Fluid flows mainly driven by capillary forces will be presented. By
means of modeling and simulations, interesting dynamics in some
capillary-driven flows can be revealed such as coalescences, breakups,
precursor films, flow instabilities, rapid spreading, rigid body
motions, and reactive wetting.

Diffuse-interface methods model a fluid interface as having a finite
thickness endowed with physical properties such as surface tension. Two
diffuse-interface models that are based on the free energy of the system
will be presented. The binary model, more specifically the coupled
Navier-Stokes/Cahn-Hilliard equations, was used to study different
two-phase flows including problems related to microfluidics. The ternary
model is developed for more complicated flows such as reactive wetting,
where the spreading liquid partially dissolves into the solid substrate.
The numerical simulations revealed two stages in the wetting process, a
convection-dominated stage where rapid spreading occurs and a
diffusion-dominated stage where depression of the liquid-substrate
interface and elevation of the contact line region can be observed.