Numerical simulation method for inter-drop dynamic behavior of immiscible solution in shear flow

Abstract

The invention provides a numerical simulation method for dynamic behaviors among immiscible solution drops in shear flow, and relates to the technical field of fluid mechanics, and the dynamic behaviors among immiscible solution drops in shear flow are calculated by combining microfluidic drop generation with dynamic strain mechanics test, constructing a water-in-oil drop interfacial membrane parameter correlation model and combining measured data of interfacial membrane strain response after progressive increase stress is applied. Systematic analysis on the initial state and the critical state of the boundary membrane is realized; the stability and the performance of the liquid drops in the shear flow are effectively optimized by identifying parameters influencing the critical state of the boundary membrane and implementing an adjusting strategy; em and Ub are accurately regulated and controlled based on definite physical and chemical parameters such as interfacial agent concentration, HLB value, temperature, pH and the like, and deformation and fracture behaviors of liquid drops in shear flow are optimized; the mechanical behavior of the liquid drop can always meet the design requirement, and accurate regulation and control are realized.

Description

Technical Field

[0001] The invention relates to the technical field of fluid mechanics, in particular to a numerical simulation method for dynamic behavior between immiscible liquid droplets in shear flow. Background Art

[0002] The researchers have systematically explored the behavior of water-in-oil droplets in shear flow by combining experiments with numerical simulations. These studies not only enhance the understanding of droplet dynamics, but also provide a basis for improving droplet stability and designing new emulsifiers. However, existing research has mainly focused on flow behavior at the macroscopic level, lacking in-depth analysis of microstructural details such as phase interfaces and boundary membranes. In addition, existing technical means are still insufficient in terms of the interaction mechanism between droplets and its impact on the behavior of boundary membranes. Under dynamic loading conditions, when droplets are subjected to stress, severe deformation and rupture of the boundary membrane may occur, and the dynamic mechanism behind it has not yet been fully revealed.

[0003] In the prior art, the publication number is CN118095131A, and the name is a numerical simulation method and device for self-migration of droplets on a wetting gradient rough surface, wherein the method includes: constructing a wetting gradient surface based on Young's equation; introducing a roughness factor based on the Wenzel model into the wetting gradient surface to construct a wetting gradient rough surface; based on an interface tracking method, performing numerical simulation calculations on the motion state of the self-migration of droplets on the wetting gradient rough surface; not only can the roughness be introduced into the numerical simulation, but also the motion morphology of the self-migration of droplets on the rough surface can be accurately captured; In the prior art, the research on the mechanical properties of droplet boundary membranes has the following significant deficiencies: there is still a lack of effective numerical simulation methods for the complex coupling behaviors between droplets under various shear flow conditions, especially the critical conditions for the instability of the boundary membrane. Related studies have shown that in many cases, under dynamic loading conditions, the correlation between the initial state parameters and the critical state parameters of the droplet boundary membrane is not clear, which leads to insufficient understanding of the interface stability analysis and rupture mechanism of the droplet; therefore, how to accurately characterize the state evolution of the boundary membrane and how to systematically link it with the dynamic behavior between droplets has become a new challenge and development direction; The above information disclosed in the above Background section is only for enhancement of understanding of the background of the present disclosure and therefore it may contain information that does not form the prior art that is already known to one of ordinary skill in the art. Summary of the invention

[0004] The object of the present invention is to provide a numerical simulation method for the dynamic behavior between immiscible liquid droplets in shear flow, so as to solve the problems raised in the above background technology.

[0005] To achieve the above object, the present invention provides the following technical solutions: A numerical simulation method for the dynamic behavior of immiscible liquid droplets in shear flow, the specific steps include: Step S1: preparing a plurality of water-in-oil droplet samples meeting the target design characteristics, wherein the water-in-oil droplet samples comprise an inner water phase core and an outer encapsulated oil phase, and the two phases are kept immiscible by a boundary membrane structure; Step S2: applying increasing stress to a plurality of water-in-oil droplet samples for dynamic loading, thereby stimulating the strain response of the boundary membrane of the water-in-oil droplet samples, and measuring the initial state parameters and critical state parameters of the boundary membrane of the water-in-oil droplet samples before and after the dynamic loading respectively; The critical state parameters of the limiting membrane are filtered, baseline drift corrected and dimensionless processed to obtain standardized critical state parameters of the limiting membrane; Step S3: constructing a bounding membrane parameter association model for the water-in-oil droplet sample, the input is the bounding membrane initial state parameter, and the output is the standardized bounding membrane critical state parameter; Step S4: inputting the initial state parameters of the boundary membrane of the current water-in-oil droplet sample into the constructed boundary membrane parameter association model to obtain a standardized boundary membrane critical state parameter output result, and comparing and analyzing the output result with the reference expected interval value to obtain a comparison analysis result; Step S5: determining the influencing factors that affect the critical state parameters of the boundary membrane, and implementing adjustment strategies for the influencing factors according to the comparison and analysis results, until the critical state parameters of the boundary membrane reach the reference expected interval value.

[0006] Compared with the prior art, the beneficial effects of the present invention are: by constructing a parameter correlation model of the bounding membrane of oil-in-water droplets, combined with the measurement data of the strain response of the bounding membrane after applying incremental stress, a systematic analysis of the initial state and critical state of the bounding membrane is achieved; and by identifying the parameters that affect the critical state of the bounding membrane and implementing an adjustment strategy, the stability and performance of the droplets in shear flow are effectively optimized. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Figure 1 It is a schematic diagram of the overall method flow of the present invention. DETAILED DESCRIPTION

[0008] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific embodiments.

