Skip to main content
SpringerLink
Log in

Effect of parallel electric field on the linear stability between a Newtonian and a power-law fluid in a microchannel

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

Applying an electric field to a two-fluid flow in a microchannel is an effective way to obtain microdroplets. For that purpose, the stability of the interface between a Newtonian and a power-law fluid flowing in a microchannel is studied. The fluids are either leaky dielectric or perfect dielectric. The effects of the applied voltage, the power-law index, and the strength of the base flow are investigated. Increasing the voltage may destabilize or stabilize the system depending on the electrical properties of the leaky dielectric fluids, similar to a system of two Newtonian fluids. When the electric field destabilizes the system, the maximum wavenumber increases, representing a droplet volume decrease. For perfect dielectric fluids, the electric field permanently stabilizes the flow independent of the electrical properties of fluids. The stability behavior of the power-law index depends on the fluids’ thickness ratio. When the power-law index is added as a new parameter, the base flow strength also affects the system stability, even when the thickness and viscosity ratios are unity, unlike two Newtonian fluid system. Depending on the fluids’ power-law index, and viscosity ratio, the base flow strength may stabilize or destabilize the system. Additionally, a sudden decrease in the droplet volume may be observed for some values of the power-law index and viscosity ratios.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Data availability statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Data sharing not applicable to this article as no datasets were generated or analysed during the current study.]

References

  1. G.M. Whitesides, The origins and the future of microfluidics. Nature 442(7101), 368–373 (2006)

    ADS  Google Scholar 

  2. S. Altundemir, A.K. Uguz, K. Ulgen, A review on wax printed microfluidic paper-based devices for international health. Biomicrofluidics 11(4), 041501 (2017)

    Google Scholar 

  3. P. Eribol, A.K. Uguz, K. Ulgen, Screening applications in drug discovery based on microfluidic technology. Biomicrofluidics 10(1), 011502 (2016)

    Google Scholar 

  4. M. R. Bringer, C. J. Gerdts, H. Song, J. D. Tice, R. F. Ismagilov, Microfluidic systems for chemical kinetics that rely on chaotic mixing in droplets. Philos. Trans. A Math. Phys. Eng. Sci. 362(1818), 1087–1104 (2004)

  5. D. T. Chiu, A. J. DeMello, D. D. Carlo, P. S. Doyle, C. Hansen, R. M. Maceiczyk, R. C. Wootton, Small but perfectly formed? Successes, challenges, and opportunities for microfluidics in the chemical and biological sciences. Chem 2(2), 201–223 (2017)

  6. D.J. Collins, A. Neild, A. DeMello, A.Q. Liu, Y. Ai, The Poisson distribution and beyond: methods for microfluidic droplet production and single cell encapsulation. Lab. Chip. 15(17), 3439–3459 (2015)

    Google Scholar 

  7. J. R. Millman, K. H. Bhatt, B. G. Prevo, O. D. Velev, Anisotropic particle synthesis in dielectrophoretically controlled microdroplet reactors. Nat. Mater. 4(1), 98–102 (2005)

  8. G. T. Vladisavljević, N. Khalid, M. A. Neves, T. Kuroiwa, M. Nakajima, K. Uemura, S. Ichikawa, I. Kobayashi, Industrial lab-on-a-chip: Design, applications and scale-up for drug discovery and delivery, Adv. Drug Deliv. Rev. 65(11–12), 1626–1663 (2013)

  9. S. Altundemir, P. Eribol, A.K. Uguz, Droplet formation and its mechanism in a microchannel in the presence of an electric field. Fluid Dyn. Res. 50(5), 051404 (2018)

    ADS  MathSciNet  Google Scholar 

  10. O. Ozen, N. Aubry, D.T. Papageorgiou, P.G. Petropoulos, Monodisperse drop formation in square microchannels. Phys. Rev. Lett. 96(14), 144501 (2006)

    ADS  Google Scholar 

  11. P. Eribol, A.K. Uguz, Experimental investigation of electrohydrodynamic instabilities in micro channels. Eur. Phys. J. Special Topics 224(2), 425–434 (2015)

  12. H. Li, T.N. Wong, N.T. Nguyen, Instability of pressure driven viscous fluid streams in a microchannel under a normal electric field. Int. J. Heat Mass Tran. 55(23–24), 6994–7004 (2012)

