Acta Mechanica

, Volume 230, Issue 2, pp 623–644 | Cite as

Toward the predictive simulation of bouncing versus coalescence in binary droplet collisions

  • M. Liu
  • D. BotheEmail author
Original Paper


Multi-scale simulations have been conducted in order to predict the collision outcome bouncing versus coalescence in numerical simulations. The flow on the macroscopic scale is solved by the Volume of Fluid code FS3D. On the microscopic scale, the flow in the gas film between the colliding droplets before possible coalescence is solved by a Sub-grid-scale (SGS) model, which is derived based on the classical lubrication theory and accounts for rarefaction effects. The SGS model has been implemented in FS3D and validated by means of comparing the obtained pressure field to that computed analytically and by means of direct numerical simulations. For the coupling of the SGS model with FS3D, the pressure field obtained from the SGS model applies as a pressure boundary condition on the collision plane. Employing the intersection of the PLIC surfaces with the collision plane as a coalescence criterion, the simulation has been able to yield both coalescence and bouncing. The predicted critical Weber number so far depends on the grid resolution; hence, further developments of the multi-scale approach are still required.




Velocity vector


Body force

\(\varvec{f}_\varSigma \)

Surface tension force


Phase indicator

\(\rho \)


\(\sigma \)

Surface tension


Cartesian coordinates








Hamaker constant


Velocity components


Weber number


Knudsen number


Normal vector


Volumetric force



\(\epsilon \)

Numerical threshold

\(\eta \)

Dynamic viscosity

\(\varphi \)





Radius coordinate



\(\lambda \)

Mean free path

h, H



Resultant velocity


Ohnesorge number



Initial value


Value on interface


Liquid phase


Critical value


Relative value


Gas phase




Van der Waals force


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Profile Area Thermo-Fluids & Interfaces and Department of MathematicsTechnische Universität DarmstadtDarmstadtGermany

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