Numerical simulation method for dynamic behavior between immiscible droplets in shear flow

Abstract

The present invention provides a numerical simulation method for the dynamic behavior between immiscible liquid droplets in shear flow, which relates to the technical field of fluid mechanics. The present invention combines microfluidic droplet generation with dynamic strain mechanics testing, constructs a boundary membrane parameter correlation model for oil-in-water droplets, and combines the measurement data of the strain response of the boundary membrane after applying incremental stress to achieve a systematic analysis of the initial state and critical state of the boundary membrane; and through the identification of parameters affecting the critical state of the boundary membrane and the implementation of an adjustment strategy, effectively optimizes the stability and performance of the droplets in shear flow; based on clear physicochemical parameters such as surfactant concentration, HLB value, temperature, pH, etc., accurately controls Em and Ub, and optimizes the deformation and rupture behavior of the droplets in shear flow; it can ensure that the mechanical behavior of the droplets always meets the design requirements and achieve precise control.

Description

Technical Field

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

[0002] Researchers have systematically explored the behavior of water-in-oil droplets in shear flows 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 the boundary membrane. Under dynamic loading conditions, when droplets are subjected to stress, they may experience severe deformation and rupture of the boundary membrane, and the dynamic mechanism behind it has not yet been fully revealed.

[0003] In the prior art, the publication number is CN118095131A, entitled "A method and apparatus for numerically simulating the self-migration of a droplet on a wettability gradient rough surface," wherein the method comprises: constructing a wettability gradient surface based on Young's equation; introducing a roughness factor based on the Wenzel model into the wettability gradient surface to construct a wettability gradient rough surface; and numerically simulating the motion state of the droplet self-migration on the wettability gradient rough surface based on an interface tracking method; not only can the roughness be introduced into the numerical simulation, but the motion morphology of the droplet self-migration on the rough surface can also be accurately captured;

[0004] In the existing technology, the research on the mechanical properties of droplet boundary membranes has the following significant deficiencies: there is a lack of effective numerical simulation methods for the complex coupling behavior between droplets under various shear flow conditions, especially the critical conditions for boundary membrane instability. Related studies have shown that in many cases, under dynamic loading conditions, the relationship between the initial state parameters and 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;

[0005] The above information disclosed in this 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 a person of ordinary skill in the art. Summary of the Invention

[0006] 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.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] A numerical simulation method for the dynamic behavior of immiscible droplets in shear flow, including the following steps:

[0009] Step S1: preparing a plurality of water-in-oil droplet samples that meet target design characteristics, wherein the water-in-oil droplet samples comprise an inner water phase core and an outer encapsulating oil phase, and the two phases are kept immiscible by a boundary membrane structure;

[0010] Step S2: applying increasing stress to the plurality of water-in-oil droplet samples to perform dynamic loading, thereby stimulating the strain response of the bounding membrane of the water-in-oil droplet samples, and measuring the initial state parameters and critical state parameters of the bounding membrane of the water-in-oil droplet samples before and after the dynamic loading;

[0011] The critical state parameters of the limiting membrane are filtered, baseline drift corrected and dimensionless processed to obtain the standardized critical state parameters of the limiting membrane;

[0012] Step S3: constructing a bounding membrane parameter correlation model for the water-in-oil droplet sample, where the input is the initial state parameters of the bounding membrane and the output is the standardized critical state parameters of the bounding membrane;

[0013] Step S4: inputting the initial state parameters of the limiting membrane of the current water-in-oil droplet sample into the constructed limiting membrane parameter correlation model to obtain a standardized limiting membrane critical state parameter output result, and performing a comparison analysis on the output result and the reference expected interval value to obtain a comparison analysis result;

[0014] Step S5: determining the influencing factors affecting the critical state parameters of the limiting membrane, and implementing adjustment strategies for the influencing factors according to the comparison and analysis results, until the critical state parameters of the limiting membrane reach the reference expected range value.

[0015] Compared with the existing technology, 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 and implementing adjustment strategies for parameters affecting the critical state of the bounding membrane, the stability and performance of the droplets in shear flow are effectively optimized. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 Schematic diagram of the overall method of the present invention. DETAILED DESCRIPTION

[0017] 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 with reference to specific embodiments.

