Anja Lippert

Dr. Anja Lippert

Thermocapillary driven Phenomena

Research Motivation

Over the last years, while space applications grew more important, thermocapillary effects gained importance. While on earth often overlayed by gravity, thermocapillary forces are the driving forces in space, where a temperature gradient is present. But also on earth the effect has an important impact on for example the stability of falling films and liquid bridges. Both applications are often present in industry where the prediction and control of the flow is essential. Here numerical two phase flow simulations offer the physical insight, additional to theoretical and experimental work.

Scientific Project

In order to perform highly resolved Direct Numerical Simulations of thermocapillary driven flows, we employ the Finite Volume Code Free Surface 3D (FS3D). This project focuses on providing a numerical framework that is capable of accurately capturing the temperature dependence of the surface tension, the temperature transport and contact line dynamics next to the hydrodynamics. A continuum mechanical sharp interface model containing the two-phase continuity, Navier-Stokes and energy equations with suitably formulated jump conditions at the phase interface for incompressible fluids is established for numerical solution using finite volume discretization. The fluid interface is captured using an extended VOF method with additional piecewise linear interface reconstruction (PLIC).

The numerical Marangoni force is calculated directly from an additional interface-temperature field along the PLIC-planes present from the so-called two-field approach for the temperature transport [1,2]. This approach is also often referred to as “cut cell method”, “Cartesian grid method” or “embedded boundary method”.

Figure 1: Velocity field (left) and temperature field (right) of a thin film above a heated crest. Image: M.Sc. Anja Fath
Figure 1: Velocity field (left) and temperature field (right) of a thin film above a heated crest. Image: M.Sc. Anja Fath

The contact line dynamics are captured with an additional boundary condition for the normal vectors and curvature to enforce the correct contact angle at the wall which can be chosen from a library containing contact angle models derived by hydrodynamic theory and experiments [3].

Within this framework thin films on heated structured surfaces have been analyzed ([E1], Figure 1). Of special interest are the occurring instabilities which , if not damped, can induce waves, flow patterns and film rupture. While waves and vortices enhance fluid mixing and lead to an increase of heat and mass transfer efficiency, film rupture leads to heat transfer deterioration.

Fig. 2: Droplet with contact angle of 70° and a non-uniform wall temperature. Image: M.Sc. Anja Fath
Fig. 2: Droplet with contact angle of 70° and a non-uniform wall temperature. Image: M.Sc. Anja Fath

Other systems under consideration are droplet-based devices. One way to actuate a droplet is by applying a non-uniform temperature gradient to the wall to which it is attached. Of special interest is the migration direction and speed of the droplet to make it suitable for industrial applications. Here, we study the movement of droplets where the interface encloses larger angles with the wall ([E2], see Figure 2).


The work of the authors is supported by the Excellence Initiative of the German Federal and State Governments, the Graduate School of Computational Engineering (GSC CE; GSC 233) and the Center of Smart Interfaces (CSI; EXC 259) at TU Darmstadt.

Project References

[1] Chen Ma and Dieter Bothe. Direct numerical simulation of thermocapillary flow based on the volume of fluid method. International Journal of Multiphase Flow, 37(9):1045 – 1058, 2011.

[2] M. Völlinger. Implementation and Analysis of a Two-Field Approach for the Enthalpy Transport Using the Flow Solver FS3D. Master 's thesis, TU Darmstadt, 2014.

[3] M. Schwieder. Implementation and Study of a Dynamic Contact Angle Model with the Flow Solver FS3D. Master's thesis, TU Darmstadt, 2014.


[E1] A. Fath and D. Bothe. Direct Numerical Simulations of thermocapillary migration of a droplet attached to a solid wall, International journal of multiphase flow, 2015, accepted.

[E2] C. Kallendorf, A. Fath, M. Oberlack, and Y. Wang. Exact solutions to the interfacial surfactant transport equation on a droplet in a Stokes flow regime, Physics of Fluids, 27, 082104 (2015), DOI

[E3] A. Fath, T. Horn, T. Gambaryan-Roisman, P. Stephan, and D. Bothe, Numerical and experimental analysis of short-scale Marangoni convection on heated structured surfaces, International Journal of Heat and Mass Transfer, 86: 764-779, 2015.

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