Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method

Journal of Computational Physics

Volumn 218, Issue 1, 2006, Pages 417-428

  Yang, Xiaofeng ^a   Feng, James J ^b   Liu, Chun ^c   Shen, Jie ^a  

^a PURDUE UNIVERSITY   (United States)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^c PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Drop formation; Incompressible flow; Phase field method; Pintching; Spectral method; Two phase flow

Indexed keywords

DIRECT NUMERICAL SIMULATION; DROPS; INCOMPRESSIBLE FLOW; NAVIER STOKES EQUATIONS; NEWTONIAN LIQUIDS; NONLINEAR EQUATIONS; NUMERICAL METHODS; NUMERICAL MODELS; PHASE INTERFACES; PHASE TRANSITIONS;

INCOMPRESSIBLE FLUID; LIQUID FILAMENTS; NEWTONIAN FLUIDS; NUMERICAL SCHEME; PHASE FIELD METHODS; PHASE FIELD MODELS; PINCHOFF; PINTCHING; SPECTRAL METHODS; TWO PHASES FLOW;

TWO PHASE FLOW;

EID: 33748521534     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.02.021     Document Type: Article

References (38)

1. Anderson D.M., McFadden G.B., and Wheeler A.A. Diffuse-interface methods in fluid mechanics. Appl. Math. Lett. 30 4 (1998) 139-165
2. Boyer F. A theoretical and numerical model for the study of incompressible mixture flows. Comput. Fluids 31 (2004) 41-68
3. Bray A.J. Theory of phase-ording kinetics. Adv. Phys. 51 (2002) 481-587
4. Cahn J.W., and Hillard J.E. Free energy of a nonuniform system. I. International free energy. J. Chem. Phys. 28 (1958) 258-267
5. Chen A.U., Notz P.K., and Basaran O.A. Computational and experimental analysis of pinch-off and scaling. Phys. Rev. Lett. 88 (2002) 17-4501
6. Shiyi Chen, Gary D. Doolen, Lattice Boltzmann method for fluid flows, in: Annual Review of Fluid Mechanics, Annu. Rev. Fluid Mech., vol. 30, Annual Reviews, Palo Alto, CA, 1998, pp. 329-364.
7. Chen S., Doolen G.D., He X., Nie X., and Zhang R. Recent advances in lattice Boltzmann methods. Fluid Dynamics at Interfaces (Gainesville, FL, 1998) (1999), Cambridge University Press, Cambridge 352-363
8. Du Q., Liu C., and Wang X. Retrieving topological information for phase field models. SIAM J. Appl. Math. 65 (2005) 1913-1923
9. Du Q., Shen J., and Guo B.Y. Fourier spectral approximation to a dissipative system modeling the flow of liquid crystals. SIAM J. Numer. Anal. 39 (2001) 735-762
10. Feng J.J., Liu C., Shen J., and Yue P. A energetic variational formulation with phase field methods for interfacial dynamics of complex fluids: advantages and challenges. In: Calderer M.T., and Terentjev E.M. (Eds). Modeling of Soft Matter vol. IMA 141 (2005), Springer, New York 1-26
11. Guermond J.L., and Shen J. On the error estimates of rotational pressure-correction projection methods. Math. Comput. 73 (2004) 1719-1737
12. Gueyffier D., Li J., Nadim A., Scardovelli R., and Zaleski S. Volume-of-fluid interface tracking with smoothed surface stress methods for three dimensional flows. J. Comput. Phys. 152 (1999) 423-456
13. Hauser E.A., Edgerton H.E., Holt B.M., and Cox Jr. J.T. The application of high speed motion picture camera to research on the surface tension of liquids. J. Phys. Chem. 40 (1936) 937-988
14. Henderson D., Segur H., Smolka L.B., and Wadati M. The motion of a falling liquid filament. Phys. Fluids 12 (2000) 550-565
15. Hohenberg P.C., and Halperin B.I. Theory of dynamic critical phenoma. Rev. Modern Phys. 49 (1977) 435-479
