  This paper is devoted to the numerical study of droplet impact on solid
substrates in presence of surfactants. We formulate the problem in an
energetically variational framework and introduce an incompressible
Cahn-Hilliard-Navier-Stokes system for the phase-field modeling of two-phase
flows. Flory-Huggins potential and generalized Navier boundary condition are
used to account for soluble surfactants and moving contact lines. Based on the
convex splitting and pressure stabilization technique, we develop
unconditionally energy stable schemes for this model. The discrete energy
dissipation law for the original energy is rigorously proved for the
first-order scheme. The numerical methods are implemented using finite
difference method in three-dimensional cylindrical coordinates with
axisymmetry. Using the proposed methods for this model, we systematically study
the impact dynamics of both clean and contaminated droplets (with surfactants)
in a series of numerical experiments. In general, the dissipation in the impact
dynamics of a contaminated drop is smaller than that in the clean case, and
topological changes are more likely to occur for contaminated drops. Adding
surfactants can significantly influence the impact phenomena, leading to the
enhancement of adherence effect on hydrophilic surfaces and splashing on
hydrophobic surfaces. Some quantitative agreements with experiments are also
obtained.
