Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-26T16:42:50.426Z Has data issue: false hasContentIssue false
  • English
  • Français

Global stability analysis of axisymmetric liquid–liquid flow focusing

Published online by Cambridge University Press:  21 December 2020

M. G. Cabezas Open the ORCID record for M. G. Cabezas [Opens in a new window] ,
N. Rebollo-Muñoz Open the ORCID record for N. Rebollo-Muñoz [Opens in a new window] ,
M. Rubio Open the ORCID record for M. Rubio [Opens in a new window] ,
M. A. Herrada Open the ORCID record for M. A. Herrada [Opens in a new window]  and
J. M. Montanero Open the ORCID record for J. M. Montanero [Opens in a new window]
M. G. Cabezas*
Affiliation:
Departamento de Ingeniería Mecánica, Energética y de los Materiales and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006, Badajoz, Spain
N. Rebollo-Muñoz
Affiliation:
Departamento de Ingeniería Mecánica, Energética y de los Materiales and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006, Badajoz, Spain
M. Rubio
Affiliation:
Departamento de Ingeniería Mecánica, Energética y de los Materiales and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006, Badajoz, Spain
M. A. Herrada
Affiliation:
Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, E-41092Sevilla, Spain
J. M. Montanero
Affiliation:
Departamento de Ingeniería Mecánica, Energética y de los Materiales and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006, Badajoz, Spain
*
†Email address for correspondence: mguadama@unex.es
Get access Rights & Permissions [Opens in a new window]

Abstract

We analyse both numerically and experimentally the stability of the steady jetting tip streaming produced by focusing a liquid stream with another liquid current when they coflow through the orifice of an axisymmetric nozzle. We calculate the global eigenmodes characterizing the response of this configuration to small-amplitude perturbations. In this way, the critical conditions leading to the instability of the steady jetting tip streaming are determined. The unstable perturbations are classified according to their oscillatory character and to the region where they originate (convective and absolute instability). We derive and explain in terms of the velocity field a simple scaling law to predict the diameter of the emitted jet. The numerical stability limits are compared with experimental results, finding reasonable agreement. The experiments confirm the existence of the two instability mechanisms predicted by the global stability analysis.