[0018] It should be noted that, unless otherwise defined, the technical or scientific terms used in the present invention should have the usual meanings understood by people with ordinary skills in the field to which the present invention belongs. The "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 position relationships. When the absolute position of the object being described changes, the relative position relationship may also change accordingly.

[0019] Example 1:

[0020] See also Figure 1 , the present invention provides a technical solution:

[0021] The numerical simulation method for 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:

[0022] Step S1: Using a microfluidic chip with a stable droplet generation structure, multiple water-in-oil droplet samples meeting target design characteristics are prepared. The water-in-oil droplet samples comprise an inner aqueous core and an outer encapsulating oil phase, with the two phases being immiscible through a boundary membrane structure. The target drug component is contained within the water-in-oil droplet samples.

[0023] Further explanation: Microfluidic chip design: A multi-layer staggered channel structure is used to ensure clear channel partitioning, achieve stable oil-in-water droplet generation and controllable shear flow; the design includes at least three independent feed channels: an upstream water phase channel, an oil phase channel, and an interruption position shear flow channel.

[0024] Target drug ingredients refer to active molecules or compositions selected for specific therapeutic or diagnostic needs. These ingredients have clear 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;

[0025] Material selection: A microfluidic chip using polydimethylsiloxane (PDMS) bonded to a glass substrate. This choice is based not only on the PDMS material's excellent gas permeability and ease of processing, but also on the glass substrate's mechanical stability and optical transparency, which facilitates subsequent monitoring and verification experiments.

[0026] Control the flow rate and ratio of oil phase to water phase:

[0027] Fluid Delivery Module: Equipped with a high-precision syringe pump to separately control the flow rates of the water and oil phases. Select advanced modules to ensure accurate flow rates and long-term stable operation.

[0028] Flow Rate Settings: Intuitively adjust the size and number of water-in-oil droplets by precisely controlling the water-to-oil flow rate ratio (e.g., 1:10 to 1:20). Stepwise changes in the flow rate ratio will gradually shift droplet formation from a steady state to a dynamically controlled region.

[0029] In the flow rate ratio of the water phase to the oil phase, the oil phase flow rate is directly proportional to the increase in shear force, which can effectively decompose the droplet size, accurately control the droplet diameter and increase the generation rate;

[0030] 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;

[0031] The oil-water interface refers to the boundary or contact area between two different liquids, the oil phase and the water phase;

[0032] The initial state parameters of the interfacial membrane include initial interfacial tension and surfactant concentration. Interfacial tension refers to the molecular interaction force between two immiscible phases and is directly measured by the drop volume method, ring method, or plate method.

[0033] The critical state parameters of the bounding membrane include the elastic modulus Em and the rupture energy Ub of the bounding membrane under the critical rupture conditions of the water-in-oil droplet sample;

[0034] The shear rate under the velocity gradient at the oil-water interface is set to , The calculation formula is as follows:

[0035] ;

[0036] 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;

[0037] set up The value range is the interval [SV1, SV2], SV1<SV2;

[0038] Lower limit SV1: ensures that the droplet can detach from the fluid boundary mold;

[0039] Upper limit SV2: avoid large shear force causing droplet breakage;

[0040] When the shear rate is within the interval [SV1, SV2], the obtained water-in-oil liquid meets the target design characteristics;

[0041] It should be noted that in the microfluidic droplet generation process, water-in-oil droplets are generated by the shear force at the interface between the oil phase and the water phase:

[0042] The source of shear force is the difference in flow rate between the oil phase and the water phase at the interface ;

[0043] Flow rate difference The larger it is, the stronger the shear force on both sides of the interface is, and the smaller the size of the separated water-in-oil droplets is;

[0044] In the experiment, the flow rate difference was adjusted The methods include:

[0045] 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.

[0046] Reason for selection: Dynamic shear flow control not only directly affects the separation and aggregation of droplet formation, but also improves the consistency and predictability of droplet generation. Compared with static mixing flow technology, this design greatly improves the efficiency and quality of droplet generation.

[0047] Droplet generation and monitoring are as follows:

[0048] Real-time imaging observation: A high-frame-rate microscopy system was introduced to record the formation process and dynamic changes in the morphology of water-in-oil droplets. This data will provide direct observational evidence for subsequent analysis and verification.

[0049] Use an automated data acquisition system: Integrate image recognition and data acquisition software to automatically analyze parameters such as the average droplet diameter, spacing, and generation rate, enabling full monitoring and recording of the experimental process.

