Towards accurate modeling of moving contact lines

Abstract: The present thesis treats the numerical simulation of immiscible incompressible two-phase flows with moving contact lines. The conventional Navier–Stokes equations combined with a no-slip boundary condition leads to a non-integrable stress singularity at the contact line. The singularity in the model can be avoided by allowing the contact line to slip. Implementing slip conditions in an accurate way is not straight-forward and different regularization techniques exist where ad-hoc procedures are common. This thesis presents the first steps in developing the macroscopic part of an accurate multiscale model for a moving contact line problem in two space dimensions. It is assumed that a micro model has been used to determine a relation between the contact angle and the contact line velocity. An intermediate region is introduced where an analytical expression for the velocity field exists, assuming the solid wall is perfectly flat. This expression is used to implement boundary conditions for the moving contact line, at the macroscopic scale, along a fictitious boundary located a small distance away from the physical boundary. Model problems where the shape of the interface is constant throughout the simulation are introduced. For these problems, experiments show that the errors in the resulting contact line velocities converge with the grid size h at a rate of convergence p ≈ 2. Further, an analytical expression for the velocity field in the intermediate region for the case with a curved solid wall is derived. The derivation is based on perturbation analysis.

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