Designing and Shaping Microfluidic Flow Profiles in Stokes Flow Regime with Deep Learning

The ability to shape flow profiles is critical for microfluidic fabrication of hydrogel fibers and particles with customizable structures and multiscale features. The flow profiles, referring to the lateral cross-sectional shape of the flow fields, can be transformed into diverse and complex shapes, depending on the flow and boundary conditions. The recently proposed inertialess flow profile engineering method deploys sequential steps in the channel to transform the flow profiles in Stokes flow regime, facilitating flow profile engineering. The steps with complex geometries are vital for diverse profile shapes; however, investigating the flow profiles and their transformations around such steps relies on iterative and time-consuming simulations or experiments. As a result, designing a flow profile with fully customized features remains computationally challenging.<br/><br/>Here we develop two deep neural networks for solving this forward design problem. The first model, based on variational autoencoder (VAE) architecture, takes the images of the step shapes as input and outputs the image of the transformed flow profiles. The model accuracy is metricized by the percentage of matched pixel values between the images of the predicted profiles and simulated profiles, and the test accuracy reaches 98.06%. Only minor differences can be visually identified between the predicted and observed profiles. Moreover, the model can predict the output flow profile of steps with unseen types of geometries, such as parallel steps or concave steps, with high accuracy, indicating the model have, to some extent, captured the underlying physical relationships between the step geometries and the output flow profiles.<br/><br/>The second model uses U-Net architecture to predict the profile transformations around a step. Before the training, the streamline data are compressed into transformation matrices, which only include the mapping of fluid element positions between the inlet and outlet profiles. The accuracy is evaluated as the percentage of matched elements in the transformation matrices between the predictions and the ground truth, and reaches 83% after 150 epochs of training. Plotting the predicted transformation matrices as the vector fields shows that the predictions can capture both the significant large-scale secondary flows as well as the small vertices. Moreover, the net transformation matrix of a step sequence can be computed by superposing the transformation matrices of the individual steps, enabling prediction of the output flow profiles of arbitrary step sequences and inlet flow profiles. With the current model accuracy, the flow profiles remain comparable to the simulation and experimental results after transformation by a sequence of 4 steps.<br/>In conclusion, the VAE-based model can predict the flow profiles accurately, and can be generalized to unseen step topologies, while the inlet profiles and the number of steps are fixed. The U-Net-based model can be used to predict the flow profiles of multiple steps, with potential to further improve the accuracy. We anticipate the model will allow predicting the flow profiles transformed by a large number of sequenced steps, thus significantly accelerating the design cycle of complicated flow profiles.