux based on the target simulation model, the following steps are also included: The geometric regions of black phosphorus quantum dots and water medium in the target simulation model are meshed.

5. The bubble formation prediction method for black phosphorus quantum dot-mediated optical perforation based on COMSOL according to claim 1, characterized in that, The step of predicting nanobubble generation based on the target simulation model to obtain bubble formation time, nanobubble region, and threshold laser flux includes the following steps: Based on the target simulation model, simulation calculations were performed to obtain the carrier-lattice temperature change curve, the lattice-water medium temperature change curve, and the water medium temperature distribution map of black phosphorus quantum dots under ultrafast laser irradiation. The formation of nanobubbles is determined based on the water medium temperature in the water medium temperature distribution diagram. When the water medium temperature at the boundary is greater than or equal to the critical temperature of water, the moment when the water medium temperature at the boundary is greater than the first preset temperature is taken as the bubble formation time. The laser flux at the highest water medium temperature at the boundary is equal to the critical temperature of water, which is taken as the threshold laser flux. The region in the water medium temperature distribution map where the water medium temperature is greater than the second preset temperature is defined as the nanobubble region.

6. A bubble formation prediction device based on COMSOL black phosphorus quantum dot-mediated optical perforation, characterized in that, include: The first module is used to construct a two-dimensional axisymmetric transient model of solid heat transfer and fluid heat transfer based on COMSOL, so as to obtain the solid heat transfer module and the fluid heat transfer module. The second module is used to set up the interface for coefficient-form partial differential equations and construct the carrier density equation. The third module is used to pre-set intermediate physical parameters according to the carrier density equation; The fourth module is used to pre-set heat source conditions based on the intermediate physical parameters, and couple the solid heat transfer module and the fluid heat transfer module according to the heat source conditions to obtain the target simulation model. The fifth module is used to predict the generation of nanobubbles based on the target simulation model, and to obtain the bubble formation time, nanobubble region and threshold laser flux. Specifically, the first module is used for: Select the solid heat transfer interface and the fluid heat transfer interface using COMSOL. Using COMSOL, construct the geometric regions of black phosphorus quantum dots and the geometric regions of water medium; The solid heat transfer module is obtained by setting the domain of the solid heat transfer interface to the geometric region of the black phosphorus quantum dot. The fluid heat transfer interface is set to the geometric region of the water medium to obtain the fluid heat transfer module; The second module is specifically used for: Configure the interface for the partial differential equation in coefficient form; The domain of the interface of the coefficient form partial differential equation is set as the geometric region of black phosphorus quantum dots to construct the carrier density equation; The carrier density equation characterizes the change in carrier density of black phosphorus quantum dots under ultrafast laser conditions. The formulas used in the second module include: ； in, Represents carrier density; Indicates time; This represents the change in carrier density over time. Indicates the linear absorption coefficient; Indicates Gaussian pulsed laser; This represents the photon energy absorbed when a single photogenerated carrier is generated. Indicates the nonlinear absorption coefficient; Indicates the composite coefficient of the composite center; Indicates the radiative recombination coefficient; This represents the Auger composite coefficient.

7. An electronic device, characterized in that, Including the processor and memory; The memory is used to store programs; The processor executes the program to implement the method as described in any one of claims 1 to 5.

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