##### Modulation of homogeneous and isotropic turbulence in emulsions: energy fluxes and droplet size distribution

Abstract: Emulsions are multiphase flows of two immiscible (totally or partially) liquid phases with similar densities. Such flows are extremely common in industrial applications and environmental flows. The problem is addressed here via direct numerical simulations, where the volume of fluid is used to represent the complex features of the liquid–liquid interface. We consider a mixture of two iso-density fluids and vary the volume fraction of the dispersed phase, the viscosity ratio and the surface tension coefficient to study the turbulence modulation. We examine integral quantities and the spectral scale-by-scale analysis, and demonstrate that energy is transported consistently from

large to small scales by the interfacial stresses, and no inverse cascade is observed. Furthermore, the total surface is found to be directly proportional to the amount of energy transported, while viscosity and surface tension alter the dynamic that regulates energy transport. We also observe the −10/3 and −3/2 scaling on droplet size distributions and demonstrate that the cross-over length scale, the so-called Hinze scale, introduced on dimensional consideration and empirical fitting, can be precisely identified as the scale at which the net energy exchange due to capillarity is zero. Droplets larger than the Hinze scale preferentially break up, thus absorbing energy from the flow; droplet smaller than this scale, instead, tend to coalesce to minimize the free energy, thus releasing energy to the flow.

References:

Modulation of homogeneous and isotropic turbulence in emulsions

M. Crialesi-Esposito, M. E. Rosti, S. Chibbaro and L. Brandt, J. Fluid Mech., 940, A19, 2022