[0009] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0010] Embodiment 1: See also Figure 1 , the present invention provides a technical solution: The numerical simulation method of the dynamic behavior of immiscible droplets in shear flow is applicable to the transport of immiscible droplets in biomedical microfluidic systems. The specific steps include: Step S1: using a microfluidic chip with a stable droplet generation structure, preparing a plurality of water-in-oil droplet samples that meet the target design characteristics, the water-in-oil droplet samples comprising an internal water phase core and an external encapsulated oil phase, the two phases being kept immiscible by a boundary membrane structure; the target drug component is contained in the water-in-oil droplet samples; Further explanation: Microfluidic chip design: adopts a multi-layer staggered channel structure to ensure clear channel partitioning, achieve stable oil-in-water droplet generation and controllability of shear flow; the design contains at least three independent feed channels: upstream water phase channel, oil phase channel, and interruption position shear flow channel.

[0011] Target drug ingredients refer to active molecules or compositions selected for specific therapeutic or diagnostic needs, which have well-defined biological activities and therapeutic functions and are optimized for pharmacokinetic and pharmacodynamic properties in the design of microfluidic systems to ensure effective encapsulation, stability, and release control in water-in-oil droplets; Material selection: A microfluidic chip made of polydimethylsiloxane (PDMS) combined with a glass substrate. This choice is not only due to the good air permeability and easy processing of the PDMS material, but also because the glass substrate provides the necessary mechanical stability and optical transparency, which is conducive to subsequent monitoring and verification experiments.

[0012] Control the flow rate and ratio of oil phase to water phase: Fluid delivery module: Equipped with high-precision injection pumps to control the flow rates of water and oil phases respectively. Select advanced modules to ensure accurate flow and long-term stable operation.

[0013] Flow rate setting: The size and number of water-in-oil droplets can be intuitively adjusted by precisely controlling the flow rate ratio of the water phase to the oil phase (e.g., 1:10 to 1:20 range). The step-wise difference in the flow rate ratio will promote the gradual realization of droplet formation from steady state to the dynamic control region.

[0014] In the flow rate ratio of water phase to oil phase, the oil phase flow rate is directly proportional to the increase of shear force, which can effectively decompose the droplet size, accurately control the droplet diameter and increase the generation rate; By utilizing the design of a microfluidic chip, the fluid flow rate at the oil-water interface is adjusted to control the velocity gradient of the shear flow, thereby obtaining multiple water-in-oil droplet samples; The oil-water interface refers to the boundary or contact area between two different liquids, the oil phase and the water phase; The initial state parameters of the boundary film include initial interfacial tension and surfactant concentration, where interfacial tension refers to the molecular interaction force between two immiscible phases, which can be directly measured by drop volume method, ring method or plate method; The critical state parameters of the bounding membrane include the elastic modulus Em and the rupture energy Ub of the bounding membrane of the water-in-oil droplet sample under the critical rupture condition; The shear rate under the velocity gradient at the oil-water interface is set to , The calculation formula is as follows: ; in, is the difference in flow rate between the oil phase and the water phase at the interface; is the lateral width at the oil-water interface; set up The value range of is the interval [SV1, SV2], SV1<SV2; Lower limit SV1: ensure that the droplet can detach from the fluid boundary mold; Upper limit SV2: avoid large shear force causing droplet breakage; When the shear rate is within the interval [SV1, SV2], the obtained water-in-oil liquid meets the target design characteristics; It should be noted that in the process of microfluidic droplet generation, water-in-oil droplets are generated by the shear force at the interface between the oil phase and the water phase: The source of shear force is the flow velocity difference between the oil phase and the water phase at the interface. ; Flow rate difference The larger it is, the stronger the shear forces on both sides of the interface are, and the smaller the size of the separated water-in-oil droplets is; In the experiment, the flow rate difference was adjusted The methods include: That is, the flow rates of the oil phase and the water phase in the two syringe pumps are controlled separately, which is directly related to the overall interfacial shear.

[0015] Reason for selection: Dynamic shear flow control can not only directly affect the separation and aggregation during the droplet formation process, but also improve the consistency and predictability of droplet generation. Compared with static mixing flow technology, this design greatly improves the efficiency and quality of droplet generation.

[0016] Droplet generation and monitoring are as follows: Real-time imaging observation: A high frame rate microscopic imaging system was introduced to timely record the formation process and dynamic changes of the morphology of oil-in-water droplets. This data will provide direct observational evidence for subsequent analysis and verification.

[0017] Use an automated data acquisition system: Integrate image recognition and data acquisition software to automatically analyze parameters such as the average diameter, spacing, and generation rate of droplets, and achieve full supervision and recording of the experimental process.

