  In this work, we propose and test the validity of a modified Phase Field
Method (PFM), which was specifically developed for large scale simulations of
turbulent flows with large and deformable surfactant-laden droplets. The time
evolution of the phase field, {\phi}, and of the surfactant concentration
field, {\psi}, are obtained from two Cahn-Hilliard-like equations together with
a two-order-parameter Time-Dependent Ginzburg-Landau (TDGL) free energy
functional. The modifications introduced circumvent existing limitations of
current approaches based on PFM and improve the well-posedness of the model.
The effect of surfactant on surface tension is modeled via an Equation Of State
(EOS), further improving the flexibility of the approach. This method can
efficiently handle topological changes, i.e. breakup and coalescence, and
describe adsorption/desorption of surfactant. The capabilities of the proposed
approach are tested in this paper against previous experimental results on the
effects of surfactant on the deformation of a single droplet and on the
interactions between two droplets. Finally, to appreciate the performances of
the model on a large scale complex simulation, a qualitative analysis of the
behavior of surfactant-laden droplets in a turbulent channel flow is presented
and discussed.
