title: VOF simulations of the contact angle dynamics during the drop spreading: standard models and a new wetting force model.
abstract: BACKGROUND
  In this study,a novel numerical implementation for the adhesion of liquid droplets impacting normally on solid dry surfaces is presented. The advantage of this new approach, compared to the majority of existing models, is that the dynamic contact angle forming during the surface wetting process is not inserted as a boundary condition, but is derived implicitly by the induced fluid flow characteristics (interface shape) and the adhesion physics of the gas-liquid-surface interface (triple line), starting only from the advancing and receding equilibrium contact angles. These angles are required in order to define the wetting properties of liquid phases when interacting with a solid surface.
  
  
  METHODS
  The physical model is implemented as a source term in the momentum equation of a Navier-Stokes CFD flow solver as an "adhesion-like" force which acts at the triple-phase contact line as a result of capillary interactions between the liquid drop and the solid substrate. The numerical simulations capture the liquid-air interface movement by considering the volume of fluid (VOF) method and utilizing an automatic local grid refinement technique in order to increase the accuracy of the predictions at the area of interest, and simultaneously minimize numerical diffusion of the interface.
  
  
  RESULTS
  The proposed model is validated against previously reported experimental data of normal impingement of water droplets on dry surfaces at room temperature. A wide range of impact velocities, i.e. Weber numbers from as low as 0.2 up to 117, both for hydrophilic (θadv=10°-70°) and hydrophobic (θadv=105°-120°) surfaces, has been examined. Predictions include in addition to droplet spreading dynamics, the estimation of the dynamic contact angle; the latter is found in reasonable agreement against available experimental measurements.
  
  
  CONCLUSIONS
  It is thus concluded that theimplementation of this model is an effective approach for overcoming the need of a pre-defined dynamic contact angle law, frequently adopted as an approximate boundary condition for such simulations. Clearly, this model is mostly influential during the spreading phase for the cases of low We number impacts (We<˜80) since for high impact velocities, inertia dominates significantly over capillary forces in the initial phase of spreading.
authors.affiliation: School of Engineering and Mathematical Sciences, City University London, Northampton Square, EC1V 0HB London, UK. Electronic address: Ilias.Malgarinos.1@city.ac.uk.
authors.forename: Ilias
authors.initials: I
authors.lastname: Malgarinos
authors.affiliation: School of Engineering and Mathematical Sciences, City University London, Northampton Square, EC1V 0HB London, UK; Centre for Research and Technology Hellas, Chemical Process and Energy Resources Institute, Egialeias 52, Marousi, Athens Gr-15125, Greece.
authors.forename: Nikolaos
authors.initials: N
authors.lastname: Nikolopoulos
authors.affiliation: Department of Engineering, University of Bergamo, viale Marconi 5, 24044 Dalmine, Italy; School of Computing, Engineering and Mathematics, University of Brighton, Brighton BN2 4GJ, UK.
authors.forename: Marco
authors.initials: M
authors.lastname: Marengo
authors.affiliation: Department of Engineering, University of Bergamo, viale Marconi 5, 24044 Dalmine, Italy; Laboratory of Thermodynamics in Emerging Technologies, Department of Mechanical and Process Engineering, ETH Zurich, Zurich 8092, Switzerland.
authors.forename: Carlo
authors.initials: C
authors.lastname: Antonini
authors.affiliation: School of Engineering and Mathematical Sciences, City University London, Northampton Square, EC1V 0HB London, UK.
authors.forename: Manolis
authors.initials: M
authors.lastname: Gavaises
keywords: CFD; Droplet impingement; Dynamic contact angle; Dynamic grid refinement; VOF