Finite element simulation of dynamic wetting flows as an interface formation process

Journal of Computational Physics

Volumn 233, Issue 1, 2013, Pages 34-65

  Sprittles, J E ^a   Shikhmurzaev, Y D ^b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

Capillary rise; Computation; Dynamic wetting; Fluid mechanics; Interface formation; Shikhmurzaev model

Indexed keywords

CONTACT ANGLE; FLUID MECHANICS; MAGNETIC BUBBLES; NUMERICAL METHODS; WETTING;

CAPILLARY RISE; DYNAMIC CONTACT ANGLE; DYNAMIC WETTING; FINITE ELEMENTS SIMULATION; FORMATION PROCESS; INTERFACE FORMATION; MODELING OF DYNAMICS; NUMERICAL CODE; SHIKHMURZAEV'S MODEL; TEST CASE;

FINITE ELEMENT METHOD;

EID: 84870588008     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2012.07.018     Document Type: Article

References (77)

1. S.J. Weinstein, K.J. Ruschak, Coating flows, Annual Review of Fluid Mechanics 36 (2004) 29-53.
2. S. Ravinutala, C. Polymeropoulos, Entrance meniscus in a pressurized optical fiber coating applicator, Experimental Thermal and Fluid Science 26 (2002) 573-580.
3. P.G. Simpkins, V.J. Kuck, On air entrainment in coatings, Journal of Colloid and Interface Science 263 (2003) 562-571.
4. D.B. van Dam, C. Le Clerc, Experimental study of the impact of an inkjet printed droplet on a solid substrate, Physics of Fluids 16 (2004) 3403-3414.
5. P. Calvert, Inkjet printing for materials and devices, Chemistry of Materials 13 (2001) 3299-3305.
6. M. Singh, H. Haverinen, P. Dhagat, G. Jabbour, Inkjet printing process and its applications, Advanced Materials 22 (2010) 673-685.
7. C. Huh, L.E. Scriven, Hydrodynamic model of steady movement of a solid/liquid/fluid contact line, Journal of Colloid and Interface Science 35 (1971) 85-101.
8. E.B. Dussan, On the spreading of liquids on solid surfaces: static and dynamic contact lines, Annual Review of Fluid Mechanics 11 (1979) 371-400.
9. Y.D. Shikhmurzaev, Capillary Flows with Forming Interfaces, Chapman & Hall/CRC, Boca Raton, 2007.
10. P. Yue, C. Zhou, J. Feng, Sharp-interface limit of the Cahn-Hilliard model for moving contact lines, Journal of Fluid Mechanics 645 (2010) 279-294.
11. G. Martic, F. Gentner, D. Seveno, D. Coulon, J. De Coninck, T.D. Blake, A molecular dynamics simulation of capillary imbibition, Langmuir 18 (2002) 7971-7976.
12. T.D. Blake, The physics of moving wetting lines, Journal of Colloid and Interface Science 299 (2006) 1-13.
13. Y.D. Shikhmurzaev, Some dry facts about dynamic wetting, The European Physical Journal, Special Topics 197 (2011) 47-60.
14. C.L.M.H. Navier, Mémoire sur les lois mouvement des fluides, Mém. de l'Acad. de Sci. l'Inst. de France 6 (1823) 389-440.
15. T.D. Blake, J.M. Haynes, Kinetics of liquid/liquid displacement, Journal of Colloid and Interface Science 30 (1969) 421-423.
16. R.G. Cox, The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow, Journal of Colloid and Interface Science 168 (1986) 169-194.
17. M.N. Popescu, J. Ralston, R. Sedev, Capillary rise with velocity-dependent dynamic contact angle, Langmuir 25 (2008) 12710-12716.
18. D. Seveno, A. Vaillant, R. Rioboo, H. Ada o, J. Conti, J. De Coninck, Dynamics of wetting revisited, Langmuir 25 (22) (2009) 13034-13044.
19. T.D. Blake, A. Clarke, K.J. Ruschak, Hydrodynamic assist of wetting, AIChE Journal 40 (1994) 229-242.
20. A. Clarke, E. Stattersfield, Direct evidence supporting nonlocal hydrodynamic influence on the dynamic contact angle, Physics of Fluids 18 (2006) 048106.
21. V.D. Sobolev, N.V. Churaev, M.G. Velarde, Z.M. Zorin, Surface tension and dynamic contact angle of water in thin quartz capillaries, Journal of Colloid and Interface Science 222 (2000) 51-54.
22. V.D. Sobolev, N.V. Churaev, M.G. Velarde, Z.M. Zorin, Dynamic contact angles of water in ultrathin capillaries, Colloid Journal 63 (2001) 119-123.
23. I.S. Bayer, C.M. Megaridis, Contact angle dynamics in droplets impacting on flat surfaces with different wetting characteristics, Journal of Fluid Mechanics 558 (2006) 415-449.
24. Š. Šikalo, H.D. Wilhelm, I.V. Roisman, S. Jakirlić, C. Tropea, Dynamic contact angle of spreading droplets: experiments and simulations, Physics of Fluids 17 (2005) 062103.
25. M.C.T. Wilson, J.L. Summers, Y.D. Shikhmurzaev, A. Clarke, T.D. Blake, Nonlocal hydrodynamic influence on the dynamic contact angle: Slip models versus experiment, Physical Review E 83 (2006) 041606.
