The nonlinear erosion of porous media

在两种可侵蚀和可变形材料之间的接触处的流体流动通常可以被视为多孔介质流动，其中通过分离两种材料的薄膜的流动起到润滑它们的接触的作用，并且可以通过驱动应力和粘性阻力之间的直接平衡来建模。在这样的系统中，通过腐蚀或流动局部化形成的不均匀膜厚度会影响材料之间的接触。该博士将使用分析和数值技术来研究接触膜的高度非线性演化，使用与多孔介质中的Saffman-Taylor指进的类比，开发指进的整个生命周期的模型，从而实现表面之间的有效接触。

Fluid flow at the contact between two erodible and deformable materials can often be treated as a porous media flow, in which the flow through the thin films separating the two materials act to lubricate their contact and may be modelled through a direct balance between driving stress and viscous resistance. In such systems, the development of non-uniform film thickness through erosion or flow localisation can affect the contact between materials. This PhD will use analytical and numerical techniques to examine the highly nonlinear evolution of the contact film, using analogies with Saffman-Taylor fingering in porous media, to develop models of the full lifecycle of fingering and hence the effective contact between surfaces.