16. Jacqmin D. Calculation of two-phase Navier-Stokes flows using phase-field modeling. J. Comput. Phys. 155 (1999) 96-127
17. Kim J.S. A continuous surface tension force formulation for diffuse-interface models. J. Comput. Phys. 204 (2005) 784-804
18. Liu C., and Shen J. A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method. Physica D 179 (2003) 211-228
19. Liu C., Shen J., Feng J.J., and Yue P. Variational approach in two-phase flows of complex fluids: transport and induced elastic stress. In: Miranville A. (Ed). Mathematical Models and Methods in Phase Transitions (2005), Nova Publications
20. Lopez J.M., and Shen J. An efficient spectral-projection method for the Navier-Stokes equations in cylindrical geometries I. Axisymmetric cases. J. Comput. Phys. 139 (1998) 308-326
21. Notz P.K., and Basaran O.A. Dynamics and breakup of a contracting liquid filament. J. Fluid Mech. 512 (2004) 223-256
22. Osher S., and Fedkiw R. Level Set Methods and Dynamic Implicit Surfaces. Applied Mathematical Sciences vol. 153 (2003), Springer-Verlag, New York
23. Renardy Y., and Renardy M. PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method. J. Comput. Phys. 183 2 (2002) 400-421
24. Robinson N.D., and Steen P.H. Observation of singularity formation during the capillary collapse and bubble pinch-off of a sop film bridge. J. Colloid Interface Sci. 241 (2001) 448-458
25. Schulkes R. The evolution and bifurcation of a pendant drop. J. Fluid Mech. 278 (1994) 83-100
26. Schulkes R. The contraction of liquid filaments. J. Fluid Mech. 309 (1996) 277-300
27. Seta T., Kono K., and Chen S. Lattice Boltzmann method for two-phase flows. Int. J. Modern Phys. B 17 (2003) 169
28. Sethian J.A. Level Set Methods and Fast Marching Methods. 2nd ed. Cambridge Monographs on Applied and Computational Mathematics vol. 3 (1999), Cambridge University Press, Cambridge
29. Shen J. Efficient spectral-Galerkin method I. Direct solvers for second- and fourth-order equations using Legendre polynomials. SIAM J. Sci. Comput. 15 (1994) 1489-1505
30. Shen J. Efficient spectral-Galerkin method III. Polar and cylindrical geometries. SIAM J. Sci. Comput. 18 (1997) 1039-1065
31. Swift M.R., Osborn W.R., and Yeomans J.M. Lattice Boltzmann simulation of nonideal fluids. Phys. Rev. Lett. 75 (1995) 83033
32. Wilkes E.D., Phillips S.D., and Basaran O.A. Computational and experimental analysis of dynamics of drop formulation. Phys. Fluids 11 (1999) 3577-3598
33. Yue P., Feng J.J., Liu C., and Shen J. A diffuse-interface method for simulating two-phase flows of complex fluids. J. Fluid Mech. 515 1 (2004) 293-317
34. Yue P., Feng J.J., Liu C., and Shen J. Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids. J. Non-Newtonian Fluid Mech. 129 (2005) 163-176
35. Yue P., Feng J.J., Liu C., and Shen J. Interfacial force and Marangoni flow on a nematic drop retracting in an isotropic fluid. J. Colloid Interface Sci. 290 (2005) 281-288
36. Zhang R., He X., and Chen S. Interface and surface tension in incompressible lattice Boltzmann multiphase model. Comput. Phys. Commun. 129 1-3 (2000) 121-130 Discrete simulation of fluid dynamics (Tokyo, 1999).
37. Zhang X. Dynamics of growth and breakup of viscous pendant drops into air. J. Collid Interface Sci. 212 (1999) 107-122
38. Zhang X., and Basaran O.A. An experimental study of dynamics of drop formation. Phys. Fluids 7 (1995) 1184-1203