Spatio-temporal reconstruction of droplet impingement dynamics by means of color-coded glare points and deep learning

Abstract The present work introduces a deep learning approach for the three-dimensional reconstruction of the spatio-temporal dynamics of the gas–liquid interface on the basis of monocular images obtained via optical measurement techniques. The method is tested and evaluated at the example of liquid droplets impacting on structured solid substrates. The droplet dynamics are captured through high-speed imaging in an extended shadowgraphy setup with additional glare points from lateral light sources that encode further three-dimensional information of the gas–liquid interface in the images. A neural network is trained for the physically correct reconstruction of the droplet dynamics on a labeled dataset generated by synthetic image rendering on the basis of gas–liquid interface shapes obtained from direct numerical simulation. The employment of synthetic image rendering allows for the efficient generation of training data and circumvents the introduction of errors resulting from the inherent discrepancy of the droplet shapes between experiment and simulation. The accurate reconstruction of the three-dimensional shape of the gas–liquid interface during droplet impingement on the basis of images obtained in the experiment demonstrates the practicality of the presented approach based on neural networks and synthetic training data generation. The introduction of glare points from lateral light sources in the experiments is shown to improve the reconstruction accuracy, which indicates that the neural network learns to leverage the additional three-dimensional information encoded in the images for a more accurate depth estimation. By the successful reconstruction of obscured areas in the input images, it is demonstrated that the neural network has the capability to learn a physically correct interpolation of missing data from the numerical simulation. Furthermore, the physically reasonable reconstruction of unknown gas–liquid interface shapes for drop impact regimes that were not contained in the training dataset indicates that the neural network learned a versatile model of the involved two-phase flow phenomena during droplet impingement.