[0050] Defining target design features includes target mean diameter and target center-to-center distance between adjacent water-in-oil droplets;

[0051] Target average diameter: This means selecting a unit surface area from the solution consisting of generated water-in-oil droplets and calculating the average diameter of all water-in-oil droplets within the unit surface area. The target average diameter range is recorded as [ASd1, ASd2], where ASd1 and ASd2 are the minimum and maximum values ​​of the target average diameter, respectively.

[0052] Target center distance between adjacent water-in-oil droplets: This means that the center distance between adjacent water-in-oil droplets should be kept within the range of 2 to 5 times the diameter;

[0053] In this embodiment, the target average diameters ASd1 and ASd2 are set to 10 μm and 50 μm respectively; within a unit surface area, they are within the range of 10 μm to 50 μm to meet different application requirements.

[0054] The target center distance between adjacent droplets is maintained in the range of 2 to 5 times the diameter to ensure stable arrangement of droplets in the flow channel.

[0055] Step S2: applying increasing stress to the plurality of water-in-oil droplet samples to perform dynamic loading, thereby stimulating the strain response of the bounding membrane of the water-in-oil droplet samples, and measuring the initial state parameters and critical state parameters of the bounding membrane of the water-in-oil droplet samples before and after the dynamic loading;

[0056] The critical state parameters of the limiting membrane are filtered, baseline drift corrected and dimensionless processed to obtain the standardized critical state parameters of the limiting membrane;

[0057] Further explanation: 1.1) Selection and assembly of dynamic strain gauge equipment:

[0058] 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 stress process;

[0059] Select a compression mode dynamic strain test platform (designed with parallel compression plates for uniform load application); the compression test module includes the following key components:

[0060] An upper pressure plate, whose position and force intensity are precisely adjusted by a micron-level displacement controller;

[0061] A fixed lower pressure plate with an oleophilic coating on its surface to enhance the stability of the droplet contact interface.

[0062] The dynamic strain testing module is integrated with a high-precision, real-time data acquisition system via the LabVIEW platform. LabVIEW is responsible for designing the signal acquisition interface, synchronously triggering the force and displacement channels, and performing data recording and real-time display. This integrated system, based on a high sampling frequency (e.g., above 10kHz) and precise timing control algorithms, ensures accurate and real-time data acquisition during the mechanical response of the droplet membrane.

[0063] 1.2) Installation and calibration of high-resolution imaging system:

[0064] Equipped with a high-frame-rate microscopic imaging system (e.g., a 1000fps high-speed camera) to capture the microscopic changes in the interface of the droplet during dynamic deformation;

[0065] 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.

[0066] 2) Specific steps for testing the mechanical response of droplet membranes:

[0067] 2.1) Droplet preparation and loading preparation:

[0068] 2.11) Single droplet generation and fixation:

[0069] The target water-in-oil droplets (O / W droplets) generated in step S1 are evenly dispersed in the microfluidic outlet area. Droplets that meet the target design characteristics are selected. The droplets are fixed in the center of the lower pressure plate coated with an oleophilic material through capillary adsorption or microneedle positioning.

[0070] 2.12) Environmental Control:

[0071] 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.

[0072] 2.13) Preparation for upper plate alignment:

[0073] 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.

[0074] 2.2) Gradually apply strain stimulation with controllable intensity and frequency:

[0075] 2.21) Dynamic compression loading method:

[0076] The strain range applied to the water-in-oil droplet is determined based on the actual application environment of the target design characteristics. Based on this strain range, the control program of the dynamic strain gauge gradually applies strain to the droplet in a linearly increasing manner, with the strain rate set between 0.1 μm / s and 1 μm / s.

[0077] The frequency is dynamically adjusted, increasing in 0.1Hz increments to 1Hz. The load application is stopped at the point where the droplet breaks, ensuring that the load-bearing strength gradually reaches the critical point of droplet breakage.

[0078] 2.22) Real-time acquisition of droplet force and deformation data:

[0079] During the test, the dynamic strain gauge records the force applied to the droplet at different loading intensities in real time, and monitors the droplet's deformation using force sensors and optical deformation technology. The droplet's recovery behavior during loading and unloading cycles is also recorded to analyze its elastic modulus Em.

[0080] 2.23) Obtaining the critical value of rupture:

[0081] 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.

