Rapid characterization of flow regimes in micro-packed bed reactors utilizing the convolutional neural network

Abstract

Micro-packed bed reactors (μPBRs), which are widely used in multiphase reactions, have the advantages of high mass transfer efficiency and excellent safety. However, the identification of flow behavior in μPBRs with various packings remains a challenge. Rapid characterization of flow regimes needs to be taken into consideration for improving reactor research efficiency. In this work, a transfer learning conventional neural network (CNN) based on LeNet-5 was developed to recognize the flow regime of μPBRs for the first time. Micropillars and spherical particles as typical packings were employed to inspect the applicability of the model successively. The flow regimes of μPBRs with micropillar structure and spherical particles were classified using a trained transfer learning model based on LeNet-5, obtaining high accuracies of 97.5% and 94.3%, respectively. Notably, a highly integrated software platform coupling the trained CNN for analyzing flow regime with a user-friendly graphical interface was constructed, achieving online acquisition and analysis of data efficiently.

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1. Introduction

Micro-packed bed reactors (μPBRs) were designed and filled with particle diameters lower than 500 μm in which gas and liquid concurrently flow down through the reactor.^1–4 The Bo number (the ratio of gravitational force and capillary force (ρ_L–ρ_G)gd_p²/σ) was less than 1 in μPBRs, indicating that capillary force significantly affects the gas–liquid flow behavior in μPBRs.^5–10 Numerous tiny liquid films and pockets as flow textures can be generated in the particle surface and interstitial space when liquid flows through the stationary packing layer of the μPBR. The mass transfer coefficient of the μPBR is at least one or two orders of magnitude higher than that of the traditional packed bed reactor. μPBRs were widely used in several applications such as hydrogenation,^11–15 oxidation,^16,17 reductive amination,¹⁸ kinetics studies,¹⁹ and catalyst screening.^20,21

Hydrodynamic characteristics were the research focus for enhancing the reactor performance, which was a crucial part of fundamental research. In the past few years, many studies have been published on the hydrodynamic characteristics of μPBRs, including flow regime,^22,23 residence time distribution,^1,23 liquid holdup,²⁴ and pressure drop.²⁵ Among them, flow regime offered a deeper perspective of the gas–liquid–solid three-phase flow in μPBRs with various packings. Identification of flow behavior remains vital and challenging for guiding the reactor design and optimization. Many researchers studied the gas–liquid flow behavior in μPBRs with pillars. Wada et al.²⁶ fabricated a μPBR with micropillars and observed slug, churn, and annular flows. Krishnamurthy et al.²⁷ obtained bridge flow in a μPBR with micropillars. Yang et al.²⁸ revealed the flow status in a micropillar-packed bed reactor by combining laser-induced fluorescence visualization and computational fluid dynamics simulation. Márquez et al.⁸ mimicked a real μPBR with various pillar sizes and arrangement types, reporting the snake flow phenomenon. To adapt the various industrial scenarios, many studies have been conducted on the flow behaviors in μPBRs with different packings. Faridkhou et al.²⁹ proposed low and high interaction flow regimes in the μPBR with spherical glass beads. Al-Rifai et al.⁵ used anomalous catalyst particles in μPBRs, exhibiting the transition of flow behavior from the liquid-dominated slug to the gas continuous-flow regime. Cao et al.³⁰ displayed a gas continuous pulsing flow regime at ultra-high gas velocity in μPBRs with copper particles. Recently, our group²² designed a 2D μPBR with glass beads and systematically studied the flow regime by coupling the pressure drop fluctuation and liquid spreading areal fraction. The study revealed four typical flow regimes: channel flow, churn flow, pseudo-static flow, and parallel flow. In the above-mentioned studies, flow regimes were obtained and presented based on direct visual observation by handling numerous experimental data manually, leading to low analytical efficiency. The different packing types, various operation conditions, and complex inner status caused by the small particles and tiny interstitial channels induced the complexity of gas–liquid flow behavior in the μPBRs. Therefore, rapid characterization and identification of flow regimes in the μPBRs need to be taken into consideration for improving reactor research efficiency.

