(546d) Numerical Simulation of Interfacial Behavior in Liquid-Liquid Systems

The interface plays an important role in chemical engineering as it determines the mass transfer between two phases and the formation of droplets in multi-phase flows. For example, in practical applications like liquid-liquid extraction columns the interfacial interactions in form of droplet coalescence and droplet breakage are decisive. Interfacial behavior in the context of multi-phase flows is in the focus of scientific discussion since decades, but there is still a lack of understanding [KAM17]. This lack of understanding mainly originates in the complexity of interfacial behavior due to the interaction between the fluid flow field, capillary forces and the superimposed mass transfer between the phases. Furthermore, a detailed investigation of the interface in the context of multi-phase flows is experimental laborious because of its small scale and its fluid character. Based on the experimental evaluations the resulting mathematical models for multi-phase flows often need expensive parametrization.

In this contribution, we suggest a thermodynamic consistent simulation approach to resolve the interface and investigate multi-phase flows in more detail. The model is based on the incompressible density gradient theory developed by Cahn and Hilliard (CH) [CAH58] and combined with the Navier-Stokes equations in a novel introduced CHNS model. Furthermore, the thermodynamic Non-Random Two-Liquid [REN68] model is incorporated into the CHNS framework. This approach allows to model interfacial properties of liquid-liquid systems and predict interfacial 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. Since the CHNS framework consists of a system of highly non-linear partial differential equations it is implemented into OpenFoam® and solved via the Finite Volume Method.

Applying the CHNS model approach enables the detailed simulation of interfacial behavior in liquid-liquid systems such as droplet coalescence and its effect on convective and diffusive mass transport. By doing so, the different gradients in velocity and chemical potential are evaluated to deepen the understanding of the interfacial behavior. Furthermore, complex interfacial effects like the Marangoni convection are investigated in more detail.

[KAM17] Kamp J., Villwock J. and Kraume M., “Drop coalescence in technical liquid/liquid applications: A review on experimental techniques and modeling approaches,” Reviews in Chemical Engineering., vol. 33, no.1, pp. 1-47, 2017.

[CAH58] 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.

[REN68] Renon H. and Prausnitz J. M., “Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures”, AIChE J., 14(1), S. 135–144, 1968.