We consider the nonlocal multiscale model for surface tension \citep{Tartakovsky2018} as an alternative to the (macroscale) Young-Laplace law. The nonlocal model is obtained in the form of an integral of a molecular-force-like function with support $\varepsilon$ added to the Navier-Stokes momentum conservation equation. Using this model, we calculate analytical forms for the steady-state equilibrium pressure gradient and pressure profile for circular and spherical bubbles and flat interfaces in two and three dimensions. According to the analytical solutions, the pressure changes continuously across the interface in a way that is quantitatively similar to what is observed in MD simulations. Furthermore, the pressure difference $P_{\varepsilon, in} - P_{\varepsilon, out}$ satisfies the Young-Laplace law for the radius of curvature greater than $3\varepsilon$ and deviates from the Young-Laplace law otherwise (i.e., $P_{\varepsilon, in} - P_{\varepsilon, out}$ goes to zero as the radius of the curvature goes to zero, where $P_{\varepsilon, out}$ is the pressure outside of the bubble at the distance greater than $3\varepsilon$ from the interface and $P_{\varepsilon, in}$ is the pressure at the center of the bubble). The latter indicates that the surface tension in the proposed model decreases with the decreasing radius of curvature, which agrees with molecular dynamics simulations and laboratory experiments with nanobubbles. Therefore, our results demonstrate that the nonlocal model behaves microscopically at scales smaller than $\varepsilon$ and macroscopically, otherwise.
Physics informed wavelet Fourier representation for multiscale fluid dynamics
College of Shipbuilding Engineering, Harbin Engineering University（哈尔滨工程大学船舶工程学院）；Qingdao Innovation and Development Base, Harbin Engineering University（哈尔滨工程大学青岛创新发展基地）；National Key Laboratory of Hydrodynamics, Harbin Engineering University（哈尔滨工程大学水动力学国家重点实验室）；Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology（南方科技大学力学与航空航天工程系）；Centre for Interdisciplinary Research in Fluids, Institute of Mechanics, Chinese Academy of Sciences（中国科学院力学研究所流体交叉研究中心）；Nanhai Institute of Harbin Engineering University, Harbin Engineering University（哈尔滨工程大学南海研究院）；Department of Modern Mechanics, University of Science and Technology of China（中国科学技术大学近代力学系）
A term-by-term variational multiscale method with dynamic subscales for incompressible turbulent aerodynamics
Computational Heat and Fluid Flow Lab, Universidad de Santiago de Chile（圣地亚哥智利大学计算热与流体流动实验室）；Department of Mechanical Engineering, University of Santiago de Chile（圣地亚哥智利大学机械工程系）；Chair for Computational Analysis of Technical Systems, RWTH Aachen University（亚琛工业大学技术系统计算分析教席）；Chair of Methods for Model-based Development in Computational Engineering, RWTH（亚琛工业大学计算工程基于模型开发方法教席）；Center for Simulation and Data Science (JARA-CSD), RWTH Aachen University（亚琛工业大学仿真与数据科学中心（JARA-CSD））
Bridging scales in multiscale bubble growth dynamics with correlated fluctuations using neural operator learning
Artificial Intelligence Innovation and Incubation Institute, Fudan University（复旦大学人工智能创新与孵化研究院）；Division of Applied Mathematics, Brown University（布朗大学应用数学系）；Department of Mechanical Engineering, Clemson University（克莱姆森大学机械工程系）