[0018] Defining target design features includes target mean diameter and target center-to-center distance between adjacent water-in-oil droplets; Target average diameter: It means selecting a unit surface area from the solution composed of generated oil-in-water droplets, and calculating the average diameter of all oil-in-water droplets in the unit surface area, and recording the value range of the target average diameter as [ASd1, ASd2], where ASd1 and ASd2 are the minimum and maximum values ​​of the target average diameter, respectively; Target center distance of adjacent water-in-oil droplets: indicates that the center distance of adjacent water-in-oil droplets is kept within the range of 2 to 5 times the diameter; In this embodiment: the target average diameters ASd1 and ASd2 are 10 μm and 50 μm respectively; within the unit surface area, they are in the range of 10 μm to 50 μm to meet different application requirements; The target center distance between adjacent droplets is maintained within the range of 2 to 5 times the diameter to ensure stable arrangement of droplets in the flow channel.

[0019] Step S2: applying increasing stress to a plurality of water-in-oil droplet samples for dynamic loading, thereby stimulating the strain response of the boundary membrane of the water-in-oil droplet samples, and measuring the initial state parameters and critical state parameters of the boundary membrane of the water-in-oil droplet samples before and after the dynamic loading respectively; The critical state parameters of the limiting membrane are filtered, baseline drift corrected and dimensionless processed to obtain standardized critical state parameters of the limiting membrane; Further explanation: 1.1) Selection and assembly of dynamic strain gauge equipment: A high-sensitivity dynamic strain gauge is selected, and a high-resolution optical imaging system is combined with the high-sensitivity dynamic strain gauge to form a "dynamic strain test module". The dynamic strain test module can simultaneously measure the deformation and rupture behavior of the boundary film of the droplet during the force process; Select the compression mode dynamic strain test platform (with parallel compression plate design to apply load evenly); the compression test module contains the following key components: An upper pressure plate, whose position and force intensity are precisely adjusted by a micron-level displacement controller; A fixed lower pressure plate with an oleophilic coating on its surface to enhance the stability of the droplet contact interface.

[0020] The dynamic strain test module and the high-precision real-time data acquisition system are integrated through the LabVIEW platform. LabVIEW is responsible for the design of the signal acquisition interface, the synchronous triggering of the force and displacement channels, and the data recording and real-time display functions. This integrated system is based on a high sampling frequency (such as above 10kHz) and a precise timing control algorithm to ensure the accuracy and real-time performance of data acquisition during the mechanical response of the droplet membrane.

[0021] 1.2) Installation and calibration of high-resolution imaging system: Equipped with a high frame rate microscopic imaging system (e.g. 1000fps high-speed camera) to capture the microscopic changes of the interface during the dynamic deformation of the droplet; The details of the droplet interface evolution are recorded by imaging equipment, while ensuring that the acquired images have sufficient frame rate and resolution to support subsequent digital image processing and analysis.

[0022] 2) Specific operation steps of droplet boundary film mechanical response test: 2.1) Droplet preparation and loading preparation: 2.11) Single droplet generation and fixation: The target oil-in-water droplets (O / W droplets) generated in step S1 are evenly dispersed in the microfluidic outlet area, and droplets that meet the target design characteristics are selected from them. The droplets are fixed in the middle of the lower pressure plate coated with the lipophilic substance by capillary adsorption or microneedle positioning.

[0023] 2.12) Environmental Control: The test device was placed in a constant temperature room at 20°C-25°C to avoid interference of ambient temperature on the physical stability and deformation characteristics of the droplets.

[0024] 2.13) Preparation for upper plate alignment: Start the micron-level displacement controller and adjust the upper pressure plate to about 100 μm away from the droplet, ensuring that the area between the two plates is in the clear focal plane of the optical lens.

[0025] 2.2) Gradually apply strain stimulation with controllable intensity and frequency: 2.21) Dynamic compression loading method: According to the actual application environment of the oil-in-water droplet of the target design feature, the strain range applied to the droplet is determined; based on the strain range, the strain is gradually applied to the droplet in a linearly increasing manner through the control program of the dynamic strain gauge, and the strain rate is set to 0.1μm / s to 1μm / s; At the same time, the frequency step is dynamically adjusted, gradually increasing to 1Hz at intervals of 0.1Hz. The load application stop point is the end point of droplet rupture, ensuring that the load-bearing strength gradually covers the critical point of droplet rupture.

[0026] 2.22) Real-time acquisition of droplet force and deformation data: During the test, the dynamic strain gauge will record the force value of the droplet under different loading intensities in real time, and monitor the deformation of the droplet through force sensors and optical deformation technology. At the same time, the droplet recovery behavior during the loading and unloading cycle is recorded to analyze its boundary membrane elastic modulus Em; 2.23) Obtaining the critical value of rupture: At the moment of droplet rupture, the maximum force value at the time of rupture is collected and combined with the maximum deformation value in the droplet deformation video record to calculate the rupture strength of the droplet boundary film and the boundary film rupture energy Ub.

[0027] 3) Optical imaging and data extraction in high-speed compression experiments: 3.1) High-speed imaging process: 3.11) Multi-angle imaging: With high-resolution microscopy and high-speed camera technology, the droplet deformation and rupture process can be recorded in real time from different angles (such as front view and side view) to ensure the integrity of subsequent image analysis; 3.12) Capturing the deformation of the boundary membrane: The microscopy system is used to clearly capture the continuous evolution of the boundary film morphology during droplet deformation, including droplet diameter, interface curvature changes, and rupture points.

