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Simulation of impulsively induced viscoelastic jets using the Oldroyd-B model. (English) Zbl 1461.76031
Summary: Understanding the physics of viscoelastic liquid jets is relevant to jet-based printing and deposition techniques. In this paper we study the behaviour of jets induced from viscoelastic liquid films, using the mechanical impulse provided by a laser pulse to actuate jet formation. We present direct numerical simulations of viscoelastic liquid jets solving the two-phase flow problem, accounting for the Oldroyd-B rheology. We describe how the jet extension time and length are controlled by the Deborah number (ratio of the elastic and inertia-capillary time scales), the viscous dissipation described by the Ohnesorge number (ratio of the viscous-capillary and inertia-capillary time scales), as well as the ratio of laser impulse energy to the energy required to create free surface during jet formation and propagation. Using the droplet ejection laser threshold energy of a Newtonian liquid, we investigate the influence of increasing viscoelastic effects. We show that viscoelastic effects can modify the effective drop size at the tip of the jet, while the maximum jet length increases with increasing Deborah number. Using the simulations, we identify a high-Deborah-number regime, where the time of maximum jet extension can be described as \(t_{\mathrm{max}} = c_1 De^{1/4}\), with \(c_1\) depending on the Ohnesorge number and blister geometry, while the length of maximum extension reaches an asymptotic value \(L_{\mathrm{max}}^\infty\) for \(De>100, L_{\mathrm{max}}^\infty\) depending on the Ohnesorge number and laser energy. The observed asymptotic relationships are in good agreement with experiments performed at much higher Deborah numbers.
76A10 Viscoelastic fluids
76Txx Multiphase and multicomponent flows
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[1] Anna, S.L. & Mckinley, G.H.2001Elasto-capillary thinning and breakup of model elastic liquids. J. Rheol.45 (1), 115-138.
[2] Ardekani, A.M., Sharma, V. & Mckinley, G.H.2010Dynamics of bead formation, filament thinning and breakup in weakly viscoelastic jets. J. Fluid Mech.665, 46-56. · Zbl 1225.76188
[3] Arnold, C.B., Serra, P. & Piqué, A.2007Laser direct-write techniques for printing of complex materials. MRS Bull.32 (1), 23-31.
[4] Basaran, O.A., Gao, H. & Bhat, P.P.2013Nonstandard inkjets. Annu. Rev. Fluid Mech.45, 85-113. · Zbl 1359.76289
[5] Berny, A., Deike, L., Séon, T. & Popinet, S.2020Role of all jet drops in mass transfer from bursting bubbles. Phys. Rev. Fluids5 (3), 033605.
[6] Bhat, P.P., Appathurai, S., Harris, M.T., Pasquali, M., Mckinley, G.H. & Basaran, O.A.2010Formation of beads-on-a-string structures during break-up of viscoelastic filaments. Nat. Phys.6 (8), 625-631.
[7] Bhat, P.P., Basaran, O.A. & Pasquali, M.2008Dynamics of viscoelastic liquid filaments: low capillary number flows. J. Non-Newtonian Fluid Mech.150 (2-3), 211-225. · Zbl 1273.76035
[8] Bhat, P.P., Pasquali, M. & Basaran, O.A.2009Beads-on-string formation during filament pinch-off: dynamics with the PTT model for non-affine motion. J. Non-Newtonian Fluid Mech.159 (1-3), 64-71. · Zbl 1274.76089
[9] Bousfield, D.W., Keunings, R., Marrucci, G. & Denn, M.M.1986Nonlinear analysis of the surface tension driven breakup of viscoelastic filaments. J. Non-Newtonian Fluid Mech.21 (1), 79-97.
[10] Brasz, C.F., Arnold, C.B., Stone, H.A. & Lister, J.R.2015Early-time free-surface flow driven by a deforming boundary. J. Fluid Mech.767, 811-841. · Zbl 1335.76009
[11] Brown, M.S., Brasz, C.F., Ventikos, Y. & Arnold, C.B.2012Impulsively actuated jets from thin liquid films for high-resolution printing applications. J. Fluid Mech.709, 341-370. · Zbl 1275.76008
[12] Brown, M.S., Kattamis, N.T. & Arnold, C.B.2010Time-resolved study of polyimide absorption layers for blister-actuated laser-induced forward transfer. J. Appl. Phys.107 (8), 083103.
[13] Brown, M.S., Kattamis, N.T. & Arnold, C.B.2011Time-resolved dynamics of laser-induced micro-jets from thin liquid films. Microfluid Nanofluid11 (2), 199-207.
[14] Clasen, C., Eggers, J., Fontelos, M.A., Li, J. & Mckinley, G.H.2006The beads-on-string structure of viscoelastic threads. J. Fluid Mech.556, 283-308. · Zbl 1095.76003
[15] Dealy, J.M.2010Weissenberg and Deborah numbers – their definition and use. Rheol. Bull.79 (2), 14-18.