[0082] 3) Optical imaging and data extraction in high-speed compression experiments:

[0083] 3.1) High-speed imaging process:

[0084] 3.11) Multi-angle imaging:

[0085] Combined with high-resolution microscopy and high-speed camera technology, the droplet deformation and breakup process is recorded in real time from different angles (such as front and side views) to ensure the integrity of subsequent image analysis;

[0086] 3.12) Capturing the deformation of the boundary membrane:

[0087] The microscopy system clearly captures the continuous evolution of the boundary membrane morphology during droplet deformation, including droplet diameter, interface curvature changes, and rupture points.

[0088] 3.13) Digital image processing and mechanical parameter calculation:

[0089] 3.14) Digital image processing to extract interface features:

[0090] Using 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:

[0091] Maximum deformation diameter of the droplet interface;

[0092] Dynamic changes in the droplet curvature radius;

[0093] The precise location of the droplet breakup point and the interface morphology at the moment of breakup.

[0094] 3.15) Quantitative calculation of the elastic modulus Em of the boundary membrane:

[0095] The initial state parameters of the boundary film, including the initial interfacial tension and surfactant concentration, are denoted as and ;

[0096] In the process of applying increasing stress to multiple water-in-oil droplet samples, the force 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:

[0097] ;

[0098] in, is the force change value, which represents the incremental force value when the oil-in-water droplet changes 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;

[0099] It refers to the absolute value of the change in force on the water-in-oil droplet during the strain stimulation process, that is, the incremental force value when the water-in-oil droplet changes from the initial unloaded state to the constant deformation during the loading process. Specifically:

[0100] Use a dynamic strain gauge to record the force sensor's force in real time during the water-in-oil droplet loading process. It is recommended that the sampling frequency be set to above 10 kHz to capture subtle force changes.

[0101] 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 ;

[0102] The constant deformation is characterized as the deformation of the water-in-oil droplet just before it breaks;

[0103] Refers to the vertical compressive deformation of a water-in-oil droplet caused by the force during dynamic stress loading. In this embodiment, the compressive deformation is the change in droplet height. This is an actual displacement, measured using a high-resolution optical system. Specifically:

[0104] The droplet changes during compression were captured in real time using a high-resolution optical microscope, and the initial droplet height was extracted through frame-by-frame image processing. and deformation height during loading , we can calculate: .

[0105] Initial thickness is an indirect measurement parameter and is estimated by the following formula:

[0106] ;

[0107] in: is the interfacial tension, measured by the drop volume method or the hanging drop method;

[0108] is the elastic modulus of the fluid, obtained by experimental fitting.

[0109] Refers to the two-dimensional projected area of ​​a water-in-oil droplet on a compression plate or microscopic field of view when stress is applied. High-speed image recording equipment is used to extract the droplet's outline in each frame of the image showing the change in the water-in-oil droplet's shape. The projected area is then calculated by binarization and pixel-by-pixel calculation. Specifically:

[0110] Projected surface area of ​​water-in-oil droplet Calculation was performed using digital image processing technology: First, a high-speed camera was used to record the projection profile of the water-in-oil droplet on the glass slide during the compression process;

[0111] Use software (such as MATLAB or OpenCV) to binarize the image;

[0112] The projected contour points of the water-in-oil droplet in each loading frame are extracted and the geometric area is calculated.

[0113] Calculation of the boundary membrane rupture energy Ub:

[0114] According to the energy conservation hypothesis, when the oil-in-water droplet is compressed to rupture, the 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 ;

[0115] Deformation energy storage The calculation is based on the relationship curve between the force and deformation of the droplet and the deformation range ;

[0116] Combining the mechanical response of the oil-in-water droplet membrane during dynamic stress 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 before rupture and the energy consumed after rupture.

[0117] This embodiment uses the trapezoidal method to approximate the integral, dividing the area under the relationship curve into multiple small trapezoids, and calculating the area of ​​each trapezoid and then accumulating them; the formula is as follows:

[0118] ;

[0119] Parameter explanation:

[0120] Ub represents the energy of rupture of the water-in-oil droplet boundary membrane (unit: Joule, J);

[0121] i represents the index number of the discrete deformation point marked on the interface of the oil-in-water droplet during the compression deformation process; and the total number of discrete deformation points is recorded as ;

[0122] is the deformation variable at the i-th deformation point The corresponding loading stress (unit: Newton, N).

