Diffuse-interface modelling of droplet impact

Journal of Fluid Mechanics

Volumn 581, Issue , 2007, Pages 97-127

  Khatavkar, V V ^a   Anderson, P D ^a   Duineveld, P C ^b,c   Meijer, H E H ^a  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b PHILIPS RESEARCH LABORATORIES   (Netherlands)

^c PHILIPS RESEARCH LABORATORIES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CONTACT ANGLE; FINITE ELEMENT METHOD; HYDRODYNAMICS; INTERFACES (MATERIALS); MATHEMATICAL MODELS; REYNOLDS NUMBER; THERMODYNAMICS; WETTING;

CAHN-HILLIARD THEORY; DIFFUSE-INTERFACE MODEL; SPECTRAL-ELEMENT METHOD; WEBER NUMBER;

DROPS;

CONTACT ANGLE; DROPS; FINITE ELEMENT METHOD; HYDRODYNAMICS; INTERFACES (MATERIALS); MATHEMATICAL MODELS; REYNOLDS NUMBER; THERMODYNAMICS; WETTING;

DIFFUSION; DROPLET; FINITE ELEMENT METHOD; HYDRODYNAMICS; INTERFACE; REYNOLDS NUMBER; SURFACE TENSION; THERMODYNAMICS; VISCOSITY; WETTABILITY;

EID: 34548175493     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S002211200700554X     Document Type: Article

References (81)

