Modeling and Simulation of droplet collisions at modified ambient pressure, with high gradients in velocity or concentration and for non-miscible fluids


Prof. Dr. rer. nat. Dieter Bothe

Prof. Dr. rer. nat. Dieter Bothe

Director subarea A7
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  • +49 6151 16-21463
Dr.-Ing. Kathrin Schulte

Dr.-Ing. Kathrin Schulte

Director subarea A7
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  • +49 711 685-62334
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Johanna Potyka, M.Sc.
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  • +49 711 685-62311


Collision processes play a major role in different science and engineering problems ranging from cloud dynamic processes to technical spray applications. A realistic description of the drop populations and their dynamics must be build on a deeper understanding of the elementary process of binary droplet collisions. Here the essential question is the collision outcome in relation to the dimensionless parameters. The modeling of the collision process with respect to the collision outcome –bouncing, coalescence or drop disintegration, in some cases with the formation of secondary droplets – makes up the foundation for simulations on bigger scales like whole sprays. The understanding of the underlying physical processes needed to model the previously described events, shall be gained by direct numerical simulation with the multi-phase code FS3D. Due to the relevance of the collision of two drops at high impact velocities for single-phase fuel sprays this topic shall be elaborated further in the current funding period to accomplish a modeling of the drop disintegration (“splashing”) with the prediction of number and size distribution of the secondary droplets as well as a preparation of the gained data for spray simulations. Whereas at high ambient pressures drops can bounce from each other more frequently. The aim of the current research is the extension of the modeling and further development of FS3D in respect of the predictive description of these phenomena to capture the complete physics of the droplet collision numerically.

Another relevant topic are binary collisions of drops made of two different miscible or immiscible fluids. The droplet collision of different miscible fluids leads to imbalanced surface tension forces. Through direct numerical simulations with FS3D, the influence of the locally varying fluid properties on the collision outcome shall be studied. If the drop disintegrates, the composition of the secondary droplets is of interest besides the formation of the rim instability. At the collision of drops of immiscible fluids the surface tensions govern the contact angle at the three phase boundary. In the collision process a (partial) encapsulation of the drop of higher surface tension can occur. The effect of the fluid properties on the collision outcome shall be quantified by Direct Numerical Simulations.



Johannes Kromer and Dieter Bothe:
Face-based Volume-of-Fluid interface positioning in arbitrary polyhedra
Journal of Computational Physics, 110776 (2021),
DOI: 10.1016/

Johannes Kromer and Dieter Bothe:
Third-order accurate initialization of VOF volume fractions on unstructured grids with arbitrary polyhedral cells
arXiv preprint (2111.01073), 2021.

Johannes Kromer, Johanna Potyka, Kathrin Schulte and Dieter Bothe:
Efficient three-phase PLIC interface positioning on unstructured meshes with arbitrary polyhedral cells
arXiv preprint (2105.08972), 2021.

Johanna Potyka and Kathrin Schulte:
New Approaches for the Interface Reconstruction and Surface Force Computation for Volume of Fluid Simulations of Droplet Interaction of Immiscible Liquids
arXiv preprint (2104.11108), 2021.


Johannes Kromer and Dieter Bothe:
Highly accurate computation of volume fractions using differential geometry.
Journal of Computational Physics, 396 (2019), pp. 761-784.
DOI: 10.1016/

Muyuan Liu and Dieter Bothe:
Toward the predictive simulation of bouncing versus coalescence in binary droplet collisions.
Acta Mechanica, 230 (2) (2019), pp. 623-644.
DOI: 10.1007/s00707-018-2290-4


Muyuan Liu:
Numerical Study of Head-on Binary Droplet Collisions: Towards Predicting the Collision Outcomes.
Darmstadt, Technische Universität Darmstadt, Dissertation, 2017.

Reitter, Louis; Liu, Muyuan; Breitenbach, Jan; Huang, Kuan-Ling; Bothe, Dieter; Brenn, Günter; Pan, Kuo-Long; Roisman, Ilia V.; Tropea, Cameron:
Experimental and computational investigation of binary drop collisions under elevated pressure.
ILASS–Europe 2017, 28th Conference on Liquid Atomization and Spray Systems, 6-8 September 2017, Valencia, Spain,
DOI: 10.4995/ILASS2017.2017.4758

Planchette, C., Hinterbichler, H., Liu, M., Bothe, D., Brenn, G.:
Colliding drops as coalescing and fragmenting liquid springs.
J. Fluid Mech. 814: 277-300, 2017.

Schulte, K.:
Modelling of the Initial Ice Growth in a Supercooled Liquid Droplet.
Dissertation, Universität Stuttgart, 2017.


Muyuan Liu, Dieter Bothe:
Numerical study of head-on droplet collisions at high Weber numbers.
J. Fluid Mech. 289 (2016), pp 785-805.

Muyuan Liu, Dieter Bothe:
Numerical study of binary droplet collisions at high Weber numbers.
Presentation for ProcessNet Annual Conference, Bingen, Germany, 2016.

Muyuan Liu, Dieter Bothe:
Numerical study of head-on collisions of water droplets at high Weber numbers.
Poster for International Conference on Multiphase Flows, Florence, Italy, 2016.

Bothe, D. und Prüss, J.:
On the interface formation model for dynamic triple lines.
Recent Developments of Mathematical Fluid Mechanics: 25-47 Springer 2016.

Eisenschmidt, K., Ertl, M., Gomaa, H., Kieffer-Roth, C., Meister, C., Rauschenberger, P., Reitzle, M., Schlottke, K. und Weigand, B.:
Direct numerical simulations for multiphase flows: An overview of the multiphase code FS3D.
Appl. Math. Comput. 272:508-517, 2016.

Dragomirescu, F.I., Eisenschmidt, K., Rohde, C., Weigand, B.:
Perturbation solutions for the finite radially symmetric Stefan problem.
Int. J. of Thermal Sciences 104: 386-395, 2016.

Bothe, D.:
Mass transfer across fluid interfaces - modeling the influence of adsorbed surfactant.
Proc. RIMS Symposium on “Mathematical Analysis of Viscous Incompressible Fluids”, Kyoto University, 2016.


Ma, C., Bothe, D.
Numerical Modeling of Thermocapillary Two-Phase Flows with Evaporation using a Two-Scalar Approach for Heat Transfer
J. Comp. Phys. 233 (2013), 552-573 (online verfügbar)

Focke, C., Bothe, D.
Direct numerical simulation of binary off-center collisions of shear thinning droplets at high Weber numbers
Physics of Fluids, 24(7) (2012), 073105

Ma, C., Bothe, D.
Direct Numerical Simulation of Thermocapillary Flow Based on the Volume of Fluid Method
Int. J. Multiphase Flow 37 (2011), 1045-1058

Focke, C. and Bothe, D.
Computational Analysis of Binary Collisions of Shear-Thinning Droplets
J.Non-Newt. Fluid Mech. 166 (2011), 799–810