[0028] 3.13) Digital image processing and mechanical parameter calculation: 3.14) Digital image processing to extract interface features: With the help of computer vision algorithms, MATLAB or Python is used to process the generated high-speed image sequences and extract the characteristic points of the droplet boundary film deformation, including: The maximum deformation diameter of the droplet interface; Dynamic changes in the droplet curvature radius; The precise location of the droplet breakup point and the interface morphology at the moment of breakup.

[0029] 3.15) Quantitative calculation of the elastic modulus Em of the boundary membrane: The initial state parameters of the boundary film, including the initial interfacial tension and the concentration of the surfactant, are respectively denoted as and ; In the process of applying increasing stress to multiple water-in-oil droplet samples, the force value and deformation change data of the oil-in-water droplet interface are collected in real time, and the elastic modulus Em of the boundary membrane of the oil-in-water droplet sample under the critical state parameters of the boundary membrane is calculated using the following formula: ; in, is the force change value, which indicates the incremental force value of the oil-in-water droplet from the initial unloaded state to the constant deformation value. The constant deformation value is characterized by the deformation value of the oil-in-water droplet at the moment before it breaks; is the maximum deformation of the water-in-oil droplet in the longitudinal direction; is the initial thickness of the water-in-oil droplet surface; is the projected surface area of ​​the water-in-oil droplet; It refers to the absolute value of the change in force that the water-in-oil droplet is subjected to during the strain stimulation process, that is, the incremental force value from the initial unloaded state to the constant deformation value during the loading process. Specifically: Use a dynamic strain tester to record the force value of the force sensor in real time during the water-in-oil droplet loading process. The sampling frequency is recommended to be set to above 10kHz to capture small force changes; Extract two key points during the loading process: the force value in the initial unloaded state and the force value when loaded to a constant deformation , the difference between the two is ; The constant deformation is characterized as the deformation of the water-in-oil droplet just before it breaks; Refers to the amount of compression deformation in the vertical direction caused by the force of the oil-in-water droplet during the dynamic stress loading process; the compression deformation in this embodiment is the height change of the droplet. This is an actual displacement, measured by a high-resolution optical system, specifically: The droplet changes during compression were captured in real time using a high-resolution optical microscope, and the initial droplet height was extracted by frame-by-frame image processing. and deformation height during loading , we can calculate: .

[0030] Initial thickness is an indirect measurement parameter, estimated by the following formula: ; in: is the interfacial tension, measured by the drop volume method or the hanging drop method; is the elastic modulus of the fluid, obtained by experimental fitting.

[0031] Refers to the two-dimensional projection area of ​​the oil-in-water droplet on the compression plate or microscopic field of view when stress is applied; through high-speed image recording equipment, the outline of the droplet is extracted in each frame of the image of the oil-in-water droplet shape change, and the projection area is obtained by binarization and pixel-by-pixel calculation. Specifically: Projected surface area of ​​water-in-oil droplet Calculated by digital image processing technology: First, a high-speed camera is used to record the projection profile of the water-in-oil droplet on the glass slide during the compression process; Binarize the image using software such as MATLAB or OpenCV. The projected contour points of the water-in-oil droplet in each loading frame are extracted and the geometric area is calculated.

[0032] Calculation of the boundary membrane rupture energy Ub: According to the energy conservation hypothesis, when the oil-in-water droplet is compressed to rupture, the boundary membrane rupture energy Ub required for rupture is equal to the total elastic energy stored in the droplet during the loading process before rupture. This total elastic energy is characterized as the deformation storage energy ; and then get ; Deformation energy storage The calculation is based on the relationship curve between the droplet force and deformation and the deformation range ; Combined with the mechanical response of the oil-in-water droplet membrane during stress dynamic loading, and based on the conservation of energy, the stress dynamic loading and deformation integral of the oil-in-water droplet deformation are calculated to obtain the droplet membrane rupture energy Ub; the droplet membrane rupture energy Ub reflects the balance between the deformation energy stored in the oil-in-water droplet membrane before rupture and the energy consumed after the final rupture. When the trapezoidal method is used in this embodiment to approximate the integral, the area under the relationship curve is divided into a plurality of small trapezoids, and the area of ​​each trapezoid is calculated and then accumulated; the formula is as follows: ; Parameter explanation: Ub represents the boundary membrane rupture energy of the oil-in-water droplet (unit: Joule, J); i represents the index number of the discrete deformation point marked on the oil-in-water droplet interface during the compression deformation process; and the total number of discrete deformation points is recorded as ; is the deformation at the i-th deformation point The corresponding loading stress (unit: Newton, N).

[0033] is the deformation of the ith deformation point (unit: meter, m), which specifically records the longitudinal deformation of the droplet when it is deformed under pressure; represents the deformation increment between the i-th deformation point and the i+1-th deformation point; represents the average value of the loading stress between the i-th deformation point and the i+1-th deformation point; by summing up the areas of all trapezoids, the approximate calculated boundary membrane rupture energy Ub is obtained; The product of loading stress and deformation is expressed as , represents the work done by the external force applied on the boundary membrane; The steps to obtain the standardized critical state parameters of the boundary membrane are as follows: The raw data collected in the experiment usually have noise interference, systematic baseline drift and measurement errors. In order to improve the accuracy of parameter data for droplet behavior simulation calculation, this embodiment proposes a feasible and optimized filtering and calibration method to process the raw data and improve the data quality. 3-1) Noise processing of the original data of boundary membrane parameters: 1. Raw data analysis: Read the collected original time series or data array of the limiting membrane elastic modulus Em and the limiting membrane rupture energy Ub.

