Interfacial dynamics with soluble surfactants: A phase-field two-phase flow model with variable densities

Abstract

In this work, we present a hydrodynamics coupled phase-field surfactant model with variable densities. Two scalar auxiliary variables are introduced to transform the original free energy functional into an equivalent form, and then a new thermodynamically consistent model can be obtained. In this model, evolutions of two phase-field variables are described by two Cahn-Hilliard-type equations, and the fluid flow is dominated by incompressible Navier-Stokes equation. The finite difference method on staggered grid is used to solve the above model. Then a classical droplet rising case and a droplet merging case are used to validate our model. Finally, we study the effect of surfactants on droplet deformation and merging. A more prolate profile of droplet is observed under a higher surfactant bulk concentration, which verifies the effect of surfactant in reducing the interfacial tension. Increases in surface P´eclet number and initial surfactant bulk concentration can enhance the non-uniformity of surfactant distribution around the interface, which will arise the Marangoni force. The Marangoni force acts as an additional repulsive force to delay the droplet merging.