Abstract

The accurate mathematical modeling of droplet impact dynamics on micro-structured surfaces is fundamental to understanding and predicting complex fluid behaviors relevant to a wide range of engineering and scientific applications. In particular, the pancake bouncing phenomenon—systematically studied by Liu et al. Nature Physics, 2014—on superhydrophobic micro-structured substrates presents significant theoretical challenges. Central to these challenges is the need to construct rigorous mathematical models that capture the intricate influence of substrate micro/nanostructures on droplet dynamics. This requires the development of robust formulations for surface tension, contact line dynamics, and the interaction forces between fluid and solid structures. In this work, we formulate a nonlocal mathematical framework for the simulation of 3D pancake bouncing on superhydrophobic micro-cone arrays. The model incorporates intermolecular attractive forces to represent droplet surface tension, and we provide a strict theoretical derivation linking these forces quantitatively to the macroscopic surface tension coefficient, thereby circumventing the reliance on empirical parameter tuning. The complex geometry of micro-cone arrays introduces fundamental difficulties in defining local normal directions for contact algorithms. To overcome this, we develop a nonlocal contact repulsion force model that governs fluid-solid interactions and ensures numerical stability under high Weber number conditions. Based on this mathematical foundation, we implement the model using smoothed particle hydrodynamics (SPH), enabling high-precision 3D simulations. Computational experiments, validated against empirical data, confirm the model’s accuracy and robustness, while underscoring the key role of numerical simulation in elucidating droplet-microstructure interactions.

Biography

Prof. Zhonghua Qiao obtained his Ph.D. from Hong Kong Baptist University in 2006 and is currently a Chair Professor in the Department of Applied Mathematics at The Hong Kong Polytechnic University. He also serves as the Deputy Director (Hong Kong side) of the Chinese Academy of Sciences Academy of Mathematics and Systems Science and the Hong Kong Polytechnic University Joint Laboratory of Applied Mathematics. Additionally, he is a council member of the China Society for Industrial and Applied Mathematics and the Vice Chairman of the China Society for Computational Mathematics.

Prof. Qiao's primary research focuses on the design and analysis of algorithms for numerical differential equations. In recent years, his work has concentrated on the numerical simulation of phase-field equations and efficient algorithms for computational fluid dynamics. To date, he has published over 90 papers, with his articles collectively cited over 4,000 times. In 2013, he was awarded the Hong Kong Research Grants Council's Early Career Award for the 2013-2014 academic year, the Hong Kong Mathematical Society's Young Scholar Award in 2018, and the RGC Research Fellow Award from the Hong Kong Research Grants Council in 2020.