With the development of artificial intelligence (AI), deep learning played a critical role in multiphase flow behavior studies increasingly. Zhang et al.³¹ proposed a state-of-the-art deep learning-based method to measure the bubble size and distribution in gas–liquid two-phase flow, demonstrating that the measurement efficiency using a convolutional neural network (CNN) increased 1000 times compared with manual calculation. Lu et al.³² achieved the classification of gas–solid flow regimes with an accuracy of 100% and an identification speed of 55.86 ms per image in a fluidized bed by trained CNN. Shen et al.³³ developed an automatic liquid–liquid two-phase flow regime recognition platform based on CNN algorithms, which achieved high-throughput experimentation for microchannels and facilitated the creation of a generalized liquid–liquid two-phase flow map. Urbina-Salas et al.³⁴ applied the CNN to classify gas–liquid two-phase flow regimes in vertical pipes. The results showed that the CNN achieved 90% accuracy for identifying five flow patterns. However, the flow behavior discrimination in the gas–liquid–solid three-phase reactor based on deep learning was scarce. In addition, research utilizing the CNN to identify the flow regime of μPBRs was not yet available because of the complexity of gas–liquid flow inside the reactor.

In this work, a convolutional neural network was developed to rapidly identify the flow regimes of the μPBR for the first time. Research strategies which include two steps were considered and displayed. Firstly, the gas–liquid flow behaviors in μPBRs with structured micropillars were captured by a high-performance camera, and images were used to train the skeleton structure of the CNN. Subsequently, the images of gas–liquid flow behaviors from the μPBRs with spherical glass beads were employed and processed to inspect the applicability of the CNN for the diversity of packing. Impressively, a highly integrated automatic software platform was designed and presented, which incorporated the trained CNN for analyzing flow regimes, achieving online acquisition for data analysis efficiently.

2. Methodology

2.1 Convolutional neural network architecture

Convolutional neural networks provide a promising approach for characterizing hydrodynamics in multiphase reactors rapidly. Much attention was given to this field and various network architectures were proposed in the past few years, including the LeNet-5,³³ AlexNet,³⁵ ResNet-50,³⁵ VGG-16,³⁶ InceptionV1,³⁷ and MobileNetV2.³⁸ Among them, LeNet-5 is a classical CNN architecture that was successfully employed in hand-written recognition. It includes three typical layers: convolutional, pooling, and fully connected layers. The specific structure is shown as follows:

(I) Convolution layer (C1): the number of filters is 6, and 5 × 5 convolutional kernels with a stride of 1 and no zero padding are applied.

(II) Pooling layer (S2): a pooling core of 2 × 2 is utilized.

(III) Convolution layer (C3): the number of filters is 6, and 5 × 5 convolutional kernels with a stride of 1 and no zero padding are applied.

(IV) Pooling layer (S4): the core of the pooling layer is also set to 2 × 2.

(V) Fully connected convolutional layer (C5): comprises 120 feature maps and each unit is linked to a 5 × 5 block on S4 feature maps.

(VI) Fully connected layer (F6): 84 neurons are contained and it employs the sigmoid activation function.

(VII) Output layer: the classification task consists of 10 neurons and employs the softmax function for multi-class predictions to the digits from 0 to 9.

Parameters such as convolutional kernels, stride, and padding have been extensively employed and reported in relevant literature.^39–41

Flow regimes in gas–liquid–solid three-phase reactors are usually intricate. Specifically, the LeNet-5 model shows significant potential for application in packed bed reactors owing to low computational requirement and processing time for addressing the complexity of the recognition task.

In this study, a transfer learning model based on the LeNet-5 was developed to classify the flow regimes of μPBRs, as presented in Fig. 1. Based on the preliminary experimental data, initial explorations on the CNN architecture, including parameters adjustment iteratively such as the number of convolutional layers, kernel sizes, and fully connected layers to optimize its performance, were conducted for flow pattern recognition tasks in μPBRs.

Fig. 1 Schematic diagram of the CNN structure for flow regime identification in the μPBR.

