Thin film Flow on Functional Surfaces: Stability and Morphology

要进行的研究包括薄膜（牛顿和非牛顿）在功能表面上体现适当的物理流动的理论研究。这种流动在加工和制造业中无处不在。重点将是：(a)在规则的、有地形图案的表面上连续薄膜的稳定性；(b)在部分湿润的表面上铺展的薄膜的部分覆盖和脱湿特性相关的形态学，当后者在化学上是均匀的或化学图案时，会导致规定位置的表面能突然变化。对于这两个问题，为演化的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；结果方程集将使用最先进的数值近似和收敛加速算法进行计算解决，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的形状和变形，在可能的情况下，将其与流体膜内的底层流动结构联系起来。对于问题(a)的简化二维情况和三维孤立的地形特征，后者将相对直接，但对于问题(b)将更具挑战性——除了在流动的孤立区域，膜破裂形成可以单独探索的液滴。

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.