Effect of Surfactants Preferential Solubility on Droplets Morphology in Turbulence

This study examines soluble surfactants in droplet-laden turbulence using direct numerical simulations of the Navier-Stokes equations coupled to the Phase Field Method in a two-order-parameter formulation. The Cahn-Hilliard equations, where diffusion is driven by a Ginzburg-Landau free energy functional, govern the transport of the parameters. Despite theoretical expectations of symmetry in oil-in-water (O/W) and water-in-oil (W/O) dispersions with matching densities and viscosities, experiments reveal asymmetries attributed to surface-active contaminants that dissolve preferentially in the aqueous phase.

Simulations with droplets matching the carrier fluid's density and viscosity introduce differential solubility by adding a non-symmetrical energy contribution to the surfactant diffusion functional, penalizing dissolution in one phase. Two scenarios are explored: Carrier Preferential Surfactant (CPS), where surfactant dissolution is penalized in the continuous phase, and Droplets Preferential Surfactant (DPS), where it is penalized in the dispersed phase. Results show that surfactant distribution at the interface varies with solubility preference, with higher concentrations in the DPS scenario. This is due to restricted surfactant desorption from the interface in the CPS scenario. Additionally, droplet morphology changes with solubility preference due to differences in surfactant coverage.