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Simulation of impulsively induced viscoelastic jets using the Oldroyd-B model

Published online by Cambridge University Press:  25 January 2021

Emre Turkoz Open the ORCID record for Emre Turkoz [Opens in a new window] ,
Howard A. Stone Open the ORCID record for Howard A. Stone [Opens in a new window] ,
Craig B. Arnold  and
Luc Deike Open the ORCID record for Luc Deike [Opens in a new window]
Emre Turkoz
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA ExxonMobil Research and Engineering Company, Annandale, NJ08801, USA
Howard A. Stone
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA
Craig B. Arnold
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA
Luc Deike*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA Princeton Environmental Institute, Princeton University, Princeton, NJ08544, USA
*
†Email address for correspondence: [email protected]
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Abstract

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 $t_{max} = c_1 De^{1/4}$, with $c_1$ depending on the Ohnesorge number and blister geometry, while the length of maximum extension reaches an asymptotic value $L_{max}^{\infty }$ for $De>100$, $L_{max}^{\infty }$ depending on the Ohnesorge number and laser energy. The observed asymptotic relationships are in good agreement with experiments performed at much higher Deborah numbers.

JFM classification

Multiphase and Particle-laden Flows: Multiphase flow Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 911 , 25 March 2021 , A14
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Anna, S.L. & McKinley, G.H. 2001 Elasto-capillary thinning and breakup of model elastic liquids. J. Rheol. 45 (1), 115–138.CrossRefGoogle Scholar
Ardekani, A.M., Sharma, V. & McKinley, G.H. 2010 Dynamics of bead formation, filament thinning and breakup in weakly viscoelastic jets. J. Fluid Mech. 665, 46–56.CrossRefGoogle Scholar
Arnold, C.B., Serra, P. & Piqué, A. 2007 Laser direct-write techniques for printing of complex materials. MRS Bull. 32 (1), 23–31.CrossRefGoogle Scholar
Basaran, O.A., Gao, H. & Bhat, P.P. 2013 Nonstandard inkjets. Annu. Rev. Fluid Mech. 45, 85–113.CrossRefGoogle Scholar
Berny, A., Deike, L., Séon, T. & Popinet, S. 2020 Role of all jet drops in mass transfer from bursting bubbles. Phys. Rev. Fluids 5 (3), 033605.CrossRefGoogle Scholar
Bhat, P.P., Appathurai, S., Harris, M.T., Pasquali, M., McKinley, G.H. & Basaran, O.A. 2010 Formation of beads-on-a-string structures during break-up of viscoelastic filaments. Nat. Phys. 6 (8), 625–631.CrossRefGoogle Scholar
Bhat, P.P., Basaran, O.A. & Pasquali, M. 2008 Dynamics of viscoelastic liquid filaments: low capillary number flows. J. Non-Newtonian Fluid Mech. 150 (2–3), 211–225.CrossRefGoogle Scholar
Bhat, P.P., Pasquali, M. & Basaran, O.A. 2009 Beads-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.CrossRefGoogle Scholar
Bousfield, D.W., Keunings, R., Marrucci, G. & Denn, M.M. 1986 Nonlinear analysis of the surface tension driven breakup of viscoelastic filaments. J. Non-Newtonian Fluid Mech. 21 (1), 79–97.Google Scholar
Brasz, C.F., Arnold, C.B., Stone, H.A. & Lister, J.R. 2015 Early-time free-surface flow driven by a deforming boundary. J. Fluid Mech. 767, 811–841.CrossRefGoogle Scholar
Brown, M.S., Brasz, C.F., Ventikos, Y. & Arnold, C.B. 2012 Impulsively actuated jets from thin liquid films for high-resolution printing applications. J. Fluid Mech. 709, 341–370.CrossRefGoogle Scholar
Brown, M.S., Kattamis, N.T. & Arnold, C.B. 2010 Time-resolved study of polyimide absorption layers for blister-actuated laser-induced forward transfer. J. Appl. Phys. 107 (8), 083103.CrossRefGoogle Scholar
Brown, M.S., Kattamis, N.T. & Arnold, C.B. 2011 Time-resolved dynamics of laser-induced micro-jets from thin liquid films. Microfluid Nanofluid 11 (2), 199–207.CrossRefGoogle Scholar