26. T.D. Blake, M. Bracke, Y.D. Shikhmurzaev, Experimental evidence of nonlocal hydrodynamic influence on the dynamic contact angle, Physics of Fluids 11 (1999) 1995-2007.
27. A.V. Lukyanov, Y.D. Shikhmurzaev, Effect of flow field and geometry on the dynamic contact angle, Physical Review E 75 (2007) 051604.
28. Y.D. Shikhmurzaev, The moving contact line on a smooth solid surface, International Journal of Multiphase Flow 19 (1993) 589-610.
29. P. Attané, F. Girard, V. Morin, An energy balance approach of the dynamics of drop impact on a solid surface, Physics of Fluids 19 (2007) 012101.
30. T.A. Baer, R.A. Cairncross, P.R. Schunk, R.R. Rao, P.A. Sackinger, A finite element method for free surface flows of incompressible fluids in three dimensions. Part 2. Dynamic wetting lines, International Journal for Numerical Methods in Fluids 33 (2000) 405-427.
31. S. Manservisi, R. Scardovelli, A variational approach to the contact angle dynamics of spreading droplets, Computers and Fluids 38 (2009) 406-424.
32. J.E. Sprittles, Y.D. Shikhmurzaev, A finite element framework for describing dynamic wetting phenomena, International Journal for Numerical Methods in Fluids 68 (2012) 1257-1298.
33. J.E. Sprittles, Y.D. Shikhmurzaev, Viscous flow in domains with corners: numerical artifacts, their origin and removal, Computer Methods in Applied Mechanics and Engineering 200 (2011) 1087-1099.
34. J.E. Sprittles, Y.D. Shikhmurzaev, The dynamics of liquid drops and their interaction with solids of varying wettabilities, Physics of Fluids 24 (2012) 082001.
35. S. Hysing, Numerical simulation of immiscible fluids with FEM level set techniques, Ph.D. thesis, University of Dortmund, Institute of Applied Mathematics, 2007.
36. T. Young, An essay on the cohesion of fluids, Philosophical Transactions of the Royal Society (London) 95 (1805) 65-87.
37. Y.D. Shikhmurzaev, Moving contact lines in liquid/liquid/solid systems, Journal of Fluid Mechanics 334 (1997) 211-249.
38. T.D. Blake, Y.D. Shikhmurzaev, Dynamic wetting by liquids of different viscosity, Journal of Colloid and Interface Science 253 (2002) 196-202.
39. Y.D. Shikhmurzaev, Singularity of free-surface curvature in convergent flow: cusp or corner?, Physics Letters A 345-385 (2005) 378.
40. Y.D. Shikhmurzaev, Capillary breakup of liquid threads: a singularity-free solution, IMA Journal of Applied Mathematics 70 (2005) 880-907.
41. Y.D. Shikhmurzaev, Macroscopic mechanism of rupture of free liquid films, Comptes Rendus Mecanique 333 (2005) 205-210.
42. J.E. Sprittles, Y.D. Shikhmurzaev, Viscous flow over a chemically patterned surface, Physical Review E 76 (2007) 021602.
43. H.K. Moffatt, Viscous and resistive eddies near a sharp corner, Journal of Fluid Mechanics 18 (1964) 1-18.
44. Y.D. Shikhmurzaev, Spreading of drops on solid surfaces in a quasi-static regime, Physics of Fluids 9 (1996) 266-275.
45. S.F. Kistler, L.E. Scriven, Coating flows, in: J.R.A. Pearson, S.M. Richardson (Eds.), Computational Analysis of Polymer Processing, Applied Science Publishers, London and New York, 1983, pp. 243-299.
46. M. Heil, An efficient solver for the fully-coupled solution of large displacement fluid-structure interaction problems, Computer Methods in Applied Mechanics and Engineering 193 (2004) 1-23.
47. O.A. Basaran, Nonlinear oscillations of viscous liquid drops, Journal of Fluid Mechanics 241 (1992) 169-198.
48. S. Meradji, T.P. Lyubimova, D.V. Lyubimov, B. Roux, Numerical simulation of a liquid drop freely oscillating, Crystal Research and Technology 36 (2001) 729-744.
49. M.J. Baines, M.E. Hubbard, P.K. Jimack, A moving mesh finite element algorithm for fluid flow problems with moving boundaries, International Journal for Numerical Methods in Fluids (2004) 1-6.
50. P.K. Jimack, A.J. Wathen, Temporal derivatives in the finite-element method on continuously deforming grids, SIAM Journal on Numerical Analysis 28 (1991) 990-1003.
51. C. Pozrikidis, A finite-element method for interfacial surfactant transport with application to the flow-induced deformation of a viscous drop, Journal of Engineering Mathematics 49 (2004) 163-180.
52. I. Babuska, A.K. Aziz, Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, Academic Press, New York, 1972.
53. T.J.R. Hughes, L.P. Franca, M. Balestra, A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuška-Brezzi condition: a stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations, Computer Methods in Applied Mechanics and Engineering 59 (1986) 85-99.
