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Level-set method for the modelling of liquid bridge formation and break-up. (English) Zbl 1245.76098

Summary: In this paper, a level-set method is used to track the free surface and velocity profile of a Newtonian filament being stretched on an extensional rheometer. The method enables simulations to be performed from initial stretching until after the filament has broken up. The method used also follows the behaviour at the plate-liquid interface, allowing the air-liquid- solid contact point to move freely rather than being pinned at the edge of the plate. The simulations were validated by comparison with analogous experiments with glycerin, with excellent agreement between the two. The simulations were able to track the free surface throughout the experiment, including after the topological change associated with the filament breaking up. For the modelling of the fluid stretching, a novel grid deformation algorithm was introduced which allowed a tailored expansion of the domain, avoiding the need for specialised re-meshing.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D45 Capillarity (surface tension) for incompressible viscous fluids
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[1] McKinley, G. H.; Sridhar, T., Filament-stretching rheometry of complex fluids, Ann Rev Fluid Mech, 34, 375-415 (2002) · Zbl 0994.76502
[2] Yao, M.; McKinley, G. H., Numerical simulation of extensional deformations of viscoelastic liquid bridges in filament stretching devices, J Non-Newton Fluid Mech, 74, 1-3, 47-88 (1998) · Zbl 0957.76005
[3] Gaudet, S.; McKinley, G. H., Extensional deformation of non-Newtonian liquid bridges, Comput Mech, 21, 461-476 (1998) · Zbl 0924.76004
[4] Kolte, M. I.; Rasmussen, H. K.; Hassager, O., Transient filament stretching rheometer II: numerical simulation, Rheol Acta, 36, 3, 285-302 (1997)
[5] Yao, M.; Spiegelberg, S. H.; McKinley, G. H., Dynamics of weakly strain-hardening fluids in filament stretching devices, J Non-Newton Fluid Mech, 89, 1-2, 1-43 (2000) · Zbl 0973.76540
[6] Matallah, H.; Banaai, M.; Sujatha, K.; Webster, M., Modelling filament stretching flows with strain-hardening models and sub-cell approximations, J Non-Newton Fluid Mech, 134, 1-3, 77-104 (2006) · Zbl 1123.76311
[7] Bonito, A.; Picasso, M.; Laso, M., Numerical simulation of 3D viscoelastic flows with free surfaces, J Comput Phys, 215, 2, 691-716 (2006) · Zbl 1173.76303
[8] Bhat, P. P.; Basaran, O. A.; Pasquali, M., Dynamics of viscoelastic liquid filaments: low capillary number flows, J Non-Newton Fluid Mech, 150, 2-3, 211-225 (2008) · Zbl 1273.76035
[9] Osher, S.; Sethian, J. A., Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J Comput Phys, 79, 1, 12-49 (1988) · Zbl 0659.65132
[10] Sethian, J. A., Evolution, implementation, and application of level set and fast marching methods for advancing fronts, J Comput Phys, 169, 2, 503-555 (2001) · Zbl 0988.65095
[11] Osher, S.; Fedkiw, R. P., Level set methods: an overview and some recent results, J Comput Phys, 169, 2, 463-502 (2001) · Zbl 0988.65093
[12] Wang, S.; Lim, K.; Khoo, B.; Wang, M., An extended level set method for shape and topology optimization, J Comput Phys, 221, 1, 395-421 (2007) · Zbl 1110.65058
[13] Kao, C.-Y.; Tsai, R., A numerical method for free-surface flows and its application to droplet impact on a thin liquid layer, J Comput Phys, 35, 170-191 (2008)
[14] Sussman, M.; Smereka, P.; Osher, S. J., A level set approach for computing solutions to incompressible two-phase flow, J Comput Phys, 114, 146-159 (1994) · Zbl 0808.76077
[15] Yokoi, K., A numerical method for free-surface flows and its application to droplet impact on a thin liquid layer, J Sci Comput, 35, 372-396 (2008) · Zbl 1203.76123