Clasen, C., Eggers, J., Fontelos, M.A., Li, J. & McKinley, G.H. 2006 The beads-on-string structure of viscoelastic threads. J. Fluid Mech. 556, 283–308.CrossRefGoogle Scholar
Dealy, J.M. 2010 Weissenberg and Deborah numbers – their definition and use. Rheol. Bull. 79 (2), 14–18.Google Scholar
Deike, L., Ghabache, E., Liger-Belair, G., Das, A.K, Zaleski, S., Popinet, S. & Séon, T. 2018 Dynamics of jets produced by bursting bubbles. Phys. Rev. Fluids 3 (1), 013603.CrossRefGoogle Scholar
Deike, L., Melville, W.K. & Popinet, S. 2016 Air entrainment and bubble statistics in breaking waves. J. Fluid Mech. 801, 91–129.CrossRefGoogle Scholar
Dinic, J., Zhang, Y., Jimenez, L.N. & Sharma, V. 2015 Extensional relaxation times of dilute, aqueous polymer solutions. ACS Macro Lett. 4 (7), 804–808.CrossRefGoogle Scholar
Eggers, J. & Fontelos, M.A. 2015 Singularities: Formation, Structure, and Propagation, vol. 53. Cambridge University Press.Google Scholar
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.CrossRefGoogle Scholar
Fattal, R. & Kupferman, R. 2005 Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation. J. Non-Newtonian Fluid Mech. 126 (1), 23–37.CrossRefGoogle Scholar
Fernandez, J.M.M. & Ganan-Calvo, A.M. 2020 Dripping, jetting and tip streaming. Rep. Prog. Phys. 83 (9), 097001.Google Scholar
Ferrás, L.L., Morgado, M.L., Rebelo, M., McKinley, G.H. & Afonso, A.M. 2019 A generalised Phan–Thien–Tanner model. J. Non-Newtonian Fluid Mech. 269, 88–99.CrossRefGoogle Scholar
Foteinopoulou, K., Mavrantzas, V.G. & Tsamopoulos, J. 2004 Numerical simulation of bubble growth in newtonian and viscoelastic filaments undergoing stretching. J. Non-Newtonian Fluid Mech. 122 (1–3), 177–200.CrossRefGoogle Scholar
Goldin, M., Yerushalmi, J., Pfeffer, R. & Shinnar, R. 1969 Breakup of a laminar capillary jet of a viscoelastic fluid. J. Fluid Mech. 38 (4), 689–711.CrossRefGoogle Scholar
Jaffe, M. & Allam, S. 2015 Safer fuels by integrating polymer theory into design. Science 350 (6256), 32–32.CrossRefGoogle ScholarPubMed
Jalaal, M., Schaarsberg, M.K., Visser, C.-W. & Lohse, D. 2019 Laser-induced forward transfer of viscoplastic fluids. J. Fluid Mech. 880, 497–513.CrossRefGoogle Scholar
Kattamis, N.T., Brown, M.S. & Arnold, C.B. 2011 Finite element analysis of blister formation in laser-induced forward transfer. J. Mater. Res. 26 (18), 2438–2449.CrossRefGoogle Scholar
Keshavarz, B., Houze, E.C., Moore, J.R., Koerner, M.R. & McKinley, G.H. 2016 Ligament mediated fragmentation of viscoelastic liquids. Phys. Rev. Lett. 117 (15), 154502.Google ScholarPubMed
Kooij, S., Sijs, R., Denn, M.M., Villermaux, E. & Bonn, D. 2018 What determines the drop size in sprays? Phys. Rev. X 8 (3), 031019.Google Scholar
Lai, C.-Y., Eggers, J. & Deike, L. 2018 a Bubble bursting: universal cavity and jet profiles. Phys. Rev. Lett. 121 (14), 144501.CrossRefGoogle ScholarPubMed
Lai, C.-Y., Rallabandi, B., Perazzo, A., Zheng, Z., Smiddy, S.E. & Stone, H.A. 2018 b Foam-driven fracture. Proc. Natl Acad. Sci. USA 115 (32), 8082–8086.CrossRefGoogle ScholarPubMed
Li, F., Yin, X.-Y. & Yin, X.-Z. 2017 Oscillation of satellite droplets in an Oldroyd-B viscoelastic liquid jet. Phys. Rev. Fluids 2 (1), 013602.CrossRefGoogle Scholar
Li, K., Jing, X., He, S., Ren, H. & Wei, B. 2016 Laboratory study displacement efficiency of viscoelastic surfactant solution in enhanced oil recovery. Energy Fuels 30 (6), 4467–4474.CrossRefGoogle Scholar
López-Herrera, J.M., Popinet, S. & Castrejón-Pita, A.A. 2019 An 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.CrossRefGoogle Scholar
Morrison, N.F. & Harlen, O.G. 2010 Viscoelasticity in inkjet printing. Rheol. Acta 49 (6), 619–632.CrossRefGoogle Scholar
Mostert, W. & Deike, L. 2020 Inertial energy dissipation in shallow-water breaking waves. J. Fluid Mech. 890, A12.CrossRefGoogle Scholar
Oldroyd, J.G. 1950 On the formulation of rheological equations of state. Proc. R. Soc. Lond. A 200 (1063), 523–541.Google Scholar
Öztekin, A., Brown, R.A. & McKinley, G.H. 1994 Quantitative 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.CrossRefGoogle Scholar
