Subproject B08

Numerical simulation of the interaction between a drop and a liquid wall film


  Name Contact
Dr. Holger Marschall (MMA)
Dr.-Ing. Holger Marschall
+49 6151 16-21465
L2|06 411
Martin Wörner, KIT
Dr. Dipl.-Ing. Martin Wörner
+49 721 608-47426
Milad Bagheri
Milad Bagheri M.Sc.
+49 6151 16-20606
L2|06 104


In internal combustions engines and in systems for exhaust gas aftertreatment, sprays interact with liquid wall films. The impact of fuel drops, for instance, may release oil from the lubricating wall film into the combustion region causing pre-ignition. Fundamental understanding of this interaction and its proper modeling are essential to increase efficiency while reducing emissions. The interaction between a drop and a liquid wall film has mainly be studied for identical or immiscible liquids so far. The focus of this subproject is on the interaction of miscible liquids, as they are used in above-mentioned applications.


This subproject aims at the numerical investigation of drop impact processes on a liquid wall film for the case when both fluids are miscible but have different properties. Depending on velocity and size of the droplets and on the thickness of the wall film, splashing might occur and secondary droplets form. The central research questions in the second funding period are:

1. How does the miscibility of droplet and wall film affect the drop impact and splashing process.

2. What is the composition and size distribution of secondary drops for different conditions?

The long-term objective is the development, implementation and application of a numerical method based on the diffuse-interface approach to enable accurate, robust and efficient simulations of droplet-wall interaction in prototypical cases.

Previous Findings

As this subproject has started in the second funding period of the Collaborative Research Centre/Transregio 150, no findings from the first funding period can be reported so far. However, experiments performed in the first funding period within subproject A02 indicate that the drop impingement process and its outcomes may differ for immiscible and miscible liquids.This gave motivation to establish the present numerical subproject as new research topic.

Picture: TRR 150
Impact of a drop (marked by red tracer) on an immiscible wall film (image from subproject A02)


The numerical simulations are performed using a diffuse-interface phase field method. In this approach, the interface is treated as a thin transition layer of finite and prescribed width across which physical properties vary rapidly but continuously (diffuse interface concept). The two-phase flow is described by the coupled Cahn-Hilliard-Navier-Stokes equations which are solved using the open source C++ library OpenFOAM (code phaseFieldFoam, developed by the PIs). The validation of hydrodynamics of the droplet-wall-film interaction is based on experiments under ambient conditions. Later on, the developed simulation code will be deployed to investigate the drop wall-film interaction under application-relevant conditions in the engine and the exhaust gas system (where drop and wall film consist of urea-water solution with different concentration).

Current Work

The simulation code phaseFieldFoam is currently restricted to immiscible two-phase flows. The first objective is to extend the methodology and code implementation to miscible fluids. The numerical simulations will allow examining the normal impact of a single droplet on a liquid wall film. Coordinated measurements in subproject A02 provide experimental data for validation.

Sketch of setup in numerical simulation


For validation of the numerical simulations and to establish fundamental understanding, coordinated and complementary experimental studies are carried out in the Collaborative Research Centre/Transregio 150: The close interplay between experimental and numerical projects aims to understand the drop wall-film interaction with miscible two-component systems under ambient conditions (A02), in the cylinder (C02) and in the exhaust gas system (C04), and to develop a parametric model for the composition and mass of secondary droplets for integration into the holistic model (C05).

Selected Publications

  • Dadvand, A., Bagheri, M., Samkhaniani, N., Marschall, H., Wörner, M.: Advected phase-field method for bounded solution of the Cahn–Hilliard Navier–Stokes equations. Physics of Fluids 33 (5), 53311,, 2021.
  • Wörner, M., Samkhaniani, N., Cai, X., Wu, Y., Majumdar, A., Marschall, H., Frohnapfel, B., Deutschmann, O.: Spreading and rebound dynamics of sub-millimetre urea-water-solution droplets impinging on substrates of varying wettability. Applied Mathematical Modelling 66, 395,, [Titel anhand dieser DOI in Citavi-Projekt übernehmen] (2021).
  • Jamshidi, F., Heimel, H., Hasert, M., Cai, X., Deutschmann, O., Marschall, H., Wörner, M.: On suitability of phase-field and algebraic volume-of-fluid OpenFOAM® solvers for gas–liquid microfluidic applications. Computer Physics Communications 236, 72–85,, [Titel anhand dieser DOI in Citavi-Projekt übernehmen] (2019).
  • Börnhorst, M., Cai, X., Wörner, M., Deutschmann, O.: Maximum Spreading of Urea Water Solution during Drop Impingement. Chem. Eng. Technol. 42 (11), 2419–2427,, [Titel anhand dieser DOI in Citavi-Projekt übernehmen] (2019).