Miniaturization of liquid handling is crucial for increasing sensitivity and throughput in life science applications like drug discovery and diagnostics. While robotic and digital microfluidic methods exist, they often lack cost-effectiveness or high throughput. Droplet microfluidics offers a promising alternative by combining high throughput, volume reduction, and sensitivity. However, its widespread adoption is hampered by the complexity of droplet formation, a lack of predictive understanding, high fabrication costs, and the limitations of numerical simulations. Flow-focusing geometries provide a wider range of performance (droplet diameter and generation rate) compared to other geometries, but lack analytical solutions or scaling laws for accurate prediction. Recent advances in low-cost rapid prototyping methods have reduced the cost and time required for exploring the design space of droplet generators experimentally. This allows for the generation of large datasets suitable for training machine learning algorithms to predict performance accurately, something that hasn't been achieved since the inception of droplet microfluidics. Machine learning excels at detecting complex patterns from large datasets and has shown success in various fields including cancer detection and drug discovery. However, its application in droplet microfluidics has been limited to real-time or post-experiment data analysis due to a lack of standardized large datasets. The ability to predict droplet generator performance based on design parameters eliminates costly iterations and enables application-specific optimization. Furthermore, accurate performance prediction enables the development of design automation tools, significantly reducing the resources and expertise required to develop functional droplet-based platforms. This study leverages low-cost rapid prototyping to fabricate and test flow-focusing droplet generators, generating a large-scale dataset to train machine learning algorithms for performance prediction and design automation. The study presents a web-based tool, DAFD (Design Automation of Fluid Dynamics), which utilizes this data and can be extended to support various fluid combinations.

The literature extensively covers droplet generation techniques in microfluidics, including T-junction, step-emulsification, co-flow, and flow-focusing methods. Flow-focusing is highlighted for its versatility in delivering various droplet sizes and generation rates. However, a significant gap exists in the predictive modeling of flow-focusing droplet generation due to the intricate fluid dynamics involved. Several studies have explored numerical simulations and scaling laws, but these often lack the generalizability needed for practical design. The application of machine learning to microfluidics is a growing area, with recent work focusing on real-time data analysis and post-experiment data processing. However, a comprehensive machine learning-based tool for predicting and automating the design of droplet generators has been absent. This research aims to bridge this gap by developing a machine learning model and a web-based design automation tool that addresses the limitations of previous approaches.

This study employed a low-cost rapid prototyping technique using a desktop CNC micromill to fabricate 43 flow-focusing droplet generators. These devices were designed using a Taguchi orthogonal array method to systematically vary six geometric parameters (orifice width, length, water inlet width, oil inlet width, outlet channel width, and channel depth). The devices were tested under a wide range of flow conditions, defined by capillary number and flow rate ratio, generating 998 data points in total. Droplet diameter, generation rate, and generation regime (dripping or jetting) were recorded for each data point. Machine learning models, specifically neural networks, were trained on this dataset to predict droplet generation regime, diameter, and rate. Separate models were created for dripping and jetting regimes to enhance accuracy and handle the different sensitivities to design parameters in each regime. The model's accuracy was evaluated using metrics such as mean absolute error (MAE) and mean absolute percentage error (MAPE). A comparison was made with existing scaling laws to demonstrate the superior accuracy of the machine learning models. To assess generalizability, the models were tested on unseen design parameters. To address the need for performance prediction with different fluid combinations, two approaches were implemented: DAFD Neural Optimizer and transfer learning. DAFD Neural Optimizer is an automated machine learning framework that enables users to train neural networks on custom datasets without requiring extensive machine learning knowledge. Transfer learning involved fine-tuning the pre-trained models (trained on the original dataset) to new datasets with different fluid combinations, requiring significantly fewer data points. A web-based tool, DAFD, was developed to integrate these machine learning models and enable design automation. This tool takes user-specified performance (droplet diameter and generation rate) as input and generates the required geometry and flow conditions. The tool uses an iterative optimization process, incorporating a cost function that minimizes the difference between desired and predicted performance, to achieve accurate design automation. A tolerance study was conducted to assess the impact of fabrication and testing tolerances on the device performance. Variance-based sensitivity analysis was used to identify the most influential design parameters and predict performance deviations. A case study focusing on single-cell encapsulation was performed to demonstrate the practical application of DAFD. The tool was used to determine the required cell concentration for single-cell encapsulation with user-specified droplet diameter, generation rate, and a target cell-to-droplet ratio. Polystyrene beads were used as cell surrogates in the experiments. The entire process, from data acquisition to automated design, is presented as an open-source platform, accessible via a web interface.

