Thin film Flow on Functional Surfaces: Stability and Morphology

将开展的研究包括对包含适当物理的功能表面上的薄膜流动(牛顿和非牛顿)的理论研究。这种流动在加工和制造行业中随处可见。重点将是：(A)规则的、有地形图案的表面上连续薄膜的稳定性；(B)当部分湿润表面的化学均质或化学图案导致指定位置的表面能量突然变化时，分布在部分湿润表面上的薄膜的部分覆盖和去湿特性相关的形态。为这两个问题的演变三维流动的行为推导适当的预测模型的主要工具将是长波近似；所产生的方程组将使用最先进的数值近似和收敛加速算法通过计算求解，并在必要时利用并行编程和计算平台。另一个简化的假设是蒸发效应将被忽略。在所有情况下，主要的诊断将是自由表面形状和变形，在可能的情况下，这与流体膜内的基本流动结构有关。对于问题(A)的简化二维情况和三维的孤立地形特征而言，后者将相对直接，但对于问题(B)而言，后者将具有相当大的挑战性--不同于在流动的孤立区域，在那里薄膜破裂形成可单独探索的液滴。

The research to be undertaken encompasses a theoretical investigation of thin film (Newtonian and non-Newtonian) flows on functional surfaces embodying the appropriate physics. Such flows are ubiquitous within the processing and manufacturing industries. The focus will be: (a) the stability of continuous films on regular, topographically patterned, surfaces; (b) the morphology associated with the partial coverage and de-wetting characteristics of thin films spreading over a partially wetting surface when the latter is chemically homogeneous or chemically patterned leading to sudden changes in the surface energy at prescribed sites. The principal vehicle for deriving appropriate predictive models for the behaviour of the evolving three-dimensional flow for both problems will be the long-wave approximation; the resulting equation set will be solved computationally using state-of-the-art numerical approximations and convergence acceleration algorithms, utilising parallel programming and computing platforms as necessary. An additional simplifying assumption is that evaporation effects will be ignored. In all cases the main diagnostic will be the free-surface shape and deformation relating this, where possible, to the underlying flow structure within the fluid film. The latter will be relatively straight forward for the simplified two-dimensional case of problem (a) and for isolated topographical features in three-dimensions, but will be considerably more challenging for problem (b) - other than in isolated regions of the flow where the film breaks up to form a droplet which can be explored individually.