1. ANDERSON, D. M., MCFADDEN, G. B. & WHEELER, A. A. 1998 Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30, 139-165.
2. ANDERSON, P. D., KEESTRA, B. J. & HULSEN, M. A. 2006 On the streamfunction-vorticity formulation in sliding bi-period frames: Application to bulk behavior for polymer blends. J. Comput. Phys. 212, 268-287.
3. ASAI, A., SHIOYA, M., HIRASAWA, S. & OKAZAKI, T. 1993 Impact of an ink drop on paper. J. Imag. Sci. Tech. 37, 205-207.
4. ATTINGER, D. & POULIKAKOS, D. 2001 Melting and resolidification of a substrate caused by molten microdroplet impact. Trans. ASME: J. Heat Transfer 123, 1110-1122.
5. ATTINGER, D., ZHAO, Z. & POULIKAKOS, D. 2000 An experimental study of molten microdroplet surface deposition and solidification: Transient behavior and wetting angle dynamics. Trans. ASME: J. Heat Transfer 122, 544-556.
6. AZIZ, S. D. & CHANDRA, S. 2000 Impact, recoil and splashing of molten metal droplets. Intl J. Heat Mass Transfer 43, 2841-2857.
7. BAROSAN, I., ANDERSON, P. D. & MEIJER, H. E. H. 2006 Application of mortar elements to diffuse-interface methods. Computers Fluids 35 (10), 1384-1399.
8. BERGERON, V., BONN, D., MARTIN, J. Y. & VOVELLE, L. 2000 Controlling droplet deposition with polymer additives. Nature 405, 772-775.
9. BEVERIDGE, G. S. G. & SCHECHTER, R. S. 1970 Optimization: Theory and Practice. McGraw-Hill.
10. BHOLA, R. & CHANDRA, S. 1999 Parameters controlling solidification of molten wax droplets falling on a solid surface. J. Mater. Sci 34, 4883-4894.
11. BLAKE, T. D. 1993 Dynamic Contact Angles and Wetting Kinetics Surfactant Science Series, vol. 49. Marcel Dekker.
12. BOETTINGER, W. J., WARREN, J. A., BECKERMANN, C. & KARMA, A. 2002 Phase-field simulation of solidification. Annu. Rev. Mater. Res. 32, 163-194.
13. BRIANT, A. J., WAGNER, A. J. & YEOMANS, J. M. 2004 Lattice Boltzmann simulations of contact line motion. I. Liquid-gas systems. Phys. Rev. E 69, 031602.
14. BRIANT, A. J. & YEOMANS, J. M. 2004 Lattice Boltzmann simulations of contact line motion. II. Binary fluids. Phys. Rev. E 69, 031603.
15. BUSSMANN, M., MOSTAGHIMI, J. & CHANDRA, S. 1999 On a three-dimensional volume tracking model of droplet impact. Phys. Fluids 11, 1406-1417.
16. CAHN, J. W. 1964 Phase separation by spinodal decomposition in isotropic systems. J. Chem. Phys. 42 (1), 93-99.
17. CAHN, J. W. 1977 Critical point wetting. J. Chem. Phys. 66 (8), 3667-3672.
18. CAHN, J. W. & HILLIARD, J. E. 1958 Free energy of a nonuniform system. I. Interfacial energy. J. Chem. Phys. 28 (2), 258-267.
19. CHANDRA, S. & AVEDISIAN, C. T. 1991 On the collision of a droplet with a solid surface. Proc. R. Soc. Lond. A 432, 13-41.
20. CHELLA, R. & VIÑALS, J. 1996 Mixing of a two-phase fluid by cavity flow. Phys. Rev. E 53 (4), 3832-3840.
21. CHEN, H.-Y., JASNOW, D. & VIÑALS, J. 2000 Interface and contact line motion in a two phase fluid under shear flow. Phys. Rev. Lett. 85 (8), 1686-1689.
22. CROOKS, R. C. & BOGER, D. V. 2001 Influence of fluid elasticity on drop impacting on dry surfaces. J. Rheol. 44, 973-996.
23. CROOKS, R. C., COOPER-WHITE, J. J. & BOGER, D. V. 2001 The role of dynamic surface tension and elasticity in the dynamics of drop impact. Chem. Engng Sci. 56, 5575-5592.
24. CROOKS, R. C., COOPER-WHITE, J. J. & BOGER, D. V. 2002 A drop impact study of worm-like viscoelastic surfactant solutions. Colloids Surf. A 210, 105-123.
25. VAN DAM, D. B. & CLERC, C. L. 2004 Experimental study of the impact of an ink-jet printed droplet on a solid substrate. Phys. Fluids 16, 3403-3414.
26. DAVIS, H. I & SCRIVEN, L. E. 1982 Stress and structure in fluid interfaces. Adv. Chem. Phys. 49, 357-454.
27. DUINEVELD, P. 2003 The stability of ink-jet printed lines of liquid with zero receding contact angle on a homogeneous substrate. J. Fluid Mech. 477, 175-200.
28. DUSSAN V., E. B. & DAVIS, S. H. 1974 On the motion of a fluid-fluid interface along a surface. J. Fluid Mech. 65, 71-95.
