Optimization of computing times in thin film flows with moving contact lines

JUAN M. GOMBA

Massachusetts Institute of Technology,Cambridge, USA

Congreso; Fifth M.I.T. Conference on Computational Fluid and Solid Mechanics - Focus: Advances in CFD; 2009

Massachusetts Institute of Technology (MIT)

Thin film flows are ubiquitous in nature and everyday technologies, such as in liquid transportation in mammalian lungs, self cleaning surfaces in Lotos leaves, coating processing and microfluidic devices. This wide application field called the attention of many researchers, and a big effort has been carried out in order to improve the modelling of the physics involved, specially in thin films with moving contact lines or under the influence of forces exerted on the fluid by molecules on the substrate. Numerical simulation plays a key role in the study of these flows and also constitutes a necessary step toward an effective and rational improvement of the technologies mentioned before. The focus of this work is the reduction of the computing time needed to solve thin films spreading on solids when a moving contact line is present. At the advancing contact line region, the surface tension induces an oscillatory structure and the thickness of the bulk suddenly reduces to the thickness of the precursor film [1]. This abrupt change requieres a dense number of nodes in this critical zone in order to obtain a converged solution in this area. If the domain is large enough, as usual in lubrication coating process, the use of a uniform mesh largely increases the computing time. On the other hand, the use of a fixed non uniform mesh has the disadvantage that the critical zone moves so, unless the period of time needed to solve is short, this approach is useless because the critical zone moves out of the refined mesh region. Other plausible procedures consist in moving the nodes with the fluid, which requieres the definition of an adequate monitor function, or implementing multigrid algorithms [2]. In contrast with the mentioned methods, here we propose to solve the fourth order nonlinear partial differential equation for the thickness h in a moving frame. A similar criteria has been used in the past for fronts moving at a constant velocity, but for lower order partial differential equations. Here, the velocity of the frame, U(t), changes with time, and its value is selected to be the one that minimizes the maximum thickness change. One of the main advantages of the proposed criteria is that it allows to apply the solving algorithm to flows driven by different forces. Here, results for flows driven by thermocapillary and gravity forces will be presented.The differential equation is solved by using finite difference method. In order to assure the positivity of the solution, we employed a positivity preserving scheme, and the resulting algebraic system of equations are evolved in time by employing a synchronized marching Crank-Nicholson scheme combined with an adaptive time stepping procedure [1]. We show that the computing time is reduced up to ten times when compared with cases solved in a laboratory frame. Comparison of numerical profiles obtained by using our and other methods will be presented.