Modeling the Settling Velocity of a Sphere in Newtonian and Non-Newtonian Fluids with Machine-Learning Algorithms

The traditional procedure of predicting the settling velocity of a spherical particle is inconvenient as it involves iterations, complex correlations, and an unpredictable degree of uncertainty. The limitations can be addressed efficiently with artificial intelligence-based machine-learning algorithms (MLAs). The limited number of isolated studies conducted to date were constricted to specific fluid rheology, a particular MLA, and insufficient data. In the current study, the generalized application of ML was comprehensively investigated for Newtonian and three varieties of non-Newtonian fluids such as Power-law, Bingham, and Herschel Bulkley. A diverse set of nine MLAs were trained and tested using a large dataset of 967 samples. The ranges of generalized particle Reynolds number (Re-G) and drag coefficient (C-D) for the dataset were 10(-3) < Re-G (-) < 10(4) and 10(-1) < C-D (-) < 10(5), respectively. The performances of the models were statistically evaluated using an evaluation metric of the coefficient-of-determination (R-2), root-mean-square-error (RMSE), mean-squared-error (MSE), and mean-absolute-error (MAE). The support vector regression with polynomial kernel demonstrated the optimum performance with R-2 = 0.92, RMSE = 0.066, MSE = 0.0044, and MAE = 0.044. Its generalization capability was validated using the ten-fold-cross-validation technique, leave-one-feature-out experiment, and leave-one-data-set-out validation. The outcome of the current investigation was a generalized approach to modeling the settling velocity.

Automated summary

The study investigated the generalized application of machine learning algorithms for predicting settling velocity in various types of fluids. Performance evaluation was done using statistical metrics like coefficient-of-determination, root-mean-square-error, mean-squared-error, and mean-absolute-error. Support vector regression with polynomial kernel displayed the best performance with high accuracy.