(54a) Interfacial Behavior and Droplet Interaction in Liquid-Liquid Systems

Multi-phase flows are a major task in chemical engineering and involve a spectrum of phenomena which are influenced by phase behavior and droplet interactions. Data concerning multi-phase flows are experimental laborious and mathematical models often need expensive parametrization. The main goal of this work is the modeling of interfacial properties due to droplet interactions in liquid-liquid systems.

In order to model the coalescence of droplets the incompressible density gradient theory¹ developed by Cahn and Hilliard (CH) is combined with the incompressible Navier-Stokes equations in a novel introduced CHNS model. Furthermore, the thermodynamic Non-Random Two-Liquid model² is incorporated into the CHNS framework. This approach allows to model interfacial properties of liquid-liquid systems and predict coalescence behavior in a thermodynamic consistent fashion. The major advantages of this model approach are the elimination of mathematical models with expensive parametrization based on multi-phase experiments and the only use of standard thermodynamic data. The CHNS framework consists of a system of highly non-linear partial differential equations which are implemented into OpenFoam® and calculated via the Finite Volume Method.

This contribution discusses the applicability of the developed CHNS framework to binary liquid-liquid systems in order to describe droplet formation. Furthermore, the behavior of phase separation and its effect on convective and diffusive mass transport is investigated in detail.

[1] Cahn J. W. and Hilliard J. E., “Free Energy of a Nonuniform System. I. Interfacial Free Energy,” J. Chem. Phys., vol. 28, no. 2, pp. 258–267, Feb. 1958.

[2] Renon H. and Prausnitz J. M., “Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures”, AIChE J., 14(1), S. 135–144, 1968.