Pasquali, M. & Scriven, L.E. 2002 Free surface flows of polymer solutions with models based on the conformation tensor. J. Non-Newtonian Fluid Mech. 108 (1–3), 363–409.CrossRefGoogle Scholar
Pasquali, M. & Scriven, L.E. 2004 Theoretical modeling of microstructured liquids: a simple thermodynamic approach. J. Non-Newtonian Fluid Mech. 120 (1–3), 101–135.CrossRefGoogle Scholar
Piqué, A. & Serra, P. 2018 Laser Printing of Functional Materials: 3D Microfabrication, Electronics and Biomedicine. John Wiley and Sons.Google Scholar
Ponce-Torres, A., Montanero, J.M., Vega, E.J. & Gañán-Calvo, A.M. 2016 The production of viscoelastic capillary jets with gaseous flow focusing. J. Non-Newtonian Fluid Mech. 229, 8–15.Google Scholar
Popinet, S. 2009 An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228 (16), 5838–5866.CrossRefGoogle Scholar
Popinet, S. 2015 A quadtree-adaptive multigrid solver for the Serre–Green–Naghdi equations. J. Comput. Phys. 302, 336–358.CrossRefGoogle Scholar
Popinet, S. 2018 Numerical models of surface tension. Annu. Rev. Fluid Mech. 50 (1), 49–75.CrossRefGoogle Scholar
Renardy, M. 1995 A numerical study of the asymptotic evolution and breakup of newtonian and viscoelastic jets. J. Non-Newtonian Fluid Mech. 59 (2–3), 267–282.CrossRefGoogle Scholar
Roché, M., Kellay, H. & Stone, H.A. 2011 Heterogeneity and the role of normal stresses during the extensional thinning of non-Brownian shear-thickening fluids. Phys. Rev. Lett. 107 (13), 134503.CrossRefGoogle ScholarPubMed
Rubinstein, M. & Colby, R.H. 2003 Polymer Physics, vol. 23. Oxford University Press.Google Scholar
Sattler, R., Gier, S., Eggers, J. & Wagner, C. 2012 The final stages of capillary break-up of polymer solutions. Phys. Fluids 24 (2), 023101.CrossRefGoogle Scholar
Szady, M.J., Salamon, T.R., Liu, A.W., Bornside, D.E., Armstrong, R.C. & Brown, R.A. 1995 A new mixed finite element method for viscoelastic flows governed by differential constitutive equations. J. Non-Newtonian Fluid Mech. 59 (2–3), 215–243.Google Scholar
Tirtaatmadja, V., McKinley, G.H. & Cooper-White, J.J. 2006 Drop formation and breakup of low viscosity elastic fluids: effects of molecular weight and concentration. Phys. Fluids 18 (4), 043101.CrossRefGoogle Scholar
Turkoz, E., Deike, L. & Arnold, C.B. 2017 Comparison of jets from newtonian and non-newtonian fluids induced by blister-actuated laser-induced forward transfer (ba-lift). Appl. Phys. A 123 (10), 652.CrossRefGoogle Scholar
Turkoz, E., Fardel, R. & Arnold, C.B. 2018 a 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.Google Scholar
Turkoz, E., Kang, S., Du, X., Deike, L. & Arnold, C.B. 2019 a Reduction of transfer threshold energy for laser-induced jetting of liquids using faraday waves. Phys. Rev. Appl. 11 (5), 054022.CrossRefGoogle Scholar
Turkoz, E., Lopez-Herrera, J.M., Eggers, J., Arnold, C.B. & Deike, L. 2018 b Axisymmetric simulation of viscoelastic filament thinning with the Oldroyd-B model. J. Fluid Mech. 851.CrossRefGoogle Scholar
Turkoz, E., Perazzo, A., Deike, L., Stone, H.A. & Arnold, C.B. 2019 b Deposition-on-contact regime and the effect of donor-acceptor distance during laser-induced forward transfer of viscoelastic liquids. Opt. Mater. Express 9 (7), 2738–2747.CrossRefGoogle Scholar
Turkoz, E., Perazzo, A., Kim, H., Stone, H.A. & Arnold, C.B. 2018 c Impulsively induced jets from viscoelastic films for high-resolution printing. Phys. Rev. Lett. 120 (7), 074501.CrossRefGoogle ScholarPubMed
Unger, C., Gruene, M., Koch, L., Koch, J. & Chichkov, B.N. 2011 Time-resolved imaging of hydrogel printing via laser-induced forward transfer. Appl. Phys. A 103 (2), 271–277.CrossRefGoogle Scholar
Villermaux, E. 2007 Fragmentation. Annu. Rev. Fluid Mech. 39, 419–446.CrossRefGoogle Scholar
Zhang, Z., Xiong, R., Corr, D.T. & Huang, Y. 2016 Study of impingement types and printing quality during laser printing of viscoelastic alginate solutions. Langmuir 32 (12), 3004–3014.CrossRefGoogle ScholarPubMed