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We perform direct numerical simulations of surfactant-laden droplets inhomogeneous-isotropic turbulence with Taylor Reynolds number$Re_\lambda\approx180$. Effects of surfactant on the droplet and local flowstatistics are well approximated using a lower, averaged value of surfacetension, allowing us to extend the framework developed by Kolmogorov (1949) andHinze (1955) for surfactant-free bubbles to surfactant-laden droplets. We findthe Kolmogorov-Hinze scale ($d_H$) is indeed a pivotal length scale in thedroplets' dynamics, separating the coalescence-dominated and thebreakage-dominated regimes in the droplet size distribution. We see thatdroplets smaller than $d_H$ have spheroid-like shapes, whereas larger dropletshave long convoluted filamentous shapes with diameters equal to $d_H$. As aresult, droplets smaller than $d_H$ have areas that scale as $d^2$, whilelarger droplets have areas that scale as $d^3$, where $d$ is the dropletequivalent diameter. We further characterise the filamentous droplets bycomputing the number of handles (loops of the dispersed phase extending intothe carrier phase) and voids (regions of the carrier phase enclosed by thedispersed phase) on each droplet. The number of handles per unit length offilament ($0.06d_H^{-1}$) scales inversely with surface tension, while thenumber of voids is independent of surface tension. Handles are indeed anunstable feature of the interface and are destroyed by the restoring effect ofsurface tension, whereas voids can move freely inside the droplets.

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