JFM classification

Interfacial Flows (free surface): Capillary flows Micro-/Nano-fluid dynamics: Microfluidics Instability: Absolute/convective instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 909 , 25 February 2021 , A10
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Acero, A. J., Rebollo-Muñoz, N., Montanero, J. M., Gañán-Calvo, A. M. & Vega, E. J. 2013 A new flow focusing technique to produce very thin jets. J. Micromech. Microengng 23, 065009.CrossRefGoogle Scholar
Cabezas, M. G., Bateni, A., Montanero, J. M. & Neumann, A. W. 2004 A new drop-shape methodology for surface tension measurement. Appl. Surf. Sci. 238, 480–484.CrossRefGoogle Scholar
Cabezas, M. G., Herrada, M. A. & Montanero, J. M. 2019 Stability of a jet moving in a rectangular microchannel. Phys. Rev. E 100, 053104.CrossRefGoogle Scholar
Chen, H., Li, J., Shum, H. C., Stone, H. A. & Weitz, D. A. 2011 Breakup of double emulsions in constrictions. Soft Matt. 7, 2345–2347.CrossRefGoogle Scholar
Chen, Y., Wub, L. & Zhang, L. 2015 Dynamic behaviors of double emulsion formation in a flow-focusing device. Intl J. Multiphase Flow 82, 42–50.CrossRefGoogle Scholar
Cohen, I., Li, H., Hougland, J. L., Mrksich, M. & Nagel, S. R. 2001 Using selective withdrawal to coat microparticles. Science 292, 265–267.CrossRefGoogle ScholarPubMed
Cruz-Mazo, F., Herrada, M. A., Gañán-Calvo, A. M. & Montanero, J. M. 2017 Global stability of axisymmetric flow focusing. J. Fluid Mech. 832, 329–344.CrossRefGoogle Scholar
Dimakopoulos, Y. & Tsamopoulos, J. 2003 A quasi-elliptic transformation for moving boundary problems with large anisotropic deformations. J. Comput. Phys. 192, 494–522.CrossRefGoogle Scholar
Dong, J., Meissner, M., Faers, M. A., Eggers, J., Seddon, A. M. & Royall, C. P. 2018 Opposed flow focusing: evidence of a second order jetting transition. Soft Matt. 14, 8344–8351.CrossRefGoogle ScholarPubMed
Eggers, J. 1997 Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69, 865–929.CrossRefGoogle Scholar
Gañán-Calvo, A. M. 1998 Generation of steady liquid microthreads and micron-sized monodisperse sprays in gas streams. Phys. Rev. Lett. 80, 285–288.CrossRefGoogle Scholar
Gañán-Calvo, A. M. & Riesco-Chueca, P. 2006 Jetting-dripping transition of a liquid jet in a lower viscosity co-flowing immiscible liquid: the minimum flow rate in flow focusing. J. Fluid Mech. 553, 75–84.CrossRefGoogle Scholar
Gordillo, J. M., Sevilla, A. & Campo-Cortés, F. 2014 Global stability of stretched jets: conditions for the generation of monodisperse micro-emulsions using coflows. J. Fluid Mech. 738, 335–357.CrossRefGoogle Scholar
Gu, H., Duits, M. H. G. & Mugele, F. 2011 Droplets formation and merging in two-phase flow microfluidics. Intl J. Mol. Sci. 12, 2572–2597.CrossRefGoogle ScholarPubMed
He, K., Campo-Cortés, F., Goral, M., López-León, T. & Gordillo, J. M. 2019 Micron-sized double emulsions and nematic shells generated via tip streaming. Phys. Rev. Fluids 4, 124201.CrossRefGoogle Scholar
Herrada, M. A. & Montanero, J. M. 2016 A numerical method to study the dynamics of capillary fluid systems. J. Comput. Phys. 306, 137–147.CrossRefGoogle Scholar
Humphry, K. J., Ajdari, A., Fernández-Nieves, A., Stone, H. A. & Weitz, D. A. 2009 Suppression of instabilities in multiphase flow by geometric confinement. Phys. Rev. E 79, 056310.CrossRefGoogle ScholarPubMed
Lee, G.-B., Hung, C.-I., Ke, B.-J., Huang, G.-R., Hwei, B.-H. & Lai, H.-F. 2001 Hydrodynamic focusing for a micromachined flow cytometer. Trans. ASME: J. Fluids Engng 123, 672–679.Google Scholar
Liu, X., Wu, L., Zhao, Y. & Chen, Y. 2017 Study of compound drop formation in axisymmetric microfluidic devices with different geometries. Colloids Surf. A 533, 87–98.CrossRefGoogle Scholar
de Luca, L., Costa, M. & Caramiello, C. 2002 Energy growth of initial perturbations in two-dimensional gravitational jets. Phys. Fluids 14, 289–299.CrossRefGoogle Scholar
Marín, A. G., Campo-Cortés, F. & Gordillo, J. M. 2009 Generation of micron-sized drops and bubbles through viscous coflows. Colloids Surf. A 344, 2–7.CrossRefGoogle Scholar
Montanero, J. M. & Gañán-Calvo, A. M. 2020 Dripping, jetting and tip streaming. Rep. Prog. Phys. 83, 097001.CrossRefGoogle ScholarPubMed
Montanero, J. M. & Gañán-Calvo, A. M. 2008 Stability of coflowing capillary jets under non-axisymmetric perturbations. Phys. Rev. E 77, 046301.CrossRefGoogle Scholar
Montanero, J. M., Rebollo-Muñoz, N., Herrada, M. A. & Gañán-Calvo, A. M. 2011 Global stability of the focusing effect of fluid jet flows. Phys. Rev. E 83, 036309.CrossRefGoogle ScholarPubMed
Morad, M., Rajabi, A., Razavi, M. & Sereshkeh, S. P. 2016 A very stable high throughput Taylor cone-jet in electrohydrodynamics. Sci. Rep. 6, 38509.CrossRefGoogle ScholarPubMed
Moyle, T. M., Walker, L. M. & Anna, S. L. 2012 Predicting conditions for microscale surfactant mediated tipstreaming. Phys. Fluids 24, 082110.CrossRefGoogle Scholar