54. R. Codina, J. Blasco, Stabilized finite element method for the transient Navier-Stokes equations based on a pressure gradient projection, Computer Methods in Applied Mechanics and Engineering 182 (2000) 277-300.
55. K.J. Ruschak, A method for incorporating free boundaries with surface tension in finite element fluid-flow simulators, International Journal for Numerical Methods in Engineering 15 (1980) 639-648.
56. L.W. Ho, A.T. Patera, Variational formulation of three-dimensional viscous free-surface flows: natural imposition of surface tension boundary conditions, International Journal for Numerical Methods in Fluids 13 (1991) 691-698.
57. R.A. Cairncross, P.R. Schunk, T.A. Baer, R.R. Rao, P.A. Sackinger, A finite element method for free surface flows of incompressible fluids in three dimensions. Part 1. Boundary fitted mesh motion, International Journal for Numerical Methods in Fluids 33 (2000) 375-403.
58. R. Aris, Vectors, Tensors, the Basic Equations of Fluid Mechanics, Dover Publications, Inc., New York, 1962.
59. M.S. Engelman, R.L. Sani, P.M. Gresho, The implementation of normal and/or tangential boundary conditions in finite element codes for incompressible flow, International Journal for Numerical Methods in Fluids 2 (1982) 225-238.
60. M. Stange, M.E. Dreyer, H.J. Rath, Capillary driven flow in circular cylindrical tubes, Physics of Fluids 15 (2003) 2587-2601.
61. I.B. Bazhlekov, A.K. Chesters, Numerical investigation of the dynamic influence of the contact line region on the macroscopic meniscus shape, Journal of Fluid Mechanics 329 (1996) 137-146.
62. E.W. Washburn, The dynamics of capillary flow, Physical Review 17 (1921) 273-283.
63. C.G. Ngan, E.B. Dussan V, On the nature of the dynamic contact angle an experimental study, Journal of Fluid Mechanics 118 (1982) 27-40.
64. J.E. Sprittles, Y.D. Shikhmurzaev, Viscous flow in corner regions: singularities and hidden eigensolutions, International Journal for Numerical Methods in Fluids 65 (2011) 372-382.
65. P. Joos, P. Van Remoortere, M. Bracke, The kinetics of wetting in a capillary, Journal of Colloid and Interface Science 136 (1990) 189-197.
66. B.V. Zhmud, F. Tiberg, K. Hallstensson, Dynamics of capillary rise, Journal of Colloid and Interface Science 228 (2000) 263-269.
67. J.D. Paulsen, J.C. Burton, S.R. Nagel, Viscous to inertial crossover in liquid drop coalescence, Physical Review Letters 106 (2011) 114501.
68. J.C. Bird, S. Mandre, H.A. Stone, Short-time dynamics of partial wetting, Physical Review Letters 100 (2008) 234501.
69. J.E. Sprittles, Y.D. Shikhmurzaev, A continuum model for the flow of thin liquid films over intermittently chemically patterned surfaces, The European Physical Journal Special Topics 166 (2009) 159-163.
70. Y.D. Shikhmurzaev, J.E. Sprittles, The dynamic contact angle on an unsaturated porous substrate, Journal of Fluid Mechanics, Submitted for publications.
71. P.M. Gresho, R.L. Sani, Incompressible Flow and the Finite Element Method, Advection-Diffusion, 1, John Wiley & Sons, Ltd., 1999.
72. P.M. Gresho, R.L. Sani, Incompressible Flow and the Finite Element Method, Isothermal Laminar Flow, 2, John Wiley & Sons, Ltd, 1999.
73. S.F. Kistler, L.E. Scriven, Coating flow theory by finite element and asymptotic analysis of the Navier-Stokes system, International Journal for Numerical Methods in Fluids 4 (1984) 207-229.
74. T.E. Tezduyar, M. Behr, S. Mittal, J. Liou, A new strategy for finite element computations involving moving boundaries and interfaces - the deformingspatial-domain/space time procedure: II. Computation of free surface flows, two-liquid flows and flows with drifting cylinders,, Computer Methods in Applied Mechanics and Engineering 94 (1992) 353-371.
75. K.N. Christodoulou, L.E. Scriven, Discretization of free surface flows and other moving boundary problems, Journal of Computational Physics 99 (1992) 39-55.
76. N. Ramanan, M.S. Engelman, An algorithm for the simulation of steady free surface flows, International Journal for Numerical Methods in Fluids 22 (1996) 103-120.
77. P. Lötstedt, L. Petzold, Numerical solution of nonlinear differential equations with an algebraic constraints 1: Convergence results for backward differentiation formulas, Mathematics of Computation 46 (1986) 491-516.