Surface structures on thin fluid layers of a binary mixture in confined geometries

• Antragsteller: Professor Dr. Michael Bestehorn
• Fachliche Zuordnung: Statistische Physik, Nichtlineare Dynamik, Komplexe Systeme, Weiche und fluide Materie, Biologische Physik
• Förderung: Förderung von 2006 bis 2010
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 34959298

• Erstellungsjahr: 2010

Zusammenfassung der Projektergebnisse

Instabilities in thin films are monotonic, the behavior above threshold is relaxational and approaches in the long time limit a certain fixed point that minimizes an expression resembling a free Ginzburg-Landau energy. If the film is heated from below, surface tension may cause such an instability. This is called Marangoni effect. The control or bifurcation parameter is the Marangoni number, which is proportional to the externally applied vertical temperature gradient. On the other hand it is well known from experiment and from theory that binary mixtures heated from below may show oscillatory (wave) instabilities and a much richer spatio-temporal behavior already close to onset of convection. A second control parameter, the Marangoni separation ratio comes into play and determines if the first instability is monotonic or oscillatory. This parameter can be adjusted by changing the mean concentration of the mixture. The basic idea of the project was to see, if thin films of binary mixtures may also show oscillatory (overstable) behavior at onset. We first proposed a phenomenological extension of the thin film eqs. that included a second field variable, namely the relative concentration of the mixture. This model showed an oscillatory unstable flat film and solutions above threshold in form of travelling drops or holes. Inspired by this result, we tried to do a systematic expansion of the full set of hydrodynamic equations (Navier- Stokes, continuity, temperature, concentration). We thereby followed the lines of the lubrication approximation, where the small expansion parameter is a geometric ratio of film thickness and lateral length scale. After some initial problems we were successful in finding a system of two coupled 2D field variables, namely the film thickness and the concentration averaged over the vertical. This system is conservative and ensures both conservation of the total mass and of the mean concentration. Its derivation is systematic up to the second order of the small geometry parameter. A linear stability analysis of the model shows indeed the possibility of an oscillatory bifurcation if the Marangoni separation ratio is sufficiently negative. Then traveling waves or drops are expected, but also more involved situations should be possible.

Projektbezogene Publikationen (Auswahl)

• Linear analysis of instability in a binary-liquid layer with deformable interface in the presence of Soret effect, DPG Tagung, Regensburg, 26-30 March 2007
  I. D. Borcia, M. Bestehorn
  
• Surface instability on thin fluid layers of a binary mixture, ECS 2007 7-th European Coating Symposium - Recent Advances in Coating, Drying and Dynamical Wetting, 12-14 September 2007, Paris, France (Poster presentation)
  I. D. Borcia, M. Bestehorn
  
• Binary mixture thin film in vertical and horizontal temperature gradients, DPG Jahrestagung 25-29 Februar 2008, Berlin, Germnay
  I. D. Borcia, M. Bestehorn
  
• Coarsening in liquid binary mixtures, The 4th International Marangoni Association Conf. on Interfacial & Micro-Fluid Dynamics & Processes, October 21-23, 2008, Tokyo, Japan
  I. D. Borcia, M. Bestehorn
  
• Numerical simulations for binary mixture thin liquid films with free surface, The Third International Topical Team Workshop on Two-Phase Systems For Ground and Space Applications, September 10-12, 2008, Brussels, Belgium
  I. D. Borcia, M. Bestehorn
  
• ”Drops on an arbitrarily wetting substrate: A phase field description”, Phys. Rev. E 78(6), 066307, 2008
  R. Borcia, I. D. Borcia, M. Bestehorn
  
• ”Liquid layers on patterned surfaces”, Soft Mater., 4, pp. 2368-2372, 2008
  R. Borcia, I. D. Borcia, M. Bestehorn
  
• Dynamically Adaptive Coordinate System for Binary Mixture Thin Films, DPG Jahrestagung, March 22-27, 2009, Dresden, Germany
  I. D. Borcia, M. Bestehorn
  
• Simulation of pattern morphology in binary liquid mixtures, 7th General Conference of the Balkan Physical Union, September 9-13, 2009, Alexandoupolis, Greece
  I. D. Borcia, M. Bestehorn
  
• Surface structures on thin fluid layers of a binary mixture, Third International Symposium on Bifurcations and Instabilities in Fluid Dynamics, August 10-13, 2009, Nottingham, UK
  I. D. Borcia, M. Bestehorn
  
• ”Static and dynamic contact angles - A phase field modeling”, Eur. Phys. J. Special Topics 166, pp. 127-131, 2009
  R. Borcia, I. D. Borcia, M. Bestehorn
  
• ”Surface instability on thin fluid layers of a binary mixture”, Eur. Phys. J. Special Topics 166, pp. 73-76, 2009
  I. D. Borcia, M. Bestehorn
  
• ”Simulation of Pattern Morphology in Binary Liquid Mixtures”, AIP Conference Proceedings, 1203, 1166-1171, 2010
  I. D. Borcia, M. Bestehorn