[0034] Perform Fourier spectrum analysis on the data to detect high-frequency noise components and low-frequency baseline drift, and clarify the main frequency range of the noise; 2. Filter design: Wavelet Transform is used as the noise removal method for the following reasons: a. Compared with the traditional low-pass filter, wavelet transform is based on multi-resolution decomposition and can process high-frequency noise and slow drift components at the same time; b. It can perform local analysis on the original signal without causing signal smoothing and thus reducing important peaks.

[0035] Specific operations: Choose an appropriate wavelet basis function (such as Daubechies wavelet).

[0036] Set the number of decomposition layers; in this embodiment, the number of decomposition layers is 4-6 layers, which is adaptively adjusted according to the data length and sampling frequency; Threshold filtering is used for each layer of coefficients to remove high-frequency noise.

[0037] 3. Data recovery after filtering: The inverse wavelet transform is performed on the signal after wavelet decomposition and noise filtering to restore the smoothed elastic modulus Em and rupture energy Ub of the boundary membrane.

[0038] 3-2) Baseline drift correction: 1. Determine the baseline drift characteristics: The local polynomial fitting method is used to fit the signal baseline trend for the following reasons: a. The local polynomial fitting method can fit the local trend of the curve through a sliding window and has high robustness; b. By automatically fitting the baseline, errors caused by human intervention can be effectively avoided.

[0039] Specific operations: Set the window size to 5%-10% of the total data.

[0040] A second-order polynomial is used to fit the local trend within the sliding window to form a baseline drift curve.

[0041] 2. Baseline correction: The baseline drift curve obtained by fitting is directly subtracted from the filtered data to obtain the data after baseline drift is removed.

[0042] 3-3) Nonlinear error correction: There are systematic nonlinear errors in the measurement process (such as insufficient measurement accuracy of the sensor or instrument calibration deviation). In order to further optimize the data quality, nonlinear error correction is required.

[0043] 1. Establish error correction model: Use dual signal cross calibration method: Utilize the mathematical model between two related characteristics in the data measurement to automatically correct nonlinear deviations.

[0044] For the elastic modulus Em and rupture energy Ub of the boundary membrane, the boundary membrane tension ( The theoretical relationship between the elastic modulus Em and the rupture energy Ub of the boundary membrane is as follows: ; ; Limiting membrane tension Defined as the interfacial force per unit length; the interfacial force in this embodiment is the tensile force between the oil phase and the water phase; : A function describing the change of elastic modulus of the boundary membrane with the boundary membrane tension, derived based on the material mechanics model; is the elastic modulus Em of the limiting membrane and the tension of the limiting membrane The correlation function of : A function describing the relationship between the energy of membrane rupture and the membrane tension, derived based on the energy dissipation model; is the boundary membrane rupture energy Ub and the boundary membrane tension The correlation function of 2. Error correction calculation: Enter the experimentally obtained tension value; Use the pre-fitted calibration curve to replace the data with deviation points and correct the nonlinear measurement error to a reasonable range; 3-4) Data smoothing and standardization: 1. Data smoothing: The filtered and corrected data is smoothed using cubic spline interpolation to ensure data stability and no mutation, making the calculation more accurate. Cubic spline interpolation can ensure the second-order continuity of the data and is very suitable for processing droplet boundary film parameter data.

[0045] 2. Data Standardization: In order to make the subsequent numerical simulation more convenient, the corrected elastic modulus Em and rupture energy Ub data of the boundary membrane are dimensionless: The corrected elastic modulus Em and rupture energy Ub of the limiting membrane are respectively expressed as and ,Will and The output values ​​after dimensionless processing are recorded as and ; and The calculation formula is as follows: ; ; This formula compresses the elastic modulus Em and the rupture energy Ub of the boundary membrane to the interval [0,1], which is convenient for subsequent modeling calculation and comparative analysis; and The indices representing the minimum and maximum values ​​of the corresponding parameters, respectively.

[0046] Step S3: constructing a bounding membrane parameter association model for the water-in-oil droplet sample, the input is the bounding membrane initial state parameter, and the output is the standardized bounding membrane critical state parameter; Further explanation: The boundary membrane parameter association model is defined as follows: ; in, is the input vector; is the output vector; is a mapping function that maps an input vector to a corresponding output vector; It is an expression of linear regression or nonlinear fitting, or a machine learning model; The initial state parameters of the boundary membrane were obtained experimentally at different shear rates. Next and ; Using the established mapping function Calculate and obtain the corresponding standardized critical state parameter output of the boundary membrane, which includes and ; This embodiment provides the following nonlinear fitting method to determine the mapping function ; 1.1) Data preparation: Collect experimental data including input vectors and output vectors; 1.2) Nonlinear model assumption: Assume that the output parameter corresponding to the output vector is described by the following nonlinear function g: ; in, is a nonlinear function, represents the parameters that need to be determined in the nonlinear model, Represents the error term between the actual observation value and the model prediction value; Gradually adjust by gradient descent To minimize the error function, the parameters are finally determined ; 1.3) Model training and validation: Divide the experimental data into training set and validation set, use the training set to fit the nonlinear model, and use the validation set to evaluate the performance.

[0047] Nonlinear functions using fit results , calculate the predicted output under the new input parameters.

