Morphology of surfactant-free and surfactant-laden droplets in homogeneous isotropic turbulence

We perform direct numerical simulations of surfactant-free and surfactant-laden droplets in statistically-stationary homogeneous isotropic turbulence at moderate Taylor Reynolds number, Re_λ≈180. The volume of fluid method is used to track the interface, while the soluble surfactant is transported using an advection-diffusion equation. Surfactants reduce surface tension at the interface according to their local concentration; surface tension gradients along the interface, generated by a inhomogeneous surfactant concentration, induce Marangoni stresses acting tangential to the interface. In our simulation setup, we find the average surface tension reduction to be the dominant effect, allowing us to extend the Kolmogorov-Hinze (KH) theory to surfactant-laden droplets: we compute the KH scale by using a lower, averaged value of surface tension. We characterize the morphology of the droplets, and find two different regimes for the interfacial area of each droplet. The interfacial area of droplets smaller than the KH scale is proportional to d², while that of larger droplets is proportional to d³, with d being the characteristic size of the droplet. The two different regimes originate from the shape of the droplets: droplets smaller than the KH scale take regular, spheroid-like shapes, whereas droplets larger than the KH scale take long, coiled, filamentous shapes.