Transient Prediction of Nanoparticle-Laden Droplet Drying Patterns through Dynamic Mode Decomposition

Nanoparticle-laden sessile droplet drying has a wide impact on applications. However, the complexity affected by the droplet evaporation dynamics and particle self-assembly behavior leads to challenges in the accurate prediction of the drying patterns. We initiate a data-driven machine learning algorithm by using a single data collection point via a top-view camera to predict the transient drying patterns of aluminum oxide (Al₂O₃) nanoparticle-laden sessile droplets with three cases according to particle sizes of 5 and 40 nm and Al₂O₃ concentrations of 0.1 and 0.2 wt %. Dynamic mode decomposition is used as the data-driven learning model to recognize each nanoparticle-laden droplet as an individual system and then apply the transfer learning procedure. Along 270 s of droplet drying experiments, the training period of the first 100 s is selected, and then the rest of the 170 s is predicted with less than a 10% error between the predicted and the actual droplet images. The developed data-driven approach has also achieved the acceptable prediction for the droplet diameter with less than 0.13% error and a coffee-ring thickness over a range of 2.0 to 6.7 μm. Moreover, the proposed machine learning algorithm can recognize the volume of the droplet liquid and the transition of the drying regime from one to another according to the predicted contact line and the droplet height.