Research Topic

Thermocapillary motions and their impact on flow stability


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. Direct numerical two phase flow simulations offer the physical insight, additional to theoretical and experimental work.


In order to perform highly resolved Direct Numerical Simulations of falling films, we employ the Finite Volume Code Free Surface 3D (FS3D). 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. For a high accuracy, which is essential for simulation of thermocapillary flow and stability analysis, the numerical Marangoni force is calculated from an additional interface-temperature field resulting from the energy jump condition at the interface.

To be capable to simulate more complex phenomena, the following aspects are treated within this project in depth:

  • Accounting for the direct connection of Marangoni forces and surface stress

  • Contact line dynamics

  • Stability analysis of three dimensional film flow including Marangoni effects

Preliminary Results

The implementation of the Marangoni forces is done in within a balanced Continuum Surface Force (CSF) framework. It is accounted for the mathematical dependency of the surface stress and the Marangoni forces, which allows a deeper insight into the behavior of migrating droplet due to thermal Marangoni. The code has been validated for thermal Marangoni driven droplet migration and Marangoni driven channel flows. A framework for three-dimensional linear stability analysis has be set up and is about to be validated.

Contact line dynamics are captured at a macroscopic range, using the latest mesh independent techniques build upon the works of Afkhami, Zaleski and Bussmann.

Squalane droplet on a heated wall with a linear temperature gradient

Key Research Area

Multiyphysics: Thermal Marangoni, Dynamic Contact Angle, Flow Stability


D. Bothe,  Mathematical Modeling and Analysis

P. Stephan,  Technische Thermodynamik


Anja Fath


Dolivostraße 15

D-64293 Darmstadt



+49 6151 16 - 24384


+49 6151 16 - 24404


fath (at) gsc.tu...

 Print |  Impressum |  Sitemap |  Search |  Contact |  Privacy Policy
zum Seitenanfangzum Seitenanfang