[16] Deike, L., Ghabache, E., Liger-Belair, G., Das, A.K, Zaleski, S., Popinet, S. & Séon, T.2018Dynamics of jets produced by bursting bubbles. Phys. Rev. Fluids3 (1), 013603.
[17] Deike, L., Melville, W.K. & Popinet, S.2016Air entrainment and bubble statistics in breaking waves. J. Fluid Mech.801, 91-129.
[18] Dinic, J., Zhang, Y., Jimenez, L.N. & Sharma, V.2015Extensional relaxation times of dilute, aqueous polymer solutions. ACS Macro Lett.4 (7), 804-808.
[19] Eggers, J. & Fontelos, M.A.2015Singularities: Formation, Structure, and Propagation, vol. 53. Cambridge University Press. · Zbl 1335.76002
[20] Eggers, J., Herrada, M.A. & Snoeijer, J.H.2019 Self-similar breakup of polymeric threads as described by the Oldroyd-B model. arXiv:1905.12343. · Zbl 1460.76127
[21] Fattal, R. & Kupferman, R.2005Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation. J. Non-Newtonian Fluid Mech.126 (1), 23-37. · Zbl 1099.76044
[22] Fernandez, J.M.M. & Ganan-Calvo, A.M.2020Dripping, jetting and tip streaming. Rep. Prog. Phys.83 (9), 097001.
[23] Ferrás, L.L., Morgado, M.L., Rebelo, M., Mckinley, G.H. & Afonso, A.M.2019A generalised Phan-Thien-Tanner model. J. Non-Newtonian Fluid Mech.269, 88-99.
[24] Foteinopoulou, K., Mavrantzas, V.G. & Tsamopoulos, J.2004Numerical simulation of bubble growth in newtonian and viscoelastic filaments undergoing stretching. J. Non-Newtonian Fluid Mech.122 (1-3), 177-200. · Zbl 1143.76329
[25] Goldin, M., Yerushalmi, J., Pfeffer, R. & Shinnar, R.1969Breakup of a laminar capillary jet of a viscoelastic fluid. J. Fluid Mech.38 (4), 689-711.
[26] Jaffe, M. & Allam, S.2015Safer fuels by integrating polymer theory into design. Science350 (6256), 32-32.
[27] Jalaal, M., Schaarsberg, M.K., Visser, C.-W. & Lohse, D.2019Laser-induced forward transfer of viscoplastic fluids. J. Fluid Mech.880, 497-513. · Zbl 1430.76038
[28] Kattamis, N.T., Brown, M.S. & Arnold, C.B.2011Finite element analysis of blister formation in laser-induced forward transfer. J. Mater. Res.26 (18), 2438-2449.
[29] Keshavarz, B., Houze, E.C., Moore, J.R., Koerner, M.R. & Mckinley, G.H.2016Ligament mediated fragmentation of viscoelastic liquids. Phys. Rev. Lett.117 (15), 154502.
[30] Kooij, S., Sijs, R., Denn, M.M., Villermaux, E. & Bonn, D.2018What determines the drop size in sprays?Phys. Rev. X8 (3), 031019.
[31] Lai, C.-Y., Eggers, J. & Deike, L.2018aBubble bursting: universal cavity and jet profiles. Phys. Rev. Lett.121 (14), 144501.
[32] Lai, C.-Y., Rallabandi, B., Perazzo, A., Zheng, Z., Smiddy, S.E. & Stone, H.A.2018bFoam-driven fracture. Proc. Natl Acad. Sci. USA115 (32), 8082-8086.
[33] Li, F., Yin, X.-Y. & Yin, X.-Z.2017Oscillation of satellite droplets in an Oldroyd-B viscoelastic liquid jet. Phys. Rev. Fluids2 (1), 013602.
[34] Li, K., Jing, X., He, S., Ren, H. & Wei, B.2016Laboratory study displacement efficiency of viscoelastic surfactant solution in enhanced oil recovery. Energy Fuels30 (6), 4467-4474.
[35] López-Herrera, J.M., Popinet, S. & Castrejón-Pita, A.A.2019An adaptive solver for viscoelastic incompressible two-phase problems applied to the study of the splashing of weakly viscoelastic droplets. J. Non-Newtonian Fluid Mech.264, 144-158.
[36] Morrison, N.F. & Harlen, O.G.2010Viscoelasticity in inkjet printing. Rheol. Acta49 (6), 619-632.
[37] Mostert, W. & Deike, L.2020Inertial energy dissipation in shallow-water breaking waves. J. Fluid Mech.890, A12. · Zbl 1460.76103
[38] Oldroyd, J.G.1950On the formulation of rheological equations of state. Proc. R. Soc. Lond. A200 (1063), 523-541. · Zbl 1157.76305
[39] Öztekin, A., Brown, R.A. & Mckinley, G.H.1994Quantitative prediction of the viscoelastic instability in cone-and-plate flow of a Boger fluid using a multi-mode Giesekus model. J. Non-Newtonian Fluid Mech.54, 351-377.