29. FEDORCHENKO, A. I., WANG, A.-B. & WANG, Y.-H. 2005 Effect of capillary and viscous forces on spreading of a liquid drop impinging on a solid surface. Phys. Fluids 17, 0931041-0931048.
30. FOURNIER, A., BUNGE, H. P., HOLLERBACH, R. & VILLOTE, J. P. 2004 Application of the spectral-element method to the axisymmetric Navier-Stokes equation. Geophys. J. Intl 156, 682-700.
31. FRANCOIS, M. & SHYY, W. 2003 Computations of drop dynamics with the immersed boundary method, Part 2: Drop impact and heat transfer. Numer. Heat Transfer B 44, 119-143.
32. FUKAI, J., SHIIBA, Y., YAMAMOTO, T., MIYATAKE, O., POULIKAKOS, D., MEGARIDIS, C. M. & ZHAO, Z. 1995 Wetting effects on the spreading of a liquid droplet colliding with a flat surface: Experiment and modeling. Phys. Fluids 7, 236-247.
33. FUKAI, J., ZHAO, Z., POULIKAKOS, D., MEGARIDIS, C. M. & MIYATAKE, O. 1993 Modeling of the deformation of a liquid droplet impinging upon a flat surface. Phys. Fluids 5, 2588-2599.
34. DE GANS, B.-J., DUINEVELD, P. & SCHUBERT, U. S. 2004 Inkjet printing of polymers: State of the art and future developments. Adv. Mater. 16, 203-213.
35. DE GENNES, P. G. 1985 Wetting: Statics and dynamics. Rev. Mod. Phys. 57, 827-862.
36. GERRITSMA, M. I. & PHILLIPS, T. N. 2000 Spectral element methods for axisymmetric Stokes problem. J. Comput. Phys. 164, 81-103.
37. GUNJAL, P. R., RANADE, V. V. & CHAUDHARI, R. V. 2005 Dynamics of drop impact on solid surface: Experiments and VOF simulations. AIChE J. 51, 59-78.
38. GUNTON, J. D., MIGUEL, M. S. & SAHNI, P. S. 1983 The Dynamics of First-order Phase Transitions. Phase Transitions and Critical Phenomena, vol. 8. Academic.
39. HOCKING, L. M. 1977 A moving fluid interface. Part 2. The removal of force singularity by a slip flow. J. Fluid Mech. 79, 209-229.
40. HUH, C. & SCRIVEN, L. E. 1971 Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Interface Sci. 35, 85-100.
41. JACQMIN, D. 1999 Calculation of two-phase Navier-Stokes flows using phase-field modeling. J. Comput. Phys. 155, 96-127.
42. JACQMIN, D. 2000 Contact-line dynamics of a diffuse fluid interface. J. Fluid Mech. 402 57-88.
43. JASNOW, D. & VIÑALS, J. 1996 Coarse-grained description of thermo-capillary flow. Phys. Fluids 8 (3), 660-669.
44. JOSEPH, D. D. & RENARDY, Y. Y. 1993 Fundamentals of Two-fluid Dynamics. Springer.
45. KAWASE, T., SHIMODA, T., NEWSOME, C., SIRRINGHAUS, H. & FRIEND, R. H. 2003 Inkjet printing of polymer thin film transistor. Thin Solid Films 438-439, 279-287.
46. KEESTRA, B. J., VAN PUYVELDE, P. C. J., ANDERSON, P. D. & MEIJER, H. E. H. 2003 Diffuse interface modeling of the morphology and rheology of immiscible polymer blends. Phys. Fluids 15, 2567-2575.
47. KHATAVKAR, V. V., ANDERSON, P. D. & MEIJER, H. E. H. 2006 On scaling of diffuse-interface models. Chem. Engng Sci. 61 (8), 2364-2378.
48. KHATAVKAR, V. V., ANDERSON, P. D. & MEIJER, H. E. H. 2007 Capillary spreading of droplet in a partially wetting regime using a diffuse-interface model. J. Fluid Mech. 572, 367-387.
49. Kim, H.-Y., PARK, S.-Y. & MIN, K. 2003 Imaging high-speed impact of mircodrop on solid surface. Rev. Sci. Instrum. 74, 4930-4937.
50. LEE, H.-G., LOWENGRUB, J. S. & GOODMAN, J. 2002a Modeling pinchoff and reconnection in a Hele-Shaw cell. I. The models and their calibration. Phys. Fluids 14 (2), 492-513.
51. LEE, H.-G., LOWENGRUB, J. S. & GOODMAN, J. 2002b Modeling pinchoff and reconnection in a Hele-Shaw cell. II. Analysis and simulation in the non-linear regime. Phys. Fluids 14 (2), 514-545.
52. LOWENGRUB, J. & TRUSKINOVSKY, L. 1998 Quasi-incompressible Cahn Hilliard fluids. Proc. R. Soc. Lond. A 454, 2617-2654.
53. MAO, T., KUHN, D. C. S. & TRAN, H. 1997 Spread and rebound of liquid droplets upon impact on flat surfaces. AIChE J. 43, 2169-2179.
54. NAUMANN, E. & HE, D. 2001 Nonlinear diffusion and phase separation. Chem. Engng Sci. 56, 1999-2018.
55. OKAMOTO, T., SUZUKI, T. & YAMAMOTO, N. 2000 Microarray fabrication with covalent attachment of DNA using bubble jet technology. Nat. Biotechnol. 18, 438-441.
