Modeling of interfacial phenomena in disperse liquid-liquid systems

Abstract

Interfaces are critical in chemical engineering, as they govern mass transfer between phases and play a key role in the formation and behavior of droplets and bubbles. This is particularly true in liquid-liquid extraction columns, where droplet interactions such as coalescence and breakage are pivotal. In decades of research, droplet coalescence remains a complex phenomenon that is not yet fully understood, partly due to the challenges in experimentally analyzing the small-scale and fluid nature of interfaces. To address this gap, we propose a thermodynamically consistent simulation approach to accurately resolve interfaces and study droplet interactions. The developed model builds on the incompressible Density Gradient Theory (DGT) by Cahn and Hilliard, coupling it with the Navier-Stokes equations to form a novel Navier-Stokes/DGT framework. Within this framework, the Non-Random Two-Liquid model is employed as the thermodynamic foundation, enabling the accurate modeling of interfacial properties and prediction of coalescence behavior in liquid-liquid systems. The Navier-Stokes/DGT model, comprising a system of highly nonlinear partial differential equations is solved using the finite volume method in OpenFOAM. This approach enables the simulation of the single stages of droplet coalescence. Furthermore, complex interfacial effects like Marangoni convection and de-mixing behavior are investigated in more detail.