Novel models for predicting the shape and motion of an ascending bubble in Newtonian liquids using machine learning

As a conventional and persistent topic, a single bubble freely ascending in Newtonian liquids is investigated based on its shape and motion predictions using the strategy of machine learning. The dataset for training, validating, and testing neural networks is composed of the current experimental results and the extensively collected data from previous research works, which covers a broad range of dimensionless parameters that are 10−3≤Re≤105, 10−2≤Eo≤103, 10−5≤We≤102, and 10−14≤Mo≤107. The novel models of the aspect ratio E and drag coefficient CD are proposed based on a backpropagation neural network. The comparisons of the conventional correlations indicate that the new E model presents a significant superiority. This E model also has a good capability to predict the minimum E as about 0.26 that is consistent with the theoretical value EWe→∞≈0.25. Moreover, the CD models are divided into E-independent and E-dependent types. The performances of these two type models are quite similar and both agree well with the experimental results. The errors of the CD predictions for Re > 1 are mostly in the range of ±20%.