Calculation of Droplet Coalescence in Binary Liquid–Liquid Systems: An Incompressible Cahn–Hilliard/Navier–Stokes Approach Using the Non-Random Two-Liquid Model

Abstract

Due to their lower costs regarding money and time compared to performing experiments, computer simulations grow in importance when developing industrial separation processes. On plant scales, process simulators are widely applied, and on particular scales, computational fluid dynamics (CFD) calculations can support design. In this work, the incompressible Cahn–Hilliard/Navier–Stokes equations and the non-random two-liquid (NRTL) model were applied to perform numerical simulations in order to investigate droplet interactions of extraction systems. In contrast to other CFD approaches, no assumptions regarding the evolution of drop size distributions are required. The impact of the influence parameter and mobility coefficient within this framework was studied for the first time. While the mobility coefficients show a low impact on the flow field, different values of the influence parameter can lead to completely different behavior, with low influence parameters causing small morphologies and requiring larger grid resolutions in the simulation. A method is proposed to incorporate various thermodynamic data like phase equilibrium, interfacial tension, and diffusion coefficients into CFD simulation. Especially, the interfacial tension is not a direct parameter but rather determines the density gradient theory (DGT) influence parameter and therefore enables us to consider the variation of interfacial tensions in a system with different temperatures or compositions.

Continuum-scale modelling of polymer blends using the Cahn–Hilliard equation: transport and thermodynamics

“…If one were to obtain κ rigourously, this would involve the use of the method of Ariyapadi and Nauman 32 , as previously discussed, which can result in an excessively complex expression for κ. When obtaining κ for the NRTL model, Zimmermann et al 18 used order-of-magnitude estimates. Other studies instead specified a constant value of κ in a semi-empirical fashion 13,111 .…”

“…However, there are a variety of more-advanced thermodynamic models that are better suited for specific systems or enable more-accurate modelling of complex systems that can be employed. To date, only a handful of studies have explored more-complex thermodynamic models, such as CALPHAD-based free-energy functions 16 , the comparatively simple activity-coefficient model Non-random Two-Liquid (NRTL) 17,18 and free-energy functions suitable for mineralic systems 19 , within the Cahn-Hilliard equation.…”

Viscous to inertial coalescence of liquid lenses: A lattice Boltzmann investigation

“…Future improvements in these technologies rely strongly on the ability to advance the understanding of the wetting behavior of droplets on liquid substrates as well as an accurate knowledge of the interaction between the liquid phases and the dynamics of their coalescence [17,18]. Previous research has primarily been focused on the coalescence of freely suspended droplets [4,[19][20][21][22][23][24] and droplets on solid substrates [25][26][27][28][29][30], while droplets on liquid substrates [31][32][33] have received less attention.…”

Fluid Simulation‐Supported Extraction Process Design: An Approach Towards Improving Current Models

“…This shall now be extended by accounting for the equations of fluid motion. The non‐random two‐liquid model of Renon and Prausnitz is an outstanding example for modeling thermodynamic equilibria with a broad bandwidth of systems and has been used to model coalescence . In this work, the DGT in combination with the KK model and the momentum as well as the mass balance is applied to model droplet interactions and breakup.…”