Rupture distances and capillary forces of liquid bridges: Closed-form expressions and ANNs-trained prediction models

Abstract

Accurate prediction of rupture distances and capillary forces of liquid bridges is crucial for studying the behaviour of wet granular materials. However, the validity of existing analytical expressions is limited to small liquid volumes, whereas current closed-form expressions require numerous calibrated coefficients, making them cumbersome. To overcome these limitations, this study employs Particle Swarm Optimization (PSO), a metaheuristic algorithm, to enhance closed-form expressions. This approach allows tuning the balance between accuracy and complexity, resulting in simplified yet accurate closed-form expressions for liquid bridges with varying volumes and contact angles between unequal-sized particles, under both volume and suction control conditions.Additionally, Artificial Neural Networks (ANNs) are used as an alternative approach. All network architectures up to three hidden layers are systematically explored, and prediction models for rupture distances and capillary forces of liquid bridges are trained using a database of numerical solutions of the Young–Laplace equation. The resulting models provide accurate predictions across a wide range of liquid volumes and contact angles.