[0123] is the deformation of the i-th deformation point (unit: meter, m), which specifically records the longitudinal deformation of the droplet when it is deformed under pressure;

[0124] represents the deformation increment between the i-th deformation point and the i+1-th deformation point;

[0125] represents the average value of the loading stress between the i-th deformation point and the i+1-th deformation point; by summing the areas of all trapezoids, the approximate calculated boundary membrane rupture energy Ub is obtained;

[0126] The product of loading stress and deformation is expressed as , represents the work done by the external force applied on the boundary membrane;

[0127] The steps to obtain the standardized critical state parameters of the limiting membrane are as follows:

[0128] The raw data collected in experiments often contain noise interference, systematic baseline drift, and measurement errors. To improve the accuracy of the parameter data used to simulate droplet behavior, this embodiment proposes a practical and optimized filtering and calibration method to process the raw data and improve data quality.

[0129] 3-1) Noise processing of the original data of the boundary membrane parameters:

[0130] 1. Raw data analysis:

[0131] Read the collected original time series or data array of the limiting membrane elastic modulus Em and limiting membrane rupture energy Ub.

[0132] 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;

[0133] 2. Filter design:

[0134] Wavelet Transform is used as the noise removal method for the following reasons:

[0135] a. Compared with traditional low-pass filters, wavelet transform is based on multi-resolution decomposition and can process high-frequency noise and slow drift components simultaneously;

[0136] b. It can perform local analysis on the original signal without causing signal smoothing and thus reducing important peaks.

[0137] Specific operations:

[0138] Choose an appropriate wavelet basis function (such as Daubechies wavelet).

[0139] 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;

[0140] Threshold filtering is used for each layer of coefficients to remove high-frequency noise.

[0141] 3. Data recovery after filtering:

[0142] 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.

[0143] 3-2) Baseline drift correction:

[0144] 1. Determine baseline drift characteristics:

[0145] The local polynomial fitting method is used to fit the signal baseline trend for the following reasons:

[0146] a. The local polynomial fitting method can fit the local trend of the curve through a sliding window and has high robustness;

[0147] b. By automatically fitting the baseline, errors caused by manual intervention can be effectively avoided.

[0148] Specific operations:

[0149] Set the window size to 5%-10% of the total data.

[0150] A second-order polynomial is used to fit the local trend within the sliding window to form a baseline drift curve.

[0151] 2. Baseline correction:

[0152] The fitted baseline drift curve is directly subtracted from the filtered data to obtain the data after baseline drift removal.

[0153] 3-3) Nonlinear error correction:

[0154] 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.

[0155] 1. Establish an error correction model:

[0156] Use dual-signal cross calibration: Utilize a mathematical model between two correlated characteristics in the data measurement to automatically correct nonlinear deviations.

[0157] 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:

[0158] ;

[0159] ;

[0160] 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;

[0161] : A function describing the change of the elastic modulus of the limiting membrane with the limiting membrane tension, derived based on the material mechanics model; is the elastic modulus Em of the boundary membrane and the tension of the boundary membrane The correlation function of

[0162] : 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

[0163] 2. Error correction calculation:

[0164] Enter the experimentally obtained tension value;

[0165] Use the pre-fitted calibration curve to replace the data with deviation points and correct the nonlinear measurement error to a reasonable range;

[0166] 3-4) Data smoothing and standardization:

[0167] 1. Data smoothing:

[0168] The filtered and corrected data are smoothed using cubic spline interpolation to ensure data stability and no sudden changes, resulting in more accurate calculations.

[0169] Cubic spline interpolation can ensure the second-order continuity of the data and is very suitable for processing droplet boundary film parameter data.

[0170] 2. Data standardization:

[0171] In order to make subsequent numerical simulations more convenient, the corrected boundary membrane elastic modulus Em and boundary membrane rupture energy Ub data are dimensionless:

[0172] The corrected elastic modulus Em and rupture energy Ub of the boundary 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:

[0173] ;

[0174] ;

[0175] This formula compresses the elastic modulus Em and the rupture energy Ub of the boundary membrane into 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.

