Phase field modeling of wetting on structured surfaces
  We study the dynamics and equilibrium profile shapes of contact lines for wetting in the case of a spatially inhomogeneous solid wall with stripe defects. Using a phase-field model with conserved dynamics, we first numerically determine the contact line behavior in the case of a stripe defect of varying width. For narrow defects, we find that the maximum distortion of the contact line and the healing length are related to the defect width, while for wide defects, they saturate to constant values. This behavior is in quantitative agreement with experimental data. In addition, we examine the shape of the contact line between two stripe defects as a function of their separation. Using the phase-field model, we also analytically estimate the contact line configuration, and find good qualitative agreement with the numerical results. 
Kaifu Luo, Mikko-Pekka Kuittu, Chaohui Tong, Sami Majaniemi and Tapio   Ala-Nissila