Mu, K., Ding, H. & Si, T. 2018 Instability analysis of the cone-jet flow in liquid-driven flow focusing. Microfluidics Nanofluidics 22, 138.CrossRefGoogle Scholar
Muñoz-Sánchez, B. N., Gañán-Calvo, A. M. & Cabezas, M. G. 2019 A new fire shaping approach to produce highly axisymmetric and reproducible nozzles. J. Mater. Process. Technol. 270, 241–253.CrossRefGoogle Scholar
Nabavi, S. A., Vladisavljevic, G. T. & Manovic, V. 2017 Mechanisms and control of single-step microfluidic generation of multi-core double emulsion droplets. Chem. Engng J. 322, 140–148.CrossRefGoogle Scholar
do Nascimento, D. F., Avendaño, J. A., Mehl, A., Moura, M. J. B., Carvalho, M. S. & Duncanson, W. J. 2017 Flow of tunable elastic microcapsules through constrictions. Sci. Rep. 7, 11898.CrossRefGoogle ScholarPubMed
Nooranidoost, M., Izbassarov, D. & Muradoglu, M. 2016 Droplet formation in a flow focusing configuration: effects of viscoelasticity. Phys. Fluids 28, 123102.CrossRefGoogle Scholar
Ponce-Torres, A., Rebollo-Muñoz, N., Herrada, M. A., Gañán-Calvo, A. M. & Montanero, J. M. 2018 The steady cone-jet mode of electrospraying close to the minimum volume stability limit. J. Fluid Mech. 857, 142–172.CrossRefGoogle Scholar
Rayleigh, Lord 1878 On the instability of jets. Proc. Lond. Math. Soc. s1-10, 4–13.CrossRefGoogle Scholar
Rubio-Rubio, M., Sevilla, A. & Gordillo, J. M. 2013 On the thinnest steady threads obtained by gravitational stretching of capillary jets. J. Fluid Mech. 729, 471–483.CrossRefGoogle Scholar
Sauter, U. S. & Buggisch, H. W. 2005 Stability of initially slow viscous jets driven by gravity. J. Fluid Mech. 533, 237–257.CrossRefGoogle Scholar
Schmid, P. J. 2007 Nonmodal stability theory. Annu. Rev. Fluid Mech. 39, 129–162.CrossRefGoogle Scholar
Stone, H. A., Bentley, B. J. & Leal, L. G. 1986 An experimental study of transient effects in the breakup of viscous drops. J. Fluid Mech. 173, 131–158.CrossRefGoogle Scholar
Sun, B. J., Shum, H. C., Holtze, C. & Weitz, D. A. 2010 Microfluidic melt emulsification for encapsulation and release of actives. ACS Appl. Mater. Interfaces 2, 3411–3416.CrossRefGoogle ScholarPubMed
Suryo, R. & Basaran, O. A. 2006 Tip streaming from a liquid drop forming from a tube in a co-flowing outer fluid. Phys. Fluids 18, 082102.CrossRefGoogle Scholar
Takeuchi, S., Garstecki, P., Weibel, D. B. & Whitesides, G. M. 2005 An axisymmetric flow-focusing microfluidic device. Adv. Mater. 17, 1067–1072.CrossRefGoogle Scholar
Tammisola, O., Lundell, F. & Soderberg, L. D. 2012 Surface tension-induced global instability of planar jets and wakes. J. Fluid Mech. 713, 632–658.CrossRefGoogle Scholar
Theofilis, V. 2011 Global linear instability. Annu. Rev. Fluid Mech. 43, 319–352.CrossRefGoogle Scholar
Tsuda, Y., Morimoto, Y. & Takeuchi, S. 2010 Monodisperse cell-encapsulating peptide microgel beads for 3D cell culture. Langmuir 26, 2645–2649.CrossRefGoogle ScholarPubMed
Utada, A. S., Lorenceau, E., Link, D. R., Kaplan, P. D., Stone, H. A. & Weitz, D. A. 2005 Monodisperse double emulsions generated from a microcapillary device. Science 308, 537–541.CrossRefGoogle ScholarPubMed
Vega, E. J., Montanero, J. M., Herrada, M. A. & Ferrera, C. 2014 Dynamics of an axisymmetric liquid bridge close to the minimum-volume stability limit. Phys. Rev. E 90, 013015.CrossRefGoogle ScholarPubMed
Vega, E. J., Montanero, J. M., Herrada, M. A. & Gañán-Calvo, A. M. 2010 Global and local instability of flow focusing: the influence of the geometry. Phys. Fluids 22, 064105.CrossRefGoogle Scholar
Vladisavljevic, G. T., Henry, J. V., Duncanson, W. J., Shum, H. C. & Weitz, D. A. 2012 Fabrication of biodegradable poly(lactic acid) particles in flow-focusing glass capillary devices. Prog. Colloid Polym. Sci. 139, 111–114.Google Scholar
Wang, J.-T., Wang, J. & Han, J.-J. 2011 Fabrication of advanced particles and particle-based materials assisted by droplet-based microfluidics. Small 4, 1728–1754.CrossRefGoogle Scholar
Wrobel, J. K., Booty, M. R., Siegel, M. & Wang, Q. 2018 Simulation of surfactant-mediated tipstreaming in a flow-focusing geometry. Phys. Rev. Fluids 3, 114003.CrossRefGoogle Scholar
Wu, L., Liu, X., Zhao, Y. & Chen, Y. 2017 a Role of local geometry on droplet formation in axisymmetric microfluidics. Chem. Engng Sci. 163, 56–67.CrossRefGoogle Scholar
Wu, T., Luo, Z., Ding, W., Cheng, Z. & He, L. 2017 c Monodisperse droplets by impinging flow-focusing. Microfluid Nanofluid 21, 129.CrossRefGoogle Scholar
Wu, Q., Yang, C. Y., Liu, G. L., Xu, W. H., Zhu, Z. Q., Si, T. & Xu, R. X. 2017 b Multiplex coaxial flow focusing for producing multicompartment janus microcapsules with tunable material compositions and structural characteristics. Lab Chip 17, 3168–3175.CrossRefGoogle ScholarPubMed
Zhu, Z., Wu, Q., Han, S., Xu, W., Zhong, F., Yuan, S., Dwivedi, P., Si, T. & Xu, R. X. 2018 Rapid production of single- and multi-compartment polymeric microcapsules in a facile 3D microfluidic process for magnetic separation and synergistic delivery. Sensors Actuators B 275, 190–198.CrossRefGoogle Scholar