标题： 惯性作用下弯曲基底上薄流体流动的精确和全面模型 显示英文标题

标题： The accurate and comprehensive model of thin fluid flows with inertia on curved substrates

摘要： 考虑粘性牛顿流体在弯曲二维基底上的三维流动，当流体薄膜很薄时，这种情况出现在许多排水、涂布和生物流动中。 我们推导了薄膜动力学的综合模型，该模型以薄膜厚度和平均横向速度来表示。 基于中心流形理论，我们可以确信该模型准确地包含了基底曲率、重力体积力、流体惯性和耗散的影响。 该模型可用于解析任意弯曲基底（如圆柱体、管道和球体）上粘性流体流动的动力学中的波状现象。 我们简要说明了其在模拟圆柱纤维上的液滴形成、波浪转换、法拉第波、粘性水跃以及复合渠道中的流动涡旋中的应用。 这些模型是牛顿流体薄层流动最完整的模型；本文给出的动力学方程的不同截断可以得到许多其他薄层流动模型。 显示英文摘要

摘要： Consider the 3D flow of a viscous Newtonian fluid upon a curved 2D substrate when the fluid film is thin as occurs in many draining, coating and biological flows. We derive a comprehensive model of the dynamics of the film, the model being expressed in terms of the film thickness and the average lateral velocity. Based upon centre manifold theory, we are assured that the model accurately includes the effects of the curvature of substrate, gravitational body force, fluid inertia and dissipation. The model may be used to resolve wave-like phenomena in the dynamics of viscous fluid flows over arbitrarily curved substrates such as cylinders, tubes and spheres. We briefly illustrate its use in simulating drop formation on cylindrical fibres, wave transitions, Faraday waves, viscous hydraulic jumps, and flow vortices in a compound channel. These models are the most complete models for thin film flow of a Newtonian fluid; many other thin film models can be obtained by different truncations of the dynamical equations given herein.