[0048] Step S4: inputting the initial state parameters of the boundary membrane of the current water-in-oil droplet sample into the constructed boundary membrane parameter association model to obtain a standardized boundary membrane critical state parameter output result, and comparing and analyzing the output result with the reference expected interval value to obtain a comparison analysis result; Further explanation: By shear rate The value range of is [SV1, SV2]; At shear rate In the value range [SV1, SV2] of ,and ; will be The critical state parameter of the boundary membrane corresponding to the value is recorded as and ; and Respectively expressed in Under the value, the elastic modulus and rupture energy of the boundary membrane after dimensionless processing; Will be in The initial state parameters of the boundary membrane corresponding to the value are recorded as and ; Based on multiple water-in-oil droplet samples that meet the target design characteristics, set and The reference expected interval values ​​are and ; when and If both are met, it means The water-in-oil droplets obtained under the given values ​​meet the expected requirements; , represents the second amplitude factor, , represents the first amplitude factor; and Determined by an expert group through statistical analysis or fuzzy analytic hierarchy process (FAHP); when and If at least one condition does not meet the requirement, it means The oil-in-water droplets obtained under the given values ​​do not meet the expected requirements.

[0049] Step S5: determining the influencing factors that affect the critical state parameters of the boundary membrane, and implementing adjustment strategies for the influencing factors according to the comparison and analysis results, until the critical state parameters of the boundary membrane reach the reference expected interval value.

[0050] Further explanation: the influencing factors include: surfactants related to the elastic modulus of the limiting membrane, and targeted triggering rupture conditions related to the rupture energy of the limiting membrane; when and When at least one of the conditions is not met, the following adjustment strategies for influencing factors are implemented: If exists When , it means that the elastic modulus of the boundary membrane is insufficient, indicating The deformation of the water-in-oil droplet obtained under the value is large; this indicates that the deformation amplitude of the droplet is large, that is, the elasticity of the boundary membrane is weak and cannot effectively suppress the deformation. It is easy to produce excessive deformation under the action of external forces (such as shear flow). Because the boundary membrane deforms too much under the action of force, the elasticity of the boundary membrane is insufficient. The boundary membrane of the droplet cannot effectively resist external stress and is prone to rupture; The elasticity of the boundary membrane is increased by selecting the surfactant, specifically: increasing the length of the hydrophobic chain; reducing the HLB value of the surfactant; introducing the polymer molecular chain structure; Increase the length of the hydrophobic chain; increasing the length of the hydrophobic chain helps to enhance the interaction between the interface molecules, increase the rigidity of the boundary membrane, and reduce deformation. For example, use long-chain fatty acids (such as C18) or long-chain alkyl polymers.

[0051] Lower the HLB value and adjust; choosing a surfactant with a lower HLB value (such as HLB4-6) can increase the hydrophobicity of the surfactant and further enhance the elasticity of the boundary membrane; Introduce polymer molecular chain structure; introduce high molecular weight polymer (such as PEG-100Stearate) to form a stronger membrane network structure; If exists When , it means that the elastic modulus of the boundary membrane is large, indicating The deformation of the water-in-oil droplet obtained under the value is small; by reducing the hydrophobic chain length of the surfactant; increasing the HLB value of the surfactant; using low molecular weight polymers or polymer-free systems to reduce the elastic modulus of the boundary membrane; until until; This indicates that the limiting membrane of the droplet is too rigid and lacks sufficient flexibility, which makes it difficult for the droplet to expand and adapt to external pressure when it ruptures; the limiting membrane of the droplet is too elastic and cannot effectively buffer the external shear stress, resulting in incomplete or delayed rupture of the droplet.

[0052] Reduce the hydrophobic chain length of the surfactant; Using shorter hydrophobic chains (such as C12 or C8) can reduce the van der Waals forces between molecules, reduce the rigidity of the boundary membrane, and increase the flexibility of the boundary membrane.

[0053] Increase the HLB value of the surfactant; Selecting a surfactant with a higher HLB value (such as HLB12-16) can enhance the hydrophilicity of the surfactant molecules, allowing them to form a more fluid structure on the surface of the boundary membrane, thereby reducing the rigidity of the boundary membrane.

[0054] Use low molecular weight polymers or polymer-free systems; Use low molecular weight surfactants (such as when the surfactant concentration is low), or reduce the proportion of polymers in the system to increase the fluidity and flexibility of the boundary film. Specifically: Prepare modified droplet solution: Add an appropriate amount of surfactant with a hydrophobic chain length of C18 at a concentration of .

[0055] The concentration of the introduced polymer (e.g. PEG-100Stearate) is set to . It is the abbreviation of "weight percent", which is used to express the mass percentage of a substance in the total mixture; If exists When The boundary membrane rupture energy of the oil-in-water droplet obtained under the value is insufficient, and the oil-in-water droplet will undergo extraction rupture, which is not conducive to the accurate release of the target drug components in the oil-in-water droplet. It is necessary to improve the targeted triggering rupture conditions of the oil-in-water droplet interface layer to increase the boundary membrane rupture energy until until; “Early critical state of rupture” means that the droplet ruptures under shear flow at a lower shear stress or earlier shear conditions than expected; this means that the droplet reaches the rupture state earlier than expected or under lower external forces during the force process; If exists In the case of , it means that the boundary membrane rupture energy is too large, which will cause the delayed release of the target drug components in the oil-in-water droplets. It is necessary to adjust the oil-in-water droplet interface layer to trigger the rupture conditions in a targeted manner, thereby reducing the boundary membrane rupture energy until until; Adjustment strategies for increasing the energy of membrane rupture: lower the ambient temperature; increase the pH fluctuation range of the solution; Lower the ambient temperature; control the system temperature to Below, in order to increase the viscoelasticity of the limiting membrane.

