Droplet-based microfluidics has rapidly advanced as a versatile tool for a wide range of applications in material synthesis, diagnostics, and biochemical analysis. This technology offers several advantages related to droplet handling at the microscale, including reduced reagent consumption, improved production throughput, and precise control over the droplet size, generation rate, and composition1. Droplets function as microreactors, facilitating chemical and biological reactions in a confined space—an essential characteristic for applications such as digital polymerase chain reaction (PCR) and drug delivery systems2,3,4,5,6. These methodologies can be categorized into passive and active mechanisms. Passive methods, particularly those that, include cross-flow, co-flow, and flow-focusing techniques, rely on fluid dynamics and channel geometries to induce droplet formation without external actuation1,7. Flow-focusing geometries not only allows for precise control over droplet size by adjusting the contraction width but also demonstrate distinct scaling behaviors under pressure-driven and flow-rate-driven conditions8,9.
Beyond individual droplet generator geometry, the overall layout of the microfluidic network plays a crucial role in determining stability under pressure-driven flow. Feedback within the network’s hydrodynamic resistance leads to slower, large-scale oscillations that are more effectively monitored accurately captured by observing changes in droplet spacing rather than droplet size throughout the circuit10.
Passive methods are favored for their simplicity and ability to produce monodisperse droplets under controlled conditions, particularly in the dripping regime, where droplets are generated directly at the nozzle orifice. Conversely, the jetting regime produces a continuous jet that fragments into droplets, often resulting in polydisperse distributions due to inherent flow instabilities1,11,12,13. Analytical and experimental studies have defined the practical limits of monodispersity, providing design guidelines for achieving ultra-monodisperse generation (coefficient of variation: CV < 0.2%) in T-junction and flow‑focusing configuration14.
T-junction devices represent another passive approach, where droplet formation scaling laws across squeezing, dripping, and transient regimes can be described by correlations based on capillary numbers. Modified capillary numbers enhance the predictive accuracy for droplet diameter15.
A novel oscillatory co-flow strategy further expands the passive toolkit: by introducing lateral oscillations of the dispersed-phase nozzle, it enables the simultaneous generation of multi-size monodisperse droplets, with droplet size inversely related to both oscillation frequency and capillary number16.
Active droplet generation employs external forces, such as electric and magnetic fields and thermal gradients, to achieve refined control over droplet formation, especially in complex scenarios involving highly viscous fluids or systems with low interfacial tension1,17,18,19,20. The regulation of droplet size, uniformity, and production rate is governed by the interplay of viscous, inertial, and interfacial tension forces. This balance is often characterized by key dimensionless numbers: the Capillary number (Ca), which represents the ratio of viscous forces to interfacial tension, and the Weber number (We), which represents the ratio of inertial forces to interfacial tension. The magnitudes of Ca and We are critical in determining the operational regime (e.g., dripping or jetting), which directly affects the final droplet characteristics1,21,22.
Machine learning (ML) is revolutionizing droplet microfluidics. Neural networks trained on glass capillary data can predict droplet diameters in both dripping and jetting regimes with over 90% accuracy23. Comprehensive reviews on AI applications emphasize the intelligent control of droplet systems, highlighting their roles in generation, material synthesis, and bioanalysis23. Machine learning and neural networks play a central role in the evolution of Biomedical Engineering24,25. These technologies provide transformative solutions that not only save time and reduce cost but also significantly outperform traditional mathematical and experimental methods in terms of accuracy. By enabling advanced data processing and predictive modeling, AI is crucial for the design and optimization of biomedical systems. The production of microfluidic droplets, particularly concerning size and flow rate, is a complex process that greatly benefits from these advancements. In this study, we focus on using AI to automate the design of microfluidic devices.
Lashkaripour et al.26 designed and developed the Design Automation of Fluid Dynamic (DAFD) tool for the automated design of microfluidic devices featuring flow-focusing geometry. This machine-learning-based tool optimizes channel geometry and predicts device performance using neural networks and fuzzy inference systems, enabling accurate predictions without the need for repetitive physical experiments. The tool can predict the droplet size and production rate with absolute errors of less than \(10 \mu m\) and \(20 Hz\), respectively. In their subsequent paper27, the authors expanded on this work by exploring machine learning methodologies to estimate the device geometry and flow conditions required to generate single- and double-emulsion droplets. They developed a user-friendly automated tool that generated droplets with minimal deviation from the target size.
In another relevant study, Talebjedi et al.28 developed a predictive platform to analyze droplet break-up characteristics, including size, frequency, and regime, within microfluidic devices with varying cross-flow angles. They compared four neural network-based predictive models and found that multi-layer perceptrons (MLPs) outperformed Linear discriminant analysis (LDA) models in predicting the droplet quality and regime.
McIntyre et al.29 investigated the optimization of the droplet quality and stability in microfluidic devices using quality metrics and automated design techniques. They introduced two key metrics for evaluating droplet production: operational versatility and stability. Operational versatility refers to the range of conditions under which a device can operate effectively, while stability measures how far the operating point is from transitioning to a less stable regime, thereby ensuring consistent performance. In their approach, they gathered experimental data on droplet production across varying conditions and trained a machine learning model to predict key parameters, such as droplet size, production rate, and stability. An optimization algorithm was subsequently applied to enhance both the droplet quality and stability, improving the reliability and reproducibility of the droplet generation.