[16] Tanguy, S.; Berlemont, A., Application of a level set method for simulation of droplet collisions, Int J Multiphase Flow, 31, 9, 1015-1035 (2005) · Zbl 1135.76560
[17] Yang, J.; Stern, F., Sharp interface immersed-boundary/level-set method for wave-body interactions, J Comput Phys, 228, 17, 6590-6616 (2009) · Zbl 1261.76040
[18] Kang, M.; Merriman, B.; Osher, S., Numerical simulations for the motion of soap bubbles using level set methods, Comput Fluids, 37, 5, 524-535 (2008) · Zbl 1237.76121
[19] Di, Y.; Li, R.; Zhang, P., Level set calculations for incompressible two-phase flows on a dynamically adaptive grid, J Sci Comput, 31, 75-98 (2007) · Zbl 1151.76548
[20] Sussman, M.; Almgren, A. S.; Bell, J. B.; Colella, P.; Howell, L. H.; Welcomey, M. L., An adaptive level set approach for incompressible two-phase flows, J Comput Phys, 1484, 81-124 (1999) · Zbl 0930.76068
[21] Shepel, S. V.; Smith, B. L., On surface tension modelling using the level set method, Int J Numer Methods Fluids, 59, 147-171 (2009) · Zbl 1394.76071
[22] Grande, E.; Laso, M.; Picasso, M., Calculation of variable-topology free surface flows using CONNFFESSIT, J Non-Newton Fluid Mech, 113, 2-3, 127-145 (2003) · Zbl 1065.76559
[23] Versteeg, H. K.; Malalasekera, W., An introduction to computational fluid dynamics: the finite volume method (1995), Prentice Hall
[24] Young, T., An essay on the cohesion of fluids, Philos Trans Roy Soc Lond, 95, 65-87 (1805)
[25] de Gennes, P.-G., Wetting: statics and dynamics, Rev Mod Phys, 57, 828-861 (1985)
[26] Wheeler D. Computational modelling of surface tension phenomena in metals processing, PhD thesis, University Of Greenwich; 2000.; Wheeler D. Computational modelling of surface tension phenomena in metals processing, PhD thesis, University Of Greenwich; 2000.
[27] Blake, T. D., The physics of moving wetting lines, J Colloid Interface Sci, 299, 1, 1-13 (2006)
[28] Croft TN, Pericleous K, Cross M. PHYSICA: a multiphysics environment for complex flow processes. In: Numerical methods in laminar and turbulent flow: part II, vol. IX. Pineridge Press; 1995. p. 1269-80.; Croft TN, Pericleous K, Cross M. PHYSICA: a multiphysics environment for complex flow processes. In: Numerical methods in laminar and turbulent flow: part II, vol. IX. Pineridge Press; 1995. p. 1269-80.
[29] Rhie, C. M.; Chow, W., Numerical study of the turbulent flow past an airfoil with trailing edge separation, AIAA J, 21, 11, 1525-1532 (1983) · Zbl 0528.76044
[30] Xu, J.-J.; Li, Z.; Lowengrub, J.; Zhao, H., A level-set method for interfacial flows with surfactant, J Comput Phys, 212, 590-616 (2006) · Zbl 1161.76548
[31] Weatherburn, C. E., Differential geometry in three dimensions (1972), Cambridge University Press · Zbl 0016.37202
[32] Yokoi, K.; Vadillo, D.; Hinch, J.; Hutchings, I., Numerical studies of the influence of the dynamic contact angle on a droplet impacting on a dry surface, Phys Fluids, 21, 072102 (2009) · Zbl 1183.76587
[33] Zahedi, S.; Gustavsson, K.; Kreiss, G., A conservative level set method for contact line dynamics, J Comput Phys, 228, 17, 6361-6375 (2009) · Zbl 1261.76042
[34] Williams, A. J.; Croft, T. N.; Cross, M., Modelling of ingot development during the start-up phase of direct chill casting, Metall Mater Trans B, 34B, 727-734 (2003)
[35] Chang, Y.; Hou, T.; Merriman, B.; Osher, S., A level set formulation of Eulerian interface capturing methods for incompressible fluid flows, J Comput Phys, 124, 2, 449-464 (1996) · Zbl 0847.76048
[36] McKinley, G. H.; Tripathi, A., How to extract the newtonian viscosity from capillary breakup measurements in a filament rheometer, J Rheol, 44, 653-670 (2000)
[37] Rodd, L. E.; Scott, T. P.; Cooper-White, J. J.; McKinley, G. H., Capillary break-up rheometry of low-viscosity elastic fluids, Appl Rheol, 15, 12-27 (2005)
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