Thin film flow over a topography and non-isothermal droplets : a numerical study

Research towards understanding continuous thin film flows and droplet spreading is as relevant today as it ever was. Theoretically, lubrication theory has played a pivotal role with the equations involved requiring numerical solution. The most commonly employed solvers are based upon either a time-splitting or multigrid strategy; no consensus has been reached as to which is the most accurate and efficient. With modern engineering applications demanding solutions at smaller and smaller scales, in turn requiring the use of finer grids to ensure mesh independent solutions, efficiency is a necessary consideration. The work of this thesis divides into two strands. First, a three-dimensional continuous film problem is modelled and formulated in two equivalent ways: as two coupled second-order equations, or as a single fourth-order equation. These are solved numerically by multigrid and time-splitting solvers, finding that, due to the larger time-steps which are possible, the multigrid scheme, when solving the coupled equations, offers the fastest route to converged solutions; the accuracy of solution for each solver is comparable. Following the use of static mesh adaptivity, the conclusions drawn for uniform meshes concerning the solvers are found to be equally valid on non-uniform meshes. Following that, a new model is proposed to investigate unpinned droplets evaporating from a thick, heated substrate into the surrounding atmosphere. A study of accuracy and efficiency is also conducted for a droplet spreading problem; it isfound that the multigrid scheme, when solving the coupled system of equations, is again the most efficient solver. This scheme is adapted for the evaporation model, leading to excellent qualitative and some quantitative agreement with previous studies of both the pinned and unpinned stages of evaporation. To the' author's knowledge, this is the first model to successfully capture the behaviour in both stages of evaporation and also the change in this behaviour depending upon the properties of the substrate and liquid considered.EThOS - Electronic Theses Online ServiceGBUnited Kingdo