Exploring the integration of machine learning with microfluidics, Siemenn et al.30 aimed to optimize droplet production across a variety of devices using a Bayesian optimization feedback loop combined with computer vision techniques. They applied computer vision to analyze the droplet image, and the results were subsequently used as inputs for the machine learning model to develop the Bayesian optimization feedback loop. This loop was designed to optimize the droplet production parameters by leveraging both machine learning and computer vision analysis.
Bartunik et al.31 proposed a sensor system designed to detect the size and color of the droplets. This system comprises an infrared sensor and a color sensor, which work in conjunction with the video processing software to measure the droplet size accurately. Additionally, the entire system employs a machine learning model to ensure precise color measurement, facilitating colorimetric data transfer and color reaction analysis.
Naji et al.32 studied droplet generation in a microfluidic chip using a non-embedded co-flow-focusing geometry. By employing a neural network for geometrical optimization, they reduced the computational time required to predict the droplet radius and the generation rate, ultimately identifying the optimal geometry that expands the region of monodispersity. Their work also revealed that the transition between the dripping and jetting regimes is significantly influenced by changes in the external diameter of the chip.
Beyond droplet-specific applications, similar intelligent frameworks have recently been employed to optimize a diverse array of microfluidic components. For instance, a controllable framework using machine learning and data-driven modeling has been proposed to optimize micromixers for general biochemical assays, which has been validated through subsequent experiments33. This approach was also extended to the development of energy-efficient micromixers specifically designed for the controlled synthesis of nanoparticles34. Additionally The use of machine learning and metaheuristics has also proven effective in optimizing microfluidic transport for processes, such as cell lysis, by integrating predictive modeling with experimental studies to enhance diagnostic accuracy35. Furthermore, these data-driven optimization techniques have been combined with response surface methodology to design complex micro-electro-mechanical systems, including acoustofluidic mixers where acoustic streaming effects are dominant36.
To achieve an accurate understanding of the droplet characteristics under specific physical conditions, traditional methods have primarily relied on solving complex partial differential equations (PDEs) or conducting empirical trial-and-error experiments. While these approaches can yield reliable results, they present significant challenges. They are time-consuming, often requiring several hours to complete simulations, and incur high costs due to their computational and resource demands. Additionally, the iterative numerical approach in the empirical cycle introduces delays and inefficiencies, making these methods less suitable for rapid design and optimization37,38,39.
This work proposes an alternative strategy that leverages machine learning models to significantly reduce the time and cost of simulations, shortening the computation time for predicting droplet features from hours to seconds. This breakthrough accelerates the design and optimization of microfluidic devices and substantially lowers associated costs.
First, we introduce two novel machine learning architectures, the Residual Block Network (ResBNet) and the Fourier-Enhanced Network (FEN), which are specifically designed to boost the accuracy of predictions for key droplet parameters such as size, generation rate, and geometric ratios. Second, beyond existing automation solutions, we present a comprehensive “reverse” design workflow that enables users to specify their desired droplet features and subsequently receive an optimized device geometry accordingly. Finally, to ensure broad accessibility and practical application, we have developed DesignFlow, a user-friendly, open-source software platform that integrates these models and workflows, making automated microfluidic design accessible to the broader research community.
While co-flow devices are classically composed of concentric capillaries, our study focuses on planar co-flow geometries, we employed the Lattice Boltzmann Method (LBM) to generate a comprehensive dataset that encompasses a range of physical conditions, including variations in capillary and Weber numbers, fluid viscosities, and device geometries. We then trained the machine learning models on this dataset, enabling efficient and accurate predictions for droplet generation.
The overall workflow of our study, which integrates our simulation methodology, novel machine learning framework, and the development of the DesignFlow software, is visually summarized in Fig. 1. In the next section, the Methodology is outlined, beginning with a discussion of the Navier–Stokes and Allen–Cahn equations used to simulate the fluid flow and droplet formation, employing the Lattice Boltzmann method. We also highlight the most important dimensionless numbers in understanding droplet dynamics, particularly within co-flow geometries. Following this, we introduce the machine learning models, including the Residual Block Network (ResBNet) and the Fourier-Enhanced Network (FEN), and detail their design and implementation. In the Results and Discussion section, we evaluate the performance of these models, focusing on their predictive accuracy and computational efficiency. Also, this section explores how various parameters influence the droplet size and production rates, offering valuable insights for optimizing the device design. Finally, we will introduce DesignFlow Software.
A comprehensive schematic of the overall study. The workflow begins with the motivation to replace the slow, traditional design cycle with an automated framework. A comprehensive dataset is generated using Lattice Boltzmann Method (LBM) simulations. This data is then used to train two novel machine learning models, ResBNet and FEN, which form the core of the open-source DesignFlow software. The platform enables both forward prediction of droplet characteristics and the reverse design of optimized microfluidic devices.
