Surface tension measurement using deep learning: Eliminating edge detection and Drop Shape Analysis

The increasing demand for low-cost, smartphone-based pendant drop tensiometers calls for alternative methods to conventional Axisymmetric Drop Shape Analysis (ADSA), which only works flawlessly under ideal imaging conditions. Deep learning models could be used to directly estimate surface tension from raw, not ideally illuminated or oriented images, eliminating the need for edge detection or fitting with only a fraction of the computational cost of ADSA. Pre-trained convolutional neural networks (CNNs) were fine-tuned on a dataset of 91,000 augmented pendant drop images acquired with a camera. The models output two geometric parameters linked to surface tension via the Bond number. Testing was conducted on images from a commercial tensiometer under varied conditions, including suboptimal lighting and optical aberrations. Smartphone-acquired images and independent user-submitted datasets to our lab-made ADSA toolkit (DropUI) were also evaluated to assess robustness and generalization. The models estimated surface tension with less than 13% error even when ADSA failed due to lighting conditions or optical aberrations. On smartphone-acquired images, predictions achieved R 2 = 0 . 709 with errors within 15%. Independent DropUI submissions confirmed good generalization with R 2 > 0 . 8 for both outputs. Inference on a GPU was at least an order of magnitude faster than ADSA running on a CPU. • Direct surface tension prediction from pendant drop images using Deep Learning (DL). • ∼ 100 k real, pendant drop images are used for training, validation and test. • Use of transfer learning and pre-trained CNNs (ResNets, MobileNets and EfficientNets). • R 2 values range from 0.7 to 0.97 for test images acquired with different cameras. • DL model predictions are acceptable even when Drop Shape Analysis completely fails.