This study generated a large dataset of 998 data points by testing 43 flow-focusing droplet generators fabricated using a low-cost rapid prototyping method. Neural networks accurately predicted droplet generation regime with 95.1% accuracy. For droplet diameter prediction, the MAE was less than 10 µm (dripping) and 6 µm (jetting). For generation rate prediction, the MAE was less than 20 Hz (dripping) and 16 Hz (jetting). The machine learning models outperformed existing scaling laws in accuracy. The developed web-based tool, DAFD, successfully predicted the performance of unseen design parameters, with an MAE of 5.41 µm (7.01% MAPE) and 38.1 Hz (24.2% MAPE) for diameter and generation rate, respectively. A data reduction study suggested that approximately 250-300 data points for the dripping regime and 200-250 data points for the jetting regime would suffice to achieve comparable accuracy. DAFD Neural Optimizer successfully generated optimized neural networks comparable to models developed with machine learning expertise, allowing community extension with various fluid combinations without extensive machine learning expertise. Transfer learning was successfully applied to fine-tune pre-trained models for new fluid combinations with small datasets. In the design automation phase, DAFD achieved an MAE (MAPE) of 4.2% (3.7 µm) and 11.5% (32.5 Hz) in delivering user-specified droplet diameter and generation rate, respectively. The tolerance study effectively quantified the impact of fabrication and flow rate tolerances on performance, identifying key influential parameters. Finally, the case study demonstrated DAFD's ability to design a device for single-cell encapsulation with specified performance and design constraints.

The results demonstrate that machine learning provides a powerful tool for accurate prediction and design automation of flow-focusing droplet generators. DAFD's ability to predict performance with high accuracy eliminates the resource-intensive design iterations typical of microfluidic device development. The successful implementation of DAFD Neural Optimizer and transfer learning greatly enhances the tool's versatility and usability, enabling community extension without requiring specialized machine learning skills. The design automation functionality further simplifies the process, allowing users to specify desired droplet characteristics and obtain optimized designs. The incorporation of a tolerance study enhances the robustness of the designs by predicting and mitigating the effects of fabrication and testing variability. The case study showcases the application of DAFD to a practical problem in single-cell encapsulation, highlighting its potential to facilitate advancements in various microfluidic applications. Future work can focus on expanding the database of fluid properties, integrating other microfluidic components into the design process, and exploring advanced machine learning techniques to further improve prediction accuracy.

This study presents DAFD, an open-source, web-based tool that accurately predicts and automates the design of flow-focusing droplet generators. DAFD's high accuracy, community extensibility through Neural Optimizer and transfer learning, and design automation capabilities significantly lower the barrier to entry for microfluidics. Future work could involve integrating DAFD with other microfluidic CAD tools, expanding its functionalities to include droplet merging and splitting, and broadening the scope to encompass other microfluidic components and applications. This platform promises to accelerate research and development in various fields that utilize droplet microfluidics.

The current version of DAFD primarily focuses on flow-focusing devices with DI water and mineral oil. While transfer learning allows for extension to other fluid combinations, the accuracy might be affected by significant differences in fluid properties. The accuracy of the design automation is dependent on the accuracy of the predictive models. Experimental variability due to flow rate fluctuations and other factors can affect the observed performance. The single-cell encapsulation case study used polystyrene beads as cell surrogates, which may not perfectly mimic the behavior of real cells.