[40] Pasquali, M. & Scriven, L.E.2002Free surface flows of polymer solutions with models based on the conformation tensor. J. Non-Newtonian Fluid Mech.108 (1-3), 363-409. · Zbl 1143.76369
[41] Pasquali, M. & Scriven, L.E.2004Theoretical modeling of microstructured liquids: a simple thermodynamic approach. J. Non-Newtonian Fluid Mech.120 (1-3), 101-135. · Zbl 1143.76360
[42] Piqué, A. & Serra, P.2018Laser Printing of Functional Materials: 3D Microfabrication, Electronics and Biomedicine. John Wiley and Sons.
[43] Ponce-Torres, A., Montanero, J.M., Vega, E.J. & Gañán-Calvo, A.M.2016The production of viscoelastic capillary jets with gaseous flow focusing. J. Non-Newtonian Fluid Mech.229, 8-15.
[44] Popinet, S.2009An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys.228 (16), 5838-5866. · Zbl 1280.76020
[45] Popinet, S.2015A quadtree-adaptive multigrid solver for the Serre-Green-Naghdi equations. J. Comput. Phys.302, 336-358. · Zbl 1349.76377
[46] Popinet, S.2018Numerical models of surface tension. Annu. Rev. Fluid Mech.50 (1), 49-75. · Zbl 1384.76016
[47] Renardy, M.1995A numerical study of the asymptotic evolution and breakup of newtonian and viscoelastic jets. J. Non-Newtonian Fluid Mech.59 (2-3), 267-282.
[48] Roché, M., Kellay, H. & Stone, H.A.2011Heterogeneity and the role of normal stresses during the extensional thinning of non-Brownian shear-thickening fluids. Phys. Rev. Lett.107 (13), 134503.
[49] Rubinstein, M. & Colby, R.H.2003Polymer Physics, vol. 23. Oxford University Press.
[50] Sattler, R., Gier, S., Eggers, J. & Wagner, C.2012The final stages of capillary break-up of polymer solutions. Phys. Fluids24 (2), 023101.
[51] Szady, M.J., Salamon, T.R., Liu, A.W., Bornside, D.E., Armstrong, R.C. & Brown, R.A.1995A new mixed finite element method for viscoelastic flows governed by differential constitutive equations. J. Non-Newtonian Fluid Mech.59 (2-3), 215-243.
[52] Tirtaatmadja, V., Mckinley, G.H. & Cooper-White, J.J.2006Drop formation and breakup of low viscosity elastic fluids: effects of molecular weight and concentration. Phys. Fluids18 (4), 043101.
[53] Turkoz, E., Deike, L. & Arnold, C.B.2017Comparison of jets from newtonian and non-newtonian fluids induced by blister-actuated laser-induced forward transfer (ba-lift). Appl. Phys. A123 (10), 652.
[54] Turkoz, E., Fardel, R. & Arnold, C.B.2018a Advances in blister-actuated laser-induced forward transfer (BA-LIFT). In Laser Printing of Functional Materials: 3D Microfabrication, Electronics and Biomedicine (ed. A. Piqué & P. Serra), pp. 91-121. Wiley-VCH Verlag GmbH & Co. KGaA Weinheim.
[55] Turkoz, E., Kang, S., Du, X., Deike, L. & Arnold, C.B.2019aReduction of transfer threshold energy for laser-induced jetting of liquids using faraday waves. Phys. Rev. Appl.11 (5), 054022.
[56] Turkoz, E., Lopez-Herrera, J.M., Eggers, J., Arnold, C.B. & Deike, L.2018bAxisymmetric simulation of viscoelastic filament thinning with the Oldroyd-B model. J. Fluid Mech.851. · Zbl 1421.76014
[57] Turkoz, E., Perazzo, A., Deike, L., Stone, H.A. & Arnold, C.B.2019bDeposition-on-contact regime and the effect of donor-acceptor distance during laser-induced forward transfer of viscoelastic liquids. Opt. Mater. Express9 (7), 2738-2747.
[58] Turkoz, E., Perazzo, A., Kim, H., Stone, H.A. & Arnold, C.B.2018cImpulsively induced jets from viscoelastic films for high-resolution printing. Phys. Rev. Lett.120 (7), 074501.
[59] Unger, C., Gruene, M., Koch, L., Koch, J. & Chichkov, B.N.2011Time-resolved imaging of hydrogel printing via laser-induced forward transfer. Appl. Phys. A103 (2), 271-277.
[60] Villermaux, E.2007Fragmentation. Annu. Rev. Fluid Mech.39, 419-446.
[61] Zhang, Z., Xiong, R., Corr, D.T. & Huang, Y.2016Study of impingement types and printing quality during laser printing of viscoelastic alginate solutions. Langmuir32 (12), 3004-3014.
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