[0176] Step S3: constructing a bounding membrane parameter correlation model for the water-in-oil droplet sample, where the input is the initial state parameters of the bounding membrane and the output is the standardized critical state parameters of the bounding membrane;

[0177] Further explanation: The bounding membrane parameter association model is defined as follows:

[0178] ;

[0179] in, is the input vector; is the output vector;

[0180] It is a mapping function that maps the input vector to the corresponding output vector; It is an expression of linear regression or nonlinear fitting, or a machine learning model;

[0181] The initial state parameters of the limiting membrane are obtained experimentally at different shear rates Next and ;

[0182] Using the established mapping function Calculate and obtain the corresponding standardized critical state parameter output of the boundary membrane, which includes and ;

[0183] This embodiment provides the following nonlinear fitting method to determine the mapping function ;

[0184] 1.1) Data preparation: Collect experimental data including input vectors and output vectors;

[0185] 1.2) Nonlinear model assumption: Assume that the output parameter corresponding to the output vector is described by the following nonlinear function g:

[0186] ;

[0187] 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;

[0188] Gradient descent method to gradually adjust To minimize the error function, the parameters are finally determined ;

[0189] 1.3) Model training and validation: Divide the experimental data into a training set and a validation set, use the training set to fit the nonlinear model, and use the validation set to evaluate the performance.

[0190] Use nonlinear functions of fitting results , calculate the predicted output under the new input parameters.

[0191] Step S4: inputting the initial state parameters of the limiting membrane of the current water-in-oil droplet sample into the constructed limiting membrane parameter correlation model to obtain a standardized limiting membrane critical state parameter output result, and performing a comparison analysis on the output result and the reference expected interval value to obtain a comparison analysis result;

[0192] Further explanation: By shear rate The value range of [SV1, SV2];

[0193] At shear rate In the value range [SV1, SV2], the jth shear rate corresponding to the preparation of the current water-in-oil droplet sample is recorded as ,and ; will be in 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;

[0194] Will be in The initial state parameters of the boundary membrane corresponding to the value are recorded as and ;

[0195] Based on multiple water-in-oil droplet samples that meet the target design characteristics, set and The reference expected interval values ​​are and ;

[0196] when and If all 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 panel through statistical analysis or fuzzy analytic hierarchy process (FAHP);

[0197] when and When at least one condition is not met, it means The water-in-oil droplets obtained under the given values ​​do not meet the expected requirements.

[0198] Step S5: determining the influencing factors affecting the critical state parameters of the limiting membrane, and implementing adjustment strategies for the influencing factors according to the comparison and analysis results, until the critical state parameters of the limiting membrane reach the reference expected range value.

[0199] 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;

[0200] when and When at least one of the conditions is not met, the following adjustment strategies for influencing factors are implemented:

[0201] If exists When the elastic modulus of the boundary membrane is insufficient, it means The deformation of the water-in-oil droplet obtained under the given value is large; this indicates that the droplet deformation amplitude is large, that is, the elasticity of the boundary membrane is weak and cannot effectively suppress 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.

[0202] The elasticity of the membrane is increased by selecting surfactants, specifically by increasing the length of the hydrophobic chain; reducing the HLB value of the surfactant; and introducing polymer molecular chain structure.

[0203] Increase the length of the hydrophobic chain; increasing the length of the hydrophobic chain helps strengthen the interaction between interfacial molecules, increase the rigidity of the membrane, and reduce deformation. For example, use long-chain fatty acids (such as C18) or long-chain alkyl polymers.

[0204] Lower the HLB value; choose a surfactant with a lower HLB value (such as HLB4-6) to increase the hydrophobicity of the surfactant and further enhance the elasticity of the boundary membrane;

[0205] Introducing polymer molecular chain structure; introducing high molecular weight polymers (such as PEG-100Stearate) to form a stronger membrane network structure;

[0206] 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;

[0207] 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 breaks; 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.

[0208] Reduce the hydrophobic chain length of the surfactant;

[0209] 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.

[0210] Increase the HLB value of the surfactant;

[0211] 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.

[0212] Use of low molecular weight polymers or polymer-free systems;

[0213] 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 membrane. Specifically:

[0214] Prepare modified droplet solution:

[0215] Add an appropriate amount of surfactant with a hydrophobic chain length of C18 at a concentration of .

[0216] The concentration of the introduced polymer (such as PEG-100Stearate) is set to . It is the abbreviation of "weight percent" and is used to express the mass percentage of a substance in the total mixture;

[0217] 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;

[0218] "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 stress process;

[0219] 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;

[0220] Adjustment strategies for increasing the energy of membrane rupture: lower the ambient temperature; increase the pH fluctuation amplitude of the solution;

[0221] Lower the ambient temperature; control the system temperature to Below, in order to increase the viscoelasticity of the limiting membrane.

