The nonlinear erosion of porous media

在两种易腐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了润滑接触的作用，并且可以通过驱动应力和粘性阻力之间的直接平衡来模拟。在这样的系统中，由于侵蚀或流动局部化而形成的不均匀膜厚会影响材料之间的接触。本博士将使用解析和数值技术来研究接触膜的高度非线性演化，使用Saffman-Taylor指进在多孔介质中的类比，以建立指进的全生命周期以及表面之间的有效接触的模型。

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.