Title: Derivation of the nonlinear equations for surface of fluid adhering to a moving plate withdrawn from a liquid pool Show Chinese title

Title: 粘附于从液体池中抽出的移动板表面的非线性方程的推导

Abstract: Many technological processes include preparing some special materials adhering to a product surface. For example, this problem is important for the magnetic tape producing, wire adhering, etc. For a surface withdrawn from the molten metal or the other liquid material there is a problem to determine a profile of a film surface. It is subject of this paper. We developed the mathematical model for the simulation of the adhering process of viscous liquid film to a slowly moving plate, which is vertically withdrawn from the molten metal or the other fluid capacity. The Navier-Stokes equations for a film flow on a surface of the withdrawn plate are considered with the corresponding boundary conditions, and the polynomial approximation is used for the film flow profile. The equations after integration across the layer of a film flow result in the system of partial differential equations for the wavy surface of a film flow, of flow rate and of flow energy.The derived equations are used for analysis of the nonlinear film flow that determines the quality of a fluid adhering on a surface of the withdrawn plate. Show Chinese abstract

Abstract: 许多技术过程包括制备一些特殊材料并使其附着在产品表面。 例如，这个问题对于磁带生产、电线附着等非常重要。 对于从熔融金属或其他液体材料中抽出的表面，存在确定薄膜表面轮廓的问题。 这是本文的研究内容。 我们开发了一个数学模型，用于模拟粘性液体薄膜附着到缓慢移动的平板上的过程，该平板垂直地从熔融金属或其他流体容器中抽出。 考虑了在抽出平板表面的薄膜流动的纳维-斯托克斯方程以及相应的边界条件，并对薄膜流动轮廓使用了多项式近似。 在薄膜流动层上积分后得到的方程导致了薄膜流动波浪表面、流量和流动能量的偏微分方程组。 推导出的方程用于分析非线性薄膜流动，这决定了附着在抽出平板表面的流体质量。