The molten sand, a mixture of calcia, magnesia, alumina, and silicate, known as CMAS, is characterized by its high viscosity, density, and surface tension. The unique properties of CMAS make it a challenging material to deal with in high-temperature applications, requiring innovative solutions and materials to prevent its buildup and damage to critical equipment. Here, we use multiphase many-body dissipative particle dynamics (mDPD) simulations to study the wetting dynamics of highly viscous molten CMAS droplets. The simulations are performed in three dimensions, with varying initial droplet sizes and equilibrium contact angles. We propose a coarse parametric ordinary differential equation (ODE) that captures the spreading radius behavior of the CMAS droplets. The ODE parameters are then identified based on the Physics-Informed Neural Network (PINN) framework. Subsequently, the closed form dependency of parameter values found by PINN on the initial radii and contact angles are given using symbolic regression. Finally, we employ Bayesian PINNs (B-PINNs) to assess and quantify the uncertainty associated with the discovered parameters. In brief, this study provides insight into spreading dynamics of CMAS droplets by fusing simple parametric ODE modeling and state-of-the-art machine learning techniques.

翻译：熔融砂，即钙镁铝硅酸盐混合物（简称CMAS），以其高黏度、高密度和高表面张力为特征。CMAS的独特性质使其成为高温应用中难以处理的材料，需要创新材料和方案来防止其在关键设备上的积聚与损坏。本文采用多相多体耗散粒子动力学（mDPD）模拟研究高黏度熔融CMAS液滴的润湿动力学。模拟在三维空间中进行，初始液滴尺寸和平衡接触角可变。我们提出一个粗粒化参数常微分方程（ODE）来描述CMAS液滴的铺展半径行为，并基于物理信息神经网络（PINN）框架辨识该ODE参数。随后，通过符号回归给出PINN所得参数值对初始半径和接触角的闭合形式依赖关系。最后，我们采用贝叶斯PINN（B-PINNs）评估并量化所发现参数的不确定性。简言之，本研究通过融合简单参数化ODE建模与前沿机器学习技术，为CMAS液滴铺展动力学提供了深入见解。