Field of research

Three-dimensional simulation of capillary bridges

Whoever tried to build a sand castle on the beach, knows the difference between wet and dry sand. While dry sand trickles easily, wet sand can be formed into a castle. The reason for this phenomenon are the strong adhesive forces between the sand particles, which occur due to capillary bridges. In order to determine these adhesive forces, the geometry of the capillary bridge must be determined exactly. This is usually not necessary for the construction of a sand castle, however, there are numerous industrial areas in which adhesive forces play such a dominant role that they must be determined. Examples are the sintering of metals or ceramics as well as almost all powder processes.

Therefore, capillary bridges are theoretically investigated at the Particle Technology Group in order to determine the resulting adhesive forces. Depending on the application, there are numerous approximation methods for the evaluation of rotationally symmetric capillary bridges. However, these methods cannot be easily extended to arbitrary, three-dimensional particles. Consequently, the calculation of the capillary forces between asymmetric particles or the consideration of surface roughness is not yet possible with sufficient accuracy. Thus, the long-term goal is to develop a method for the three-dimensional simulation of capillary bridges between arbitrarily shaped particles. Optimization methods for the calculation of energy-minimal surfaces seem to be promising for this purpose. The Young-Laplace equation is formulated as a partial differential equation and solved by a finite element method.

The development of a method optimized for capillary bridges is carried out in close cooperation with PD Dr Stephan Schmidt from the Institute of Mathematics at Humboldt University Berlin.


Publications and conference proceedings

  • Stephan Schmidt, Melanie Gräßer, Hans-Joachim Schmid
    A Shape Newton Scheme for Deforming Shells with Application to Capillary Bridges
    Submitted (29.12.2020): SIAM Journal on Scientific Computing
  • Melanie Gräßer, Andreas Brümmer
    Influence of water and oil clearance flow on the operational behavior of screw expanders
    Journal of process mechanical engineering (2016)
  • Melanie Gräßer, Andreas Brümmer
    Influence of liquid in clearances on the operational behavior of twin screw expanders
    9th International Conference on Compressors and their Systems, IOP Conf. Series: Materials Science and Engineering 90 (2015)
  • Melanie Gräßer, Andreas Brümmer
    An analytic model of the incompressible one-phase clearance flow in liquid injected screw expanders
    9th International Conference on Screw Machines 2014, VDI Bericht 2228 (2014), pp. 71-89

Supervised student work


David Klein: "Weiterentwicklung eines freiwilligen Zusatzkurse zur Vermittlung von Selbstlernkompetenzen in der Studieneingangsphase im ingenieurwissenschaftlichen Bereich im Hinblick auf die Teilnehmeranzahl" (Masterarbeit)

Mats Vernholz: "Entwicklung eines Evaluationskonzeptes für einen neu entwickelten Kurs zur Vermittlung von Selbstlernkompetenzen in der Studieneingangsphase im ingenieurwissenschaftlichen Bereich" (Masterarbeit)


Benjamin Elmar: " Entwicklung eines Algorithmus zur Erzeugung von rauen Partikeln" (Bachelorarbeit)

Vassil Rägo: " Berechnung der Kapillarkraft für eine beliebig geformte dreidimensionale Kapillarbrücke" (Masterarbeit)


Christian Bähr: "Numerische Simulation von Flüssigkeitstropfen mittels OpenFOAM" (Studienarbeit)

Steffen Loeck: "Numerische Simulation von zweidimensionalen Kapillarbrücken mittels OpenFOAM" (Bachelorarbeit)

Julian Winkelhake: "Numerische Simulation von zwei- und dreidimensionalen Kapillarbrücken mittels OpenFOAM" (Masterarbeit)

Kathrin Faupel: "Entwicklung eines Konzepts zur Vermittlung von Selbstlernkompetenzen zur Verbesserung der Studieneingangsphase von Studierenden im ingenieurwissenschaftlichen Bereich" (Masterarbeit)

Tarek Remmert: "Analyse der Selbsteinschätzung der Studierenden hinsichtlich ihrer Selbstlernkompetenzen im Vergleich zur Empfehlung der Lehrenden in der Fakultät Maschinenbau der Universität Paderborn" (Masterarbeit)