[0222] Increase the pH fluctuation amplitude of the solution; adjust the pH of the solution to a lower (such as pH 4) or higher (such as pH 10) to affect the molecular structure of the interface and increase the rupture energy.

[0223] Adjustment strategies for reducing the energy of membrane rupture: increase the ambient temperature; reduce the pH fluctuation range of the solution.

[0224] 2. The specific steps are:

[0225] Temperature control:

[0226] Use a thermostat to maintain the system temperature at .

[0227] pH adjustment:

[0228] 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).

[0229] Adjust the shear rate: If you still need to further increase the fracture energy, reduce the shear rate to .

[0230] 4.2.2. Operation process:

[0231] 1. Regulate ambient temperature and pH:

[0232] The experimental environment temperature was set to .

[0233] Use a pH meter to accurately measure and adjust the pH of the solution to 4, and slowly add concentrated hydrochloric acid to the target pH value to achieve a stable solution environment.

[0234] 2. Repeat the experiment under optimized external conditions:

[0235] Droplet deformation and breakup experiments were performed under adjusted temperature and pH conditions.

[0236] Numerical simulation calibration: Update the Ub value in the numerical model and re-simulate the droplet breakup process to ensure consistency with experimental data.

[0237] 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.

[0238] By precisely adjusting external conditions, precise control of droplet breakup behavior can be achieved to meet the needs of different application scenarios.

[0239] The beneficial effects brought about by this embodiment are:

[0240] 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.

[0241] Systematic optimization process: From obtaining reference values ​​and comparative analysis to specific adjustment measures, a closed-loop optimization process is formed to ensure that the droplet mechanical behavior meets the design requirements.

[0242] The above formulas are all dimensionless and numerical calculations. The formulas are obtained by collecting a large amount of data and performing software simulation to obtain the most recent real situation. The preset parameters in the formulas are set by technicians in this field according to actual conditions.

[0243] The above embodiments can be implemented in whole or in part by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed by hardware or software depends on the specific application and design constraints of the technical solution.

[0244] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, and may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment as needed.

[0245] The above is only a specific implementation method of the present application, but the scope of protection of the present application is not limited thereto. Any technician familiar with this technical field can easily think of changes or replacements within the technical scope disclosed in this application, which should be covered by the scope of protection of the present application.

Claims

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

2. The method for numerically simulating the dynamic behavior between immiscible 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; 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: ensures 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 force on both sides of the interface is, and the smaller the size of the separated oil-in-water droplets is; Target design characteristics are defined including a target mean diameter and a target center-to-center distance between adjacent water-in-oil droplets.

3. The method for numerically simulating the dynamic behavior between immiscible 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 surfactant concentration, are denoted as and ; In the process of applying increasing stress to multiple water-in-oil droplet samples, the force and deformation change data of the oil-in-water droplet interface are collected in real time, and the elastic modulus Em 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 represents the incremental force value when the oil-in-water droplet changes 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, which indicates the compression deformation of the water-in-oil droplet in the vertical direction caused by the force when the droplet is initially unloaded and deformed to a constant value; is the initial thickness of the water-in-oil droplet surface; is the projected area of ​​the droplet surface, which represents 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; Combined with the mechanical response of the oil-in-water droplet's bounding 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's deformation are calculated to obtain the bounding membrane rupture energy Ub of the oil-in-water droplet sample under the critical state parameters of the bounding membrane.

4. The method for numerically simulating the dynamic behavior between immiscible droplets in shear flow according to claim 3, characterized in that: The corrected elastic modulus Em and rupture energy Ub of the boundary 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], the jth shear rate corresponding to the preparation of the current water-in-oil droplet sample is recorded as ,and ; will be in 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 the input vector to the corresponding output vector; set up and The reference expected interval values ​​are and ; when and If all 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 When at least one condition is not met, it means The water-in-oil droplets obtained under the given values ​​do not meet the expected requirements.

5. The method for numerically simulating the dynamic behavior between immiscible 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 means 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; and 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 the 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 target the trigger rupture conditions, 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 amplitude of the solution; Adjustment strategies for reducing the energy of membrane rupture: increase the ambient temperature; reduce the pH fluctuation range of the solution.

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