Marangoni Convection At Deformable Single Rising Droplets – a Numerical Investigation of Fluid Dynamics and Mass Transfer

Marangoni convection at deformable single rising droplets
– a numerical investigation of fluid dynamics and mass transfer

R.F. Engberg, E.Y. Kenig

University of Paderborn, Chair of Fluid Process Engineering,

D-33098 Paderborn, Germany

Exact knowledge on fluid dynamics and mass transfer characteristics of rising droplets is essential for the design of liquid-liquid extraction processes. In particular, the complex interaction of various transport phenomena has to be taken into account. Mass transfer, for instance, can lead to a tangential variation of interfacial tension which may cause Marangoni convection. This phenomenon can affect the fluid dynamics of rising droplets considerably; in general, the rise velocity is reduced [1].

Along with experimental investigations, numerical simulations contribute more and more to the understanding of complex transport phenomena at moving boundaries. In this work, the impact of Marangoni convection on mass transfer and fluid dynamics of single droplets in liquid-liquid systems was studied numerically. For this purpose, we developed a CFD code which employs the classical level set method to capture the moving interface. A well-known drawback of this method is unsatisfactory volume (or mass) conservation – usually, the droplet volume decreases in the course of a simulation. Therefore, we implemented two recently published methods [2,3] that improve the level set approach ensuring exact conservation of the initial droplet volume. The code was supplemented with a concentration-dependent interfacial tension and with a model for mass transfer taking the concentration jump at the interface into account. The model equations were implemented in the open-source CFD toolbox OpenFOAM®.

To the best of our knowledge, no three-dimensional simulations of mass transfer with Marangoni convection at deformable droplets in liquid-liquid systems have been published up to now. Wang et al. [4] performed axisymmetric two-dimensional simulations of deformable droplets which are unable to describe the inherent three-dimensional character of Marangoni convection. In contrast, Wegener et al. [1] investigated Marangoni convection with three-dimensional simulations, however their study was limited to rigid spherical droplets.

In this work, full three-dimensional simulations of deformable toluene droplets rising in water were performed. The concentration of the transferring component acetone was varied. While the mass transfer rates were found to be higher than the experimental and numerical results published by Wegener et al [1], the fluid dynamics and the reduction of the rise velocity is well reproduced. 

[1]	Wegener, M.; Eppinger, T.; Bäumler, K.; Kraume, M.; Paschedag, A.R.; Bänsch, E: Transient rise velocity and mass transfer of a single drop with interfacial instabilities-Numerical investigations. Chem. Eng. Sci. 64 (2009), 4835-4845.
[2]	Groß, S.: Numerical methods for three-dimensional incompressible two-phase flow problems. PhD thesis, RWTH Aachen, 2008.
[3]	Hartmann, D.; Meinke, M.; Schröder, W.: The constrained reinitialization equation for level set methods. J. Comput. Phys. 229 (2010), 1514-1535.
[4]	Wang, J.F.; Wang, Z.H.; Lu, P.; Yang, C.; Mao, Z.S.: Numerical simulation of the Marangoni effect on transient mass transfer from single moving deformable drops. AIChE Journal 57 (2011), 2670-2683.