[0056] Increase the pH fluctuation of the solution; adjust the pH of the solution to a lower (such as pH 4) or higher (such as pH 10) level to affect the molecular structure of the interface and increase the rupture energy.

[0057] Adjustment strategies for reducing the energy of membrane rupture: increase the ambient temperature; reduce the pH fluctuation range of the solution.

[0058] 2. The specific steps are: Temperature Control: Use a thermostat to maintain the system temperature at .

[0059] pH adjustment: Add an appropriate amount of acid (such as HCl) or base (such as NaOH) to the system to adjust the pH of the solution to the target value (such as pH 4 or pH 10).

[0060] Adjust the shear rate: If you still need to further increase the fracture energy, reduce the shear rate to .

[0061] 4.2.2. Operation process: 1. Regulate ambient temperature and pH: The experimental environment temperature was set to .

[0062] Use a pH meter to accurately measure and adjust the solution pH to 4, and slowly add concentrated hydrochloric acid to the target pH value to achieve a stable solution environment.

[0063] 2. Repeat the experiment under optimized external conditions: Droplet deformation and breakup experiments were performed under adjusted temperature and pH conditions.

[0064] Numerical simulation calibration: Update the Ub value in the numerical model and re-simulate the droplet breakup process to ensure consistency with the experimental data.

[0065] By regulating the ambient temperature and pH, the physical and chemical properties of the boundary membrane can be effectively changed, thereby adjusting the rupture energy.

[0066] By precisely adjusting external conditions, precise control of droplet rupture behavior can be achieved to meet the needs of different application scenarios.

[0067] The beneficial effects brought by this embodiment are: Quantitative adjustment strategy: The boundary membrane is regulated through specific parameters (such as surfactant concentration, HLB value, temperature, pH, etc.) to achieve precise adjustment of the boundary membrane elastic modulus Em and the boundary membrane rupture energy Ub.

[0068] Systematic optimization process: From obtaining reference values, comparative analysis to specific adjustment measures, a closed-loop optimization process is formed to ensure that the droplet mechanical behavior meets the design requirements.

[0069] The above formulas are all dimensionless and numerical calculations. The formula is a formula for the most recent real situation obtained by collecting a large amount of data and performing software simulation. The preset parameters in the formula are set by technicians in this field according to actual conditions.

[0070] The above embodiments may be implemented in whole or in part by software, hardware, firmware or any other combination thereof. When implemented by software, the above embodiments may be implemented in whole or in part in the form of a computer program product. Those skilled in the art may appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein may be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed by hardware or software methods depends on the specific application and design constraints of the technical solution.

[0071] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, and may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0072] The above description is only a specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application.

Claims

1. A numerical simulation method for the dynamic behavior of immiscible liquid droplets in shear flow, characterized in that: The specific steps include: Step S1: preparing a plurality of water-in-oil droplet samples meeting the target design characteristics, wherein the water-in-oil droplet samples comprise an inner water phase core and an outer encapsulated oil phase, and the two phases are kept immiscible by a boundary membrane structure; Step S2: applying increasing stress to a plurality of water-in-oil droplet samples for dynamic loading, thereby stimulating the strain response of the boundary membrane of the water-in-oil droplet samples, and measuring the initial state parameters and critical state parameters of the boundary membrane of the water-in-oil droplet samples before and after the dynamic loading respectively; The critical state parameters of the limiting membrane are filtered, baseline drift corrected and dimensionless processed to obtain standardized critical state parameters of the limiting membrane; Step S3: constructing a bounding membrane parameter association model for the water-in-oil droplet sample, the input is the bounding membrane initial state parameter, and the output is the standardized bounding membrane critical state parameter; Step S4: inputting the initial state parameters of the boundary membrane of the current water-in-oil droplet sample into the constructed boundary membrane parameter association model to obtain a standardized boundary membrane critical state parameter output result, and comparing and analyzing the output result with the reference expected interval value to obtain a comparison analysis result; Step S5: determining the influencing factors that affect the critical state parameters of the boundary membrane, and implementing adjustment strategies for the influencing factors according to the comparison and analysis results, until the critical state parameters of the boundary membrane reach the reference expected interval value.

