Phase-field modeling of complex interface dynamics in drop-laden turbulence

Turbulent flows laden with large, deformable drops are ubiquitous in nature and in a wide range of industrial processes. Prediction of the interactions between drops, which deform under the action of turbulence, exchange momentum via surface tension, and that can also exchange heat or mass, are complicated due to the wide range of scales involved: from the largest scales of the flow, down to the Kolmogorov scales of turbulence, and further down to the molecular scale of the interface. Due to this wide range of scales, the numerical description of these flows is challenging and requires robust and accurate numerical schemes that are able to capture both the turbulence characteristics and the dynamics of ever-moving and deforming interfaces including their topological changes (i.e., coalescence and breakage). In the past decades, various numerical methods have been proposed for simulating two-phase flows, from interface-tracking methods, where the interface is explicitly tracked with the use of marker points to interface-capturing methods, where the interface is identified as the isovalue of a color/marker function. Phase-field methods belong to the category of interface-capturing methods, and have emerged as promising approaches to simulate complex two-phase flows. In phase-field methods, the transport equation to describe the drop motion is obtained from first thermodynamics principles, and phenomena acting at the interface scale can be conveniently modeled. Although in realistic case scenarios, the physical thickness of the interface cannot be directly simulated, this family of methods offers desirable properties that have attracted the interest of researchers in recent years. In this work, we describe the fundamentals of the phase-field modeling associated with the direct numerical simulation of turbulence in the context of drop-laden flows. We discuss the potentials of the phase-field method with reference to breakage and coalescence phenomena, and to the corresponding drop size distribution; we examine how to model surface tension changes due to surfactant distribution, and we outline the framework to model heat and mass transfer fluxes. Finally, we present our perspectives for future developments of phase-field modeling of drop-laden turbulent flows in the context of the current available literature.