Transfer of Periodic Phenomena in Multiphase Capillary Flows to a Quasi-Stationary Observation Using U-Net
Authors: Oldach Bastian , Wintermeyer Philipp , Kockmann Norbert 
Published: September 2024

Miniaturization promotes the efficiency and exploration domain in scientific fields such as computer science, engineering, medicine, and biotechnology. In particular, the field of microfluidics is a flourishing technology, which deals with the manipulation of small volumes of liquid. Dispersed droplets or bubbles in a second immiscible liquid are of great interest for screening applications or chemical and biochemical reactions. However, since very small dimensions are characterized by phenomena that differ from those at macroscopic scales, a deep understanding of physics is crucial for effective device design. Due to small volumes in miniaturized systems, common measurement techniques are not applicable as they exceed the dimensions of the device by a multitude. Hence, image analysis is commonly chosen as a method to understand ongoing phenomena. Artificial Intelligence is now the state of the art for recognizing patterns in images or analyzing datasets that are too large for humans to handle. X-ray-based Computer Tomography adds a third dimension to images, which results in more information, but ultimately, also in more complex image analysis. In this work, we present the application of the U-Net neural network to extract certain states during droplet formation in a capillary, which forms a constantly repeated process that is captured on tens of thousands of CT images. The experimental setup features a co-flow setup that is based on 3D-printed capillaries with two different cross-sections with an inner diameter, respectively edge length of 1.6 mm. For droplet formation, water was dispersed in silicon oil. The classification into different droplet states allows for 3D reconstruction and a time-resolved 3D analysis of the present phenomena. The original U-Net was modified to process input images of a size of 688 × 432 pixels while the structure of the encoder and decoder path feature 23 convolutional layers. The U-Net consists of four max pooling layers and four upsampling layers. The training was performed on 90% and validated on 10% of a dataset containing 492 images showing different states of droplet formation. A mean Intersection over Union of 0.732 was achieved for a training of 50 epochs, which is considered a good performance. The presented U-Net needs 120 ms per image to process 60,000 images to categorize emerging droplets into 24 states at 905 angles. Once the model is trained sufficiently, it provides accurate segmentation for various flow conditions. The selected images are used for 3D reconstruction enabling the 2D and 3D quantification of emerging droplets in capillaries that feature circular and square cross-sections. By applying this method, a temporal resolution of 25–40 ms was achieved. Droplets that are emerging in capillaries with a square cross-section become bigger under the same flow conditions in comparison to capillaries with a circular cross section. The presented methodology is promising for other periodic phenomena in different scientific disciplines that focus on imaging techniques.