Predicting liquid properties and behavior via droplet pinch-off and machine learning

Abstract

Here we demonstrate that the time-evolving interface observed during droplet formation, and consequently the resulting morphology nearing pinch-off, encode sufficient physical information for machine-learning (ML) frameworks to accurately infer key fluid properties, including viscosity and surface tension. Snapshots of dripping drops at the moment of break-up, together with their liquid properties and the flow rate, are used to form a data set for training ML algorithms. Experiments consisted of visualizing, using high-speed imaging, the process of droplet formation and identifying the frame closest to break-up. Experiments were conducted using Newtonian fluids under controlled flow conditions. In terms of the Reynolds (Re) and Ohnesorge (Oh) numbers, our conditions cover the domains 0.001< Re< 200 and 0.01 < Oh < 20, by using silicon oils, aqueous solutions of ethanol and glycerin, and methanol. For each case, flow parameters were recorded, along with images capturing the final stages of droplet break-up. Supervised regression models were trained to predict fluid parameters from the extracted contours of the breaking droplets. Our data set contains 840 examples. Our results demonstrate that the droplet geometry at pinch-off contains sufficient information to infer fluid properties by machine learning approaches. Our methods can predict surface tension, viscosity, or the droplet shape at pinch-off. These approaches provide alternatives to conventional methods to measure liquid properties while reducing measurement complexity and evaluation time and facilitating integration into automation. Unsupervised clustering is performed; the clusters represent regions in the Re-Oh and Bo-Oh planes, indicating that the latent representation may reveal physical properties and offering insight into droplet dynamics.

Figures (5)

• Figure 1: a) Examples of breaking up droplets at various conditions of Reynolds numbers for different liquids. As expected, pure water shows self-similarity near the pinch-off point and pure glycerin presents long filaments that break-up from the middle. Snapshots of pure glycerin are not to scale. Data domains in terms of Reynolds and Ohnesorge numbers. b) Parametric space of fluid properties and flow characteristics in terms of liquid type and formulation. c) Parametric space expressed in dripping length to nozzle-diameter ratio; many different conditions collapse onto the same $l/D.$
• Figure 2: Predicted vs. true values on the test set for Models 1–3 (MLP). Model 1 (a) predicts the viscosity, Model 2 (b) predicts surface tension, and Model 3 predicts both the viscosity (c) and the surface tension (d).
• Figure 3: Predicted vs. true values on the test set for Models 1--3 (XGBoost).Model 1 (a) predicts the viscosity, Model 2 (b) predicts surface tension, and Model 3 predicts both the viscosity (c) and the surface tension (d).
• Figure 4: Model 4 predictions: experimental vs. predicted droplet shapes for both (a) MLP and (b) XGBoost variants. (c) Unsupervised learning results: average droplet shapes in each GMM and K-Means cluster.
• Figure 5: Clustering of droplet breakup regimes in the $Bo$–$Oh$ and $Re$–$Oh$ spaces. Results for K-means is seen in (a) and (b), while GMM is found in (c) and (d).