A comparison of models for predicting the maximum spreading factor in droplet impingement

The maximum spreading factor during droplet impact on a dry surface is a pivotal parameter of a range of applications, including inkjet printing, anti-icing, and micro-droplet transportation. It is determined by a combination of the inertial force, viscous force, surface tension, and fluid–solid interaction. There are currently a series of qualitative and quantitative prediction models for the maximum spreading factor rooted in both momentum and energy conservation. However, the performance of these models on consistent experimental samples remains ambiguous. In this work, a comprehensive set of 785 experimental samples spanning the last four decades is compiled. These samples encompass Weber numbers ranging from 0.038 to 2447.7 and Reynolds numbers from 9 to 34 339. A prediction model is introduced that employs a neural network, which achieves an average relative error of less than 16.6% with a standard error of 0.018 08 when applied to the test set. Following this, a fair comparison is presented of the accuracy, generality, and stability of different prediction models. Although the neural network model provides superior accuracy and generality, its stability is weaker than that of Scheller's We-Re-dependent formula, chiefly due to the absence of physical constraints. Subsequently, a physics-informed prediction model is introduced by considering a physical loss term. This model demonstrates comprehensive enhancements compared to the original neural network, and the average relative and standard errors for this model are reduce to 13.6% and 0.010 59, respectively. This novel model should allow for the rapid and precise prediction of the maximum spreading factor across a broad range of parameters for various applications.