2. The method for numerical simulation of dynamic behavior between immiscible liquid droplets in shear flow according to claim 1, characterized in that: By utilizing the design of a microfluidic chip, the fluid flow rate at the oil-water interface is adjusted to control the velocity gradient of the shear flow, thereby obtaining multiple water-in-oil droplet samples; The oil-water interface refers to the boundary or contact area between two different liquids, the oil phase and the water phase; The initial state parameters of the boundary film include initial interfacial tension and surfactant concentration, where interfacial tension refers to the molecular interaction force between two immiscible phases; The critical state parameters of the bounding membrane include the elastic modulus Em and the rupture energy Ub of the bounding membrane of the water-in-oil droplet sample under the critical rupture condition; At the oil-water interface, the shear rate under the velocity gradient is set to , The calculation formula is as follows: ； in, is the difference in flow rate between the oil phase and the water phase at the interface; is the lateral width at the oil-water interface; set up When the value of is within the interval [SV1, SV2], the obtained water-in-oil liquid meets the target design characteristics, and SV1<SV2; Lower limit SV1: ensure that the droplet can detach from the fluid boundary mold; Upper limit SV2: avoid large shear force causing droplet breakage; Flow rate difference The larger the shear rate, the The larger it is, the stronger the shear forces on both sides of the interface are, and the smaller the size of the separated water-in-oil droplets is; Defining target design features includes a target mean diameter and a target center-to-center distance between adjacent water-in-oil droplets.

3. The method for numerical simulation of dynamic behavior between immiscible liquid droplets in shear flow according to claim 2, characterized in that: The initial state parameters of the boundary film, including the initial interfacial tension and the concentration of the surfactant, are respectively denoted as and ; In the process of applying increasing stress to multiple water-in-oil droplet samples, the force value and deformation change data of the oil-in-water droplet interface are collected in real time, and the elastic modulus Em of the boundary membrane of the oil-in-water droplet sample under the critical state parameters of the boundary membrane is calculated using the following formula: ； in, is the force change value, which indicates the incremental force value of the oil-in-water droplet from the initial unloaded state to the constant deformation value. The constant deformation value is characterized by the deformation value of the oil-in-water droplet at the moment before it breaks; is the maximum deformation of the oil-in-water droplet in the longitudinal direction, indicating the compression deformation of the oil-in-water droplet in the vertical direction caused by the force when the oil-in-water droplet changes from the initial unloaded state to the constant deformation; is the initial thickness of the water-in-oil droplet surface; is the projected area of ​​the droplet surface, which means the two-dimensional projected area of ​​the droplet in the compressed flat plate or microscopic field of view when the droplet is at a constant deformation amount; Combined with the mechanical response of the oil-in-water droplet boundary membrane during stress dynamic loading and based on the conservation of energy, the stress dynamic loading and deformation integral of the oil-in-water droplet deformation variable are calculated to obtain the boundary membrane rupture energy Ub of the oil-in-water droplet sample under the critical state parameters of the boundary membrane.

4. The method for numerical simulation of dynamic behavior between immiscible liquid droplets in shear flow according to claim 3, characterized in that: The corrected elastic modulus Em and rupture energy Ub of the limiting membrane are respectively expressed as and ; Will and The output values ​​after dimensionless processing are recorded as and ; At shear rate In the value range [SV1, SV2] of ,and ; will be The critical state parameter of the boundary membrane corresponding to the value is recorded as and ; and Respectively expressed in Under the value, the elastic modulus and rupture energy of the boundary membrane after dimensionless processing; Will be in The initial state parameters of the boundary membrane corresponding to the value are recorded as and ; The bounding membrane parameter association model is defined as follows: ； in, is the input vector; is the output vector; is a mapping function used to map an input vector to a corresponding output vector; set up and The reference expected interval values ​​are and ; when and If both are met, it means The water-in-oil droplets obtained under the given values ​​meet the expected requirements; , represents the second amplitude factor, , represents the first amplitude factor; when and If at least one condition does not meet the requirement, it means The oil-in-water droplets obtained under the given values ​​do not meet the expected requirements.

5. The method for numerical simulation of dynamic behavior between immiscible liquid droplets in shear flow according to claim 4, characterized in that: The influencing factors include: surfactants related to the elastic modulus of the limiting membrane, and targeted triggering rupture conditions related to the rupture energy of the limiting membrane; when and When at least one of the conditions is not met, the following adjustment strategies for influencing factors are implemented: If exists When , it indicates that the elastic modulus of the boundary membrane is insufficient. The deformation of the water-in-oil droplet obtained under the value is large; The adjustment strategy is to increase the length of the hydrophobic chain; reduce the HLB value of the surfactant, which represents the hydrophilic / lipophilic balance value; introduce the polymer molecular chain structure; If exists When , it means that the elastic modulus of the boundary membrane is large. The deformation of the water-in-oil droplet obtained under the value is small; The adjustment strategy is to reduce the hydrophobic chain length of the surfactant; increase the HLB value of the surfactant; use low molecular weight polymers or polymer-free systems to reduce the elastic modulus of the boundary membrane; until until; If exists When The boundary membrane rupture energy of the oil-in-water droplet obtained under the value is insufficient, and the oil-in-water droplet will undergo extraction rupture, which is not conducive to the accurate release of the target drug components in the oil-in-water droplet. The adjustment strategy is to improve the targeted triggering rupture conditions of the oil-in-water droplet interface layer, thereby increasing the boundary membrane rupture energy until until; If exists In the case of , it means that the boundary membrane rupture energy is too large, which will cause delayed release of the target drug components in the oil-in-water droplets. The adjustment strategy is to adjust the oil-in-water droplet interface layer to trigger the rupture conditions in a targeted manner, thereby reducing the boundary membrane rupture energy until until; Adjustment strategies for increasing the energy of membrane rupture: lower the ambient temperature; increase the pH fluctuation range of the solution; Adjustment strategies for reducing the energy of membrane rupture: increase the ambient temperature; reduce the pH fluctuation range of the solution.

Images