    Google Scholar 

  13. D. Saville, Electrohydrodynamics: The Taylor-Melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29(1), 27–64 (1997)

    ADS  MathSciNet  Google Scholar 

  14. C.T. Okonski, H.C. Thacher, The distortion of aerosol droplets by an electric field. J. Phys. Chem. Biophys. 57(9), 955–958 (1953)

    Google Scholar 

  15. R. S. Allan, S. G. Mason, Particle behaviour in shear and electric fields, 1. Deformation and burst of fluid drops. Proc. R. Soc. Lond. A Math. Phys. Sci. 267(1328), 45–61 (1962)

  16. B. Dinesh, R. Narayanan, Nature of branching in electrohydrodynamic instability. Phys. Rev. Fluids 6(5), 054001 (2021)

    ADS  Google Scholar 

  17. J. R. Melcher, W. J. Schwarz, Interfacial relaxation overstability in a tangential electric-field. Phys. Fluids 11(12), 2604–2616 (1968)

    ADS  Google Scholar 

  18. D. Tseluiko, D.T. Papageorgiou, Nonlinear dynamics of electrified thin liquid films. Siam J. On Appl. Math. 67(10), 1310–1329 (2006)

    MathSciNet  MATH  Google Scholar 

  19. V. Shankar, A. Sharma, Instability of the interface between thin fluid films subjected to electric fields. J. Colloid Interface Sci. 274(1), 294–308 (2004)

    ADS  Google Scholar 

  20. G. I. Taylor, Studies in electrohydrodynamics. I. The circulation produced in a drop by an electric field. Proc. R. Soc. Lond. A 291(1425), 159–166 (1966)

  21. J. R. Melcher, G. I. Taylor, Electrohydrodynamics: a review of role of interfacial shear stresses. Annu. Rev. Fluid Mech. 1(1), 111–146 (1969)

    ADS  Google Scholar 

  22. O. Ozen, N. Aubry, D.T. Papageorgiou, P.G. Petropoulos, Electrohydrodynamic linear stability of two immiscible fluids in channel flow. Electrochim. Acta 51(25), 5316–5323 (2006)

    Google Scholar 

  23. A. K. Uguz, O. Ozen, N. Aubry, Electric field effect on a two-fluid interface instability in channel flow for fast electric times. Phys. Fluids 20(3), 031702 (2008)

    ADS  MATH  Google Scholar 

  24. A. K. Uguz, N. Aubry, Quantifying the linear stability of a flowing electrified two-fluid layer in a channel for fast electric times. Phys. Fluids 20(9), 092103 (2008)

    ADS  MATH  Google Scholar 

  25. S. C. Ozan, A. K. Uguz, Nonlinear evolution of the interface between immiscible fluids in a micro channel subjected to an electric field. Eur. Phys. J. Special Topics 226(6), 1207–1218 (2017)

    ADS  Google Scholar 

  26. S. I. Kaykanat, A. K. Uguz, The linear stability between a Newtonian and a power-law fluid under a normal electric field. J. Nonnewton. Fluid Mech. 277, 104220 (2020)

    MathSciNet  Google Scholar 

  27. M. Firouznia, D. Saintillan, Electrohydrodynamic instabilities in freely suspended viscous films under normal electric fields. Phys. Rev. Fluids 6(10), 103703 (2021)

    ADS  Google Scholar 

  28. N. T. Eldabe, Electrohydrodynamic stability of two superposed elastoviscous liquids in plane couette-flow. J. Math. Phys. 28(11), 2791–2800 (1987)

    ADS  MathSciNet  MATH  Google Scholar 

  29. G. Ersoy, A. K. Uguz, Electro-hydrodynamic instability in a microchannel between a Newtonian and a non-Newtonian liquid. Fluid Dyn. Res. 44(3), 031406 (2012)

    ADS  MathSciNet  MATH  Google Scholar 

  30. P. Eribol, S. I. Kaykanat, S. C. Ozan, A. K. Uguz, Electrohydrodynamic instability between three immiscible fluids in a microchannel: lubrication analysis. Microfluid. Nanofluid. 26(2), 1–26 (2022)

    Google Scholar 

  31. J. D. Zahn, V. Reddy, Two phase micromixing and analