a b s t r a c tLattice Boltzmann models (LBM) and phase field models (PFM) are two of the most widespread approaches for the numerical study of multicomponent fluid systems. Both methods have been successfully employed by several authors but, despite their popularity, still remains unclear how to properly compare them and how they perform on the same problem. Here we present a unified framework for the direct (one-to-one) comparison of the multicomponent LBM against the PFM. We provide analytical guidelines on how to compare the Shan-Chen (SC) lattice Boltzmann model for non-ideal multicomponent fluids with a corresponding free energy (FE) lattice Boltzmann model. Then, in order to properly compare the LBM vs. the PFM, we propose a new formulation for the free energy of the Cahn-Hilliard/Navier-Stokes equations. Finally, the LBM model is numerically compared with the corresponding phase field model solved by means of a pseudo-spectral algorithm. This work constitute a first attempt to set the basis for a quantitative comparison between different algorithms for multicomponent fluids. We limit our scope to the few of the most common variants of the two most widespread methodologies, namely the lattice Boltzmann model (SC and FE variants) and the phase field model.

Coalescence and breakup of large deformable droplets dispersed in a wall-bounded turbulent flow are investigated. Droplets much larger than the Kolmogorov length scale and characterized by a broad range of surface tension values are considered. The turbulent field is a channel flow computed with pseudo-spectral direct numerical simulations, while phase interactions are described with a phase field model. Within this physically consistent framework, the motion of the interfaces, the capillary effects, and the complex topological changes experienced by the droplets are simulated in detail. An oil-water emulsion is mimicked: the fluids are considered of same density and viscosity for a range of plausible values of surface tension, resulting in a simplified system that sets a benchmark for further analysis. In the present conditions, the Weber number (W e), that is, the ratio between inertia and surface tension, is a primary factor for determining the droplets coalescence rate and the occurrence of breakups. Depending on the value of W e, two different regimes are observed: when W e is smaller than a threshold value (W e < 1 in our simulations), coalescence dominates until droplet-droplet interactions are prevented by geometric separation; when W e is larger than the threshold value (W e > 1), a permanent dynamic equilibrium between coalescence and breakup events is established.

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