The input layer of LeNet-5 was preprocessed to 120 × 192 × 3 pixels. Five convolutional layers (C1, C3, C5, C7, and C9), including 32 × 64 convolutional kernels, strides of 8, 16, 32, 64, and 128, and no zero padding, were utilized to extract the feature of images, respectively. As the core component in feature learning, convolutional layers were designed to capture local spatial features within input images, such as edge contours, textural gradients, and morphological primitives, which significantly reduced the number of trainable parameters and computational overhead compared to fully connected architectures, preserving the spatial hierarchy of features.

Four max-pooling layers (S2, S4, S6 and S8) with a 2 × 2 pooling region and a stride of 2 were used to reduce the computation while maintaining the feature of images. Operating on the feature maps output by convolutional layers and pooling layers achieved dimensionality reduction and feature selection by computing the maximum value within each non-overlapping subregion. This process alleviates the computational burden for subsequent layers and enhances the model's invariance to shrink translations or distortions in input patterns, improving robustness against noise and subtle variations in the input data.

Then, the extracted features were fed into a fully connected hidden layer (F10) with 100 neurons using the sigmoid activation function. In the latter stage of the network, fully connected layers established dense interconnections from each neuron to all neurons in the preceding layer. Their primary role is to integrate high-level abstract features into a flattened representation. By learning complex nonlinear mappings between aggregated features and output labels, they enable the network to derive final decision-making criteria based on a comprehensive representation of the input data.

The output layer was a softmax layer with multiple neurons for different flow regimes, specifically for the classification task in μPBRs. In this work, images were extracted from the captured gas–liquid flow videos and manually labeled to form the dataset for CNN training.

2.2 Confusion matrix

A confusion matrix is a valuable tool for evaluating the performance of the classification model, illustrating the comparison of predicted and actual labels.⁴² The diagonal elements of the confusion matrix represent the number of correct classified samples, reflecting the model accuracy for each class. Non-diagonal elements indicate the number of misclassifications about the inaccurate classified samples made by the model.

True positives (TPs) represent the number of instances where the model correctly predicted a specific flow pattern, aligning the predicted flow pattern with the actual flow pattern. True negatives (TNs) refer to the number of samples that the model predicted results as negative correctly when they are actually negative. Specifically, the elements from the diagonal upper parts are defined as false positives (FPs), which are the samples about incorrectly predicted results as positive when they are actually negative. The elements from the diagonal lower parts denote false negatives (FNs), representing the samples that are incorrectly predicted as negative when they are actually positive. The schematic of the confusion matrix is shown in Fig. 2.

Fig. 2 Schematic diagram of the confusion matrix.

The following criteria are commonly used to evaluate the accuracy and sensitivity of the trained model, which is calculated by the values inside the confusion matrix. Precision indicates the proportion of predicted positive samples that are actually positive (the proportion of correct predictions among the total predictions for a given flow regime); it can be calculated as:

In general, a high precision value indicates that the model has strong predictive capability for the given dataset, allowing it to identify the target categories accurately.

Recall (known as sensitivity or true positive rate) is defined as the proportion of actual positive instances (a specific flow pattern) that are correctly identified by the model's results. It is used to evaluate the model's monitoring coverage of all target instances. The formula for recall calculation is:

F1 score (F1s) is the harmonic mean of precision and recall, providing a balance about the above two parameters (the larger the F1s, the better the overall performance); it can be calculated as:

Accuracy represents the overall correctness of the prediction model, as shown in eqn (4).

3. Experimental section

To obtain high-resolution images for flow regime identification and train the skeleton structure of the CNN, a highly transparent μPBR with micropillars was fabricated using 3D printing technology. Specifically, the fabrication process used TOP11BT photosensitive resin as the printing material and employed stereolithography (SLA) photopolymerization technology using a Shanghai UnionTech Lite800HD-B 3D printer. The dimensions of the μPBR were 30 mm length, 6 mm width, and 0.4 mm depth. A T-junction inlet mixer with a horizontal channel (1 mm width and 0.6 mm depth) for the liquid phase and a vertical channel (0.4 mm width and 0.6 mm depth) for the gas phase were printed synchronously. Fig. 3 shows the structural diagram of the μPBR with micropillar packing used in this work (3D view and top view). The diameter of a single micropillar was 150 μm, and the center distance was 300 μm among the adjacent micropillars in horizontal and vertical directions.

