剪切作用与均匀加热电场共同驱动下倾斜平板奇粘度流体薄膜的线性稳定性分析

Linear Stability Analysis of Odd-Viscous Fluid Films on an Inclined Plane Driven by Combined Shear Action and Uniformly Heated Electric Field

摘要: 倾斜平板液膜流动的稳定性调控是多相流与界面流体力学的核心研究方向，广泛应用于微纳涂层、工业换热等工程场景。本研究聚焦剪切–均匀热毛细–电场–奇粘度四场耦合的倾斜平板液膜流动，通过构建耦合数学模型、长波近似简化、线性与弱非线性稳定性分析及有限差分数值模拟，结合自由表面时空演化观测，系统探究多场协同调控机制。研究构建含奇粘度非对称应力张量的自由表面演化方程，明确马兰戈尼数Ma、电参数E及剪切应力τ的增大显著加剧流动失稳，奇粘度μ₁通过修正应力张量实现稳定化；确定热毛细力与电场麦克斯韦应力相互抵消的临界条件，流动达到动态平衡；发现奇粘度与剪切应力的耦合效应具有波数依赖性，波数k < P₁时剪切增强稳定性，k > P₁时剪切加剧失稳，且μ₁ = 1时可放大τ对自由表面演化的调控差异。通过弱非线性分析划分四类失稳区域，量化各参数对临界振幅ζa的影响规律。本研究建立的四场耦合模型与揭示的调控机制，为液膜流动精准控制提供理论支撑。

Abstract: The stability control of liquid film flow on an inclined plate is a core research direction in multiphase flow and interfacial fluid mechanics, which is widely applied in engineering scenarios such as micro-nano coating and industrial heat transfer. This study focuses on liquid film flow on an inclined plate coupled with four fields: shear, uniform thermocapillary, electric field, and odd viscosity. Through the establishment of a coupled mathematical model, long-wave approximation simplification, linear and weakly nonlinear stability analysis, finite difference numerical simulation, combined with the observation of space-time evolution of the free surface, the synergistic regulation mechanism of multiple fields is systematically explored. The study constructs a free surface evolution equation containing an asymmetric stress tensor of odd viscosity, and clarifies that the increase of Marangoni number Ma, electric parameter E, and shear stress τ significantly intensifies flow instability, while odd viscosity μ₁ achieves stabilization by modifying the stress tensor; the critical condition is determined, at which point the thermocapillary force and the Maxwell stress of the electric field cancel each other out, and the flow reaches a dynamic equilibrium; it is found that the coupling effect between odd viscosity and shear stress has a wave number dependence: when the wave number k is less than the wave number for P₁, shear enhances stability; when k is greater than the wave number for P₁, shear intensifies instability. In addition, when μ₁ = 1, it can significantly amplify the regulation difference of τ On evolution of the free surface. Four types of instability regions are divided through weakly nonlinear analysis, and the influence of each parameter on critical amplitude ζa is quantified. The four-field coupling model and the revealed regulation mechanism established in this study provide theoretical support for the precise control of liquid film flow.