发表机构
School of Mathematics and Statistics, Huazhong University of Science and Technology; Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology; The State Key Laboratory of Intelligent Manufacturing Equipment and Technology, Huazhong University of Science and Technology（华中科技大学数学与统计学院; 华中科技大学工程建模与科学计算湖北省重点实验室; 华中科技大学智能装备与技术国家重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对含固体吸附的表面活性剂接触线动力学，提出热力学一致且守恒的Allen-Cahn-Navier-Stokes相场模型，采用二阶方程与非线性守恒量，实现二阶精度并改善体积守恒，揭示吸附对润湿和剪切流下液滴行为的影响。
AI 中文摘要
固体-流体界面上的表面活性剂吸附强烈影响接触线动力学，然而大多数含表面活性剂的相场模型忽略了固体吸附，并依赖于Cahn-Hilliard型方程。我们开发了一个热力学一致且守恒的Allen-Cahn-Navier-Stokes模型，用于描述含固体吸附的表面活性剂接触线动力学。一个统一的自由能公式同时考虑了表面活性剂输运、吸附和润湿动力学，导出了一致的润湿和吸附边界条件。二阶Allen-Cahn型方程同时控制相场和表面活性剂浓度，避免了四阶公式的数值复杂性。一个经典线性约束确保了表面活性剂总质量的精确守恒，而为相场引入了一个广义非线性守恒量以改善几何体积守恒。由此产生的加权拉格朗日乘子修正项在体相中消失，并局限于扩散界面，抑制了与线性约束相关的前导阶曲率引起的体相偏移，同时保持了能量耗散结构。匹配渐近分析表明，非线性公式可实现形式上的二阶几何体积精度。我们开发了一种格子玻尔兹曼方法来求解耦合系统。数值结果证实了预测的二阶收敛性，展示了高曲率液滴体积保持的增强效果，并重现了由优先固体吸附引起的润湿响应，包括亲水化和自憎效应。在剪切流下，结果还表明固体吸附能显著影响接触线回退和液滴脱离。
英文摘要
Surfactant adsorption at solid-fluid interfaces strongly influences contact line dynamics, yet most surfactant-laden phase-field models neglect solid adsorption and rely on Cahn-Hilliard-type equations. We develop a thermodynamically consistent and conservative Allen-Cahn-Navier-Stokes model for surfactant-laden contact line dynamics with solid adsorption. A unified free-energy formulation accounts for surfactant transport, adsorption, and wetting dynamics, yielding consistent wetting and adsorption boundary conditions. Second-order Allen-Cahn-type equations govern both the phase field and surfactant concentration, avoiding the numerical complexity of fourth-order formulations. A classical linear constraint ensures exact conservation of total surfactant mass, whereas a generalized nonlinear conserved quantity is introduced for the phase field to improve geometric volume conservation. The resulting weighted Lagrange-multiplier correction vanishes in the bulk phases and is confined to the diffuse interface, suppressing the leading-order curvature-induced bulk shift associated with the linear constraint while preserving the energy-dissipation structure. Matched asymptotic analysis shows that the nonlinear formulation can achieve formal second-order geometric-volume accuracy. A lattice Boltzmann method is developed to solve the coupled system. Numerical results confirm the predicted second-order convergence, demonstrate enhanced volume preservation for high-curvature droplets, and reproduce wetting responses induced by preferential solid adsorption, including hydrophilization and autophobing. Under shear flow, the results also show that solid adsorption can significantly influence contact line recession and droplet detachment.
Comments30 pages, 12 figures