Fig. 3 Structural diagram of the μPBR with micropillars in this work.

The schematic overview of the experimental setup is shown in Fig. 4. A syringe pump (0–10 mL min⁻¹) and a mass flow controller (MFC, 0–100 mL min⁻¹) were used to control the liquid (water) and gas (N₂) flow rates, respectively. The liquid and gas phases were injected into the horizontal and vertical channels. Mixed by a T-junction mixer, the gas–liquid mixture flowed into the reactor, traversing the whole reactor space and exhibiting various flow regimes. Moreover, the μPBR was installed on a moveable platform, allowing rapid observation of different positions along the axial direction of the reactor. This work maintained the experimental temperature at 20 °C under atmospheric pressure. Each experiment was repeated at least three times to minimize experimental error. Detailed information on the μPBR, T-junction mixer, micropillar size, and operation conditions is summarized in Table 1.

Fig. 4 Schematic diagram of the experimental setup in this work.

Table 1 Detailed information on the μPBR, T-junction mixer, pillar size, and operation conditions in this study

Items	Unit	Values
μPBR
Length	mm	30
Width	mm	6
Depth	mm	0.4
T-junction mixer
Liquid inlet width	mm	1
Gas inlet width	mm	0.4
Micropillar structure
Diameter	μm	150
Height	μm	400
Center distance of adjacent pillars	μm	300
Void fraction	%	81.58
Operating conditions
Liquid superficial velocity	mm s^−1	1–10
Gas superficial velocity	mm s^−1	10–400
Temperature	°C	20
Pressure	kPa	101.3

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Specifically, an online observation platform was constructed, which consisted of a high-performance CCD camera (acA1920-160um, Basler Corp., Germany) with a 1920 × 1200 pixels resolution and a microscope lens (View Solutions, USA). For different gas/liquid superficial velocities, flow behavior images in the μPBRs were captured with a field of view zone measuring 11 mm × 6.875 mm. Several lamps were positioned at the back of the reactor to ensure a uniform visible field of view.

4. Results and discussion

4.1 Flow regime identification in the μPBR with micropillar structure

Flow regimes are significantly affected by various factors, including the type of gas distributor, liquid physical properties, particle wettability, and gas/liquid superficial velocities.^43,44 In the T-junction inlet mixer, the liquid phase flows in the horizontal channel and the gas phase flows in the vertical channel. Based on the observation platform used in this work, three typical flow regimes—slug flow, churn flow, and pseudo-static flow—were obtained in the μPBR with micropillar structure, as shown in Fig. 5.

Fig. 5 Flow regime characterization in the μPBR with small pillar structures. (a) Slug flow (U_L = 4 mm s⁻¹, U_G = 15 mm s⁻¹), (b) churn flow (U_L = 4 mm s⁻¹, U_G = 50 mm s⁻¹), (c) pseudo-static flow (U_L = 4 mm s⁻¹, U_G = 200 mm s⁻¹).

Slug flow was formed at low gas superficial velocities, where the gas was dispersed under the shear effect of the liquid phase, creating gas columns that flow through the reactor (Fig. 5(a)). Both gas and liquid were dispersed phases under the slug flow, and this regime is presented in Video S1(a) of the SI. With the increase of gas superficial velocity, a drastic gas–liquid interaction resulted in the churn flow regime, where the gas and liquid were observed as continuous phases (Fig. 5(b)). The violent interaction between the liquid and the solid packing induced an intense gas–liquid flow status characterized by a large range of gas–liquid dispersion within the reactor. This regime is displayed in Video S1(b) of the SI. With a further increase of gas superficial velocity, the gas and liquid phases were segregated and formed a pseudo-static flow regime due to the high gas–liquid ratio, as shown in Fig. 5(c). In this regime, the gas and liquid phases occupied the upper and lower sides of the reactor, as shown in Video S1(c) of the SI. More details regarding the classification and definition of flow regimes have been reported in our previous work and other relevant studies.^22,28