56. PARK, H., CARR, W. W., ZHU, J. & MORRIS, J. F. 2003 Single drop impaction on a solid surface. AIChE J. 49, 2461-2471.
57. PASANDIDEH-FARD, M., QIAO, Y. M., CHANDRA, S. & MOSTAGHIMI, J. 1996 Capillary effects during droplet impact on a solid surface. Phys. Fluids 8, 650-659.
58. PASANDIDEH-FARD, M., QIAO, Y. M., CHANDRA, S. & MOSTAGHIMI, J. 2002 On a three-dimensional model of droplet impact and solidification. Intl J. Heat Mass Transfer 45, 2229-2242.
59. PATERA, A. T. 1984 A spectral element method for fluid dynamics. J. Comput. Phys. 54, 468-488.
60. RANGE, K. & FEUILLEBOIS, F. 1998 Influence of surface roughness on liquid drop impact. J. Colloid Interface Sci. 203, 16-30.
61. REIN, M. 1993 Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dyn. Res. 12, 61-93.
62. RENARDY, M., RENARDY, Y. & LI, J. 2001 Numerical simulation of moving contact line problems using a volume-of-fluid method. J. Comput. Phys. 171, 243-263.
63. RENARDY, Y., POPINET, S., DUCHEMIN, L., RENARDY, M., ZALESKI, S., JOSSERAND, C., DRUMRIGHT-CLARKE, M. A., RICHARD, D., CLANET, C. & QUERE, D. 2003 Pyramidal and toroidal water drops after impact on a solid surface. J. Fluid Mech. 484, 69-83.
64. ROISMAN, I. V., RIOBOO, R. & TROPEA, C. 2002 Normal impact of a liquid drop on a dry surface: Model for spreading and receding. Proc. R. Soc. Lond. A 458, 1411-1430.
65. ROWLINSON, J. S. & WIDOM, B. 1989 Molecular Theory of Capillarity. Clarendon.
66. SCHIAFFINO, S. & SONIN, A. 1997 Molten droplet deposition and solification at low Weber number. Phys. Fluids 9, 3172-3187.
67. SEGAL, A. 1995 SEPRAN manual. Leidschendam, The Netherlands.
68. SEKERKA, R. 2004 Morphology: From sharp interface to phase field models. J. Crystal Growth 264, 530-540.
69. SEPPECHER, P. 1996 Moving contact lines in the Cahn-Hilliard theory. Intl J. Engng Sci. 34 (9), 977-992.
70. S̃IKALO, S̃., WILHELM, H.-D., ROISMAN, I. V., JAKIRLIC̀, S. & TROPEA, C. 2005 Dynamic contact angle of spreading droplets: Experiments and simulations. Phys. Fluids 17, 0621031-06210313.
71. SIRRINGHAUS, H., KAWASE, T., FRIEND, R. H., SHIMODA, T., INBASEKARAN, M., WU, W. & WOO, E. P. 2000 High-resolution inkjet printing of all-polymer transistor circuits. Science 290, 2123-2126.
72. TIMMERMANS, L. J. P., VAN DE VOSSE, F. N. & MINEV, P. D. 1994 Taylor-Galerkin-based spectral element methods for convection-diffusion problems. Intl J. Numer. Meth. Fluids 18, 853-870.
73. VERSCHUEREN, M. 1999 A diffuse-interface model for structure development in flow. PhD thesis, Eindhoven University of Technology, The Netherlands (downloadable from http://www.mate.tue.nl/mate/pdfs/56.pdf).
74. VERSCHUEREN, M., VAN DE VOSSE, F. N. & MEIJER, H. E. H. 2000 Diffuse-interface modelling of thermocapillary flow instabilities in a Hele-Shaw cell. J. Fluid Mech. 434, 153-166.
75. VAN DER WAALS, J. D. 1893 The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density. Verhandel. Konink. Akad. Weten. Amsterdam 1 (English translation by J. S. Rowlinson in J. Statist. Phys. 20 (1979), 197-244).
76. WORTHINGTON, A. M. 1876 On the forms assumed by drops of liquids falling vertically on a horizontal plate. Proc. R. Soc. Lond. A 25, 261-271.
77. YARIN, A. L., YAZICIOGLU, A. G., MEGARIDIS, C. M., ROSSI, M. P. & GOGOTSI, Y. 2005 Theoretical and experimental investigation of aqueous liquids contained in carbon nanotubes. J. Appl. Phys. 97, 1243091.
78. YUE, P., FENG, J. J., LIU, C. & SHEN, J. 2004 A diffuse-interface method for simulating two-phase flows of complex fluids. J. Fluid Mech. 515, 293-317.
79. ZHANG, X. & BASARAN, O. A. 1997 Dynamic Surface Tension Effects in Impact of a Drop with a Solid Surface. J. Colloid Interface Sci. 187, 166-178.
80. ZHAO, Z., POULIKAKOS, D. & FUKAI, J. 1996a Heat transfer and fluid dynamics during the collision of a liquid droplet on a substrate-I. Modeling. Intl J. Heat Mass Transfer 39, 2771-2789.
81. ZHAO, Z., POULIKAKOS, D. & FUKAI, J. 1996b Heat transfer and fluid dynamics during the collision of a liquid droplet on a substrate-II. Experiments. Intl J. Heat Mass Transfer 39, 2791-2802.