Fig. 6(a) shows the typical images of different flow regimes in the μPBR with micropillar structure. Over 1000 images representing various flow regimes were used to train the model. These images were randomly partitioned into two datasets: 70% of the images were allocated to the training set, while the remaining 30% were assigned to the test set for assessment purposes. The initial weight and basis of the network were random small values and updated using the backpropagation technique.^45,46 A stochastic gradient descent with momentum (SGDM) optimizer was employed to train the model. SGDM was commonly used as an optimization algorithm that combined the stochastic gradient descent and momentum methods, accelerating convergence and mitigating data fluctuation. The initial learning rate was set to 0.0001, and the maximum number of training rounds was set to 10 in this work. Additionally, the training data were randomly rearranged after each epoch to prevent overfitting.

Fig. 6 Flow regime images and confusion matrix in this work. (a) Input images, (b) confusion matrix.

Fig. 6(b) shows the confusion matrix of the trained CNN for the μPBR with micropillar structure. According to the results of the confusion matrix, precision, recall, F1 scores, and accuracy for each flow regime from the trained LeNet-5 model are summarized in Table 2. Notably, the trained LeNet-5 model rapidly recognized flow regimes of the μPBR with micropillar structure with at least 97.5% accuracy.

Table 2 The evaluation metrics of the trained LeNet-5 model with pillar structure

Items	Precision	Recall	F1 score	Accuracy
Slug flow	0.979	1	0.989	0.989
Churn flow	1	0.949	0.974	0.986
Pseudo-static flow	0.932	0.944	0.938	0.975

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Fig. 7 depicts the flow regime map based on the trained CNN model. For the flow regime classification process, the specific steps are as follows: firstly, a high-performance camera is used to capture images of flow regimes in the reactor under different gas–liquid superficial velocities. Subsequently, the collected images are input into a trained CNN for flow regime recognition to determine the flow patterns corresponding to each operating condition. Finally, by systematically acquiring and identifying flow pattern images under various operating conditions, a gas–liquid flow pattern map within the entire operating range is ultimately constructed.

Fig. 7 Flow regime map in the μPBR with micropillar structure.

The predicted results indicate that slug flow was formed easily at low gas superficial velocities (U_G) and high liquid superficial velocities (U_L). As the gas superficial velocity increased, the flow regime transitioned from slug flow to churn flow. At ultra-high gas superficial velocities, the churn flow further transitioned into a pseudo-static flow. These results were consistent with previous findings observed in μPBRs with circular packing.²²

To verify the suitability of the trained model, the data from published studies were considered. In 2015, Yang et al.²⁸ studied the gas–liquid flow and liquid/liquid biphasic flow in microreactor with the micropillar structure by laser-induced fluorescence visualization. Differences in the inlet mixer and pillar gaps within the reactor affect the flow regime characteristics. Under the experimental conditions reported by Yang et al., the flow regimes observed in the reactor primarily consist of slug flow, churn flow, annular flow, and slug/annular flow, as depicted in Fig. 8(a).

Fig. 8 Suitability of the trained LeNet-5 model for published results. (a) Image of Yang et al.'s study,²⁸ (b) values of the confusion matrix.

A total of 400 images were obtained by cropping their videos for different flow regimes (100 images for each flow regime) to evaluate the model. Fig. 8(b) shows the information on the confusion matrix based on the trained model. The values of non-diagonal elements were nearly zero, indicating that the trained model exhibited high reliability and accuracy (96.7%) in identifying the flow regime of the μPBR with micropillar structure.

4.2 Flow regime identification in the μPBR with spherical particles

Spherical particles as packings or catalysts are widely used in gas–liquid–solid multiphase reactions. However, the limitation of the micro-scale and sophisticated inner status caused by the small dense particles and tiny interstitial channels inevitably brings considerable challenges for gas–liquid flow behavior study. In our previous studies, the flow regimes of μPBRs filled with spherical particles were extensively studied based on direct visual observation by handling numerous experimental data manually with low analytical efficiency.^22,47 Four typical flow regimes were captured, which were channel flow, churn flow, pseudo-static flow, and parallel flow. By integrating automated image processing and deep learning techniques, this section aims to improve the efficiency and precision of flow regime identification, enabling more accurate classification in complex multiphase flow systems.

The original images of gas–liquid flow behavior about the μPBR with spherical particles are shown in Fig. 9 from our previous study.²² The small and dense particles within the μPBR induce strong capillary forces that significantly affect the gas–liquid flow status, leading to substantial liquid retention among the particle interstices. When original images of different flow regimes were directly inputted into the deep learning network for classification, notable recognition errors were observed due to the high liquid holdup and dense particles. To address this, a frame difference method was considered and applied to preprocess images for constructing the dataset to train the model. After processing the gas–liquid flow images via the frame difference method, black denotes the invariant elements within the reactor during gas–liquid flow, whereas white signifies the changes between two successive frames.

Fig. 9 Original and processed images of different flow regimes in the μPBR with spherical particles.²² (a) Channel flow, (b) churn flow, (c) pseudo-static flow, (d) parallel flow.

The original images were captured at 10 ms intervals to record the dynamic movement characteristics of various flow regimes within the reactor. This method identifies motion regions by analyzing the differences between consecutive images, allowing for effective target detection and tracking. The processed images with black background reveal the distinctive characteristics of various flow regimes, as illustrated in Fig. 9. Channel flow is characterized by fluid movement along a specific pathway, with distinct variations observed along the flow path in consecutive images. The extensive and dynamic areas occupying the whole reactor are presented in churn flow. For pseudo-static flow, minimal changes among the consecutive frames lead to almost non-differential images, effectively reflecting the static nature of this flow regime. Moreover, parallel flow can be considered a special case of pseudo-static flow. After processing using the frame difference method, flow regimes exhibit significant changes appearing in a black background. Finally, the characteristics of three distinct flow regimes were used as the training sets to train the model.

Subsequently, the processed images were fed into the developed CNN model. Given the complexity of gas–liquid flow status in the μPBR with spherical particles, a smaller learning rate (5 × 10⁻⁶), a longer training epoch (20), and a higher validation frequency (3) were selected to optimize the model training process. The confusion matrix for the μPBR with spherical particles is presented in Fig. 10. The results indicated that the model achieved over 90% recognition accuracy for each flow regime, with an overall identification accuracy of 94.3% within the μPBR with spherical particles.

Fig. 10 Confusion matrix for the μPBR with the spherical particles.

In our work, the trained LeNet-5 model was successfully applied in the μPBR for gas–liquid–solid systems, achieving accuracies of 97.5% and 94.3% for different packings. This high performance reflects not only LeNet-5's adaptability to different packing structures within μPBRs but also its effectiveness in addressing the unique challenges posed by these reactors. This approach significantly reduces the time requirement for flow regime identification in μPBRs with high accuracy.

In recent years, various CNN models have been developed and applied for different multiphase reactors about flow regime identification and classification. To better understand the applicability and performance differences of these models, Table 3 summarizes typical studies on flow regime classification models in different reactors, highlighting the effectiveness of various CNN architectures. The results reveal that CNN models, like VGG-16³⁶ and LeNet-5^33–35 exhibit high adaptability and efficiency in flow regime recognition. However, due to the varying complexities of flow regimes in different reactors and limitations in computational resources, it is crucial to design and develop CNN models tailored to specific application scenarios by utilizing insights from existing research and published findings. By selecting suitable CNN architectures, it becomes possible to achieve a balance between model complexity and computational cost while optimizing the accuracy and efficiency of flow regime classification.

Table 3 CNN model application for flow regime classification in various reactors

Authors	Reactors	Systems	Models	Accuracy (%)
Du et al.^36	Vertical pipe	Liquid–liquid	VGG-16	99.3
Zhang et al.^48	Horizontal pipe	Gas–liquid	SVM	93.1
Kuang et al.^49	Vertical pipe	Gas–liquid	FCN	99.95
Urbina-Salas et al.^34	Vertical pipe	Gas–liquid	LeNet-5	95
Shen et al.^33	Microchannel	Liquid–liquid	LeNet-5	98
Zhang et al.^35	Fluidized bed	Gas–solid	LeNet-5, AlexNet	100, 100
This work	μPBR	Gas–liquid–solid	LeNet-5	97.5 (pillar)
				94.3 (particle)

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4.3 Automatic software platform for flow regime classification

Many researchers have given deep insights into the flow behavior of μPBRs. As mentioned above, the published results relied on the repetitive analysis and screening of extensive experimental data artificially, leading to inefficiencies. To address this problem, developing an integrated software platform for studying hydrodynamics with the purpose of μPBR optimization is necessary. To the best of our knowledge, there are no reports about this idea in previous studies. Therefore, the flow regime classification was constructed and incorporated into the software platform to enhance experimental efficiency and accuracy.

In this paper, a user interface was built using MATLAB, which enabled rapid data extraction during the experiments and CNN training. MATLAB did not participate in the control of the experimental process.

Fig. 11 displays the graphical user interface (GUI) of an automatic software platform for flow regime classification of the μPBR utilizing the MATLAB software. The interface consists of three main sections: training parameters, confusion matrix, and flow regime identification. For CNN network training, a feature extraction backbone based on the LeNet-5 transfer learning model was embedded into the software. The GUI offered interactive control to adjust essential training parameters, including the ratio of training and testing data (training set), initial learning rate, max epochs, and validation frequency (MATLAB computation language). These adjustable parameters enabled the rapid training of the developed LeNet-5 model by loading labeled images. After completing the deep learning network training, a confusion matrix was presented in the GUI to illustrate the accuracy and stability of the CNN model.

Fig. 11 Graphical user interface for flow regime classification in the μPBR.

In the training process of deep learning, preprocessed datasets are used to train the model, resulting in a mature CNN model. After the CNN has been trained, new flow pattern images that are not included in the training dataset are input into the model to verify its accuracy. In particular, an interactive button (Imread) was available to select a new image address, facilitating robustness testing by allowing the trained model to recognize the flow regime for the new input image. The simplified running process of the GUI for the flow regime classification can be observed in Video S2 of the SI.

5. Conclusion

In this work, a convolutional neural network was developed with the purpose of flow regime identification in the μPBR for the first time. Two typical packings, micropillars and spherical particles, were selected to evaluate the applicability of the CNN. Three distinct flow regimes in the μPBR with micropillar structure were observed clearly: slug flow, churn flow, and pseudo-static flow. These flow regimes were successfully classified by the trained LeNet-5 model using transfer learning, achieving an accuracy of 97.5%. In contrast, the gas–liquid flow dynamics in the μPBR with spherical particles were more complex than those observed with the micropillar structure. To address this, a frame difference method was applied to preprocess the original images, revealing the distinctive characteristics of various flow regimes and constructing the dataset for model training. The developed model obtained an accuracy of 94.3% for the flow regime classification in the μPBR with spherical particles. Notably, a highly integrated software platform coupling the CNN with a user-friendly graphical interface was designed and presented, enabling efficient online data acquisition and analysis for flow regime identification rapidly.

Conflicts of interest

The authors declare no competing financial interest.

Data availability

Supplementary information (SI) is available for flow regime map data and model accuracy calculation process. See DOI: https://doi.org/10.1039/D5RE00293A.

The flow regime map data of Fig. 7 are tabulated in the SI. The model accuracy calculations from confusion matrix data for Fig. 8 and 10 are presented in the SI. The image and code that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgements

We gratefully acknowledge the support of the National Natural Science Foundation of China (22308188, 22022809, 21991103) and the National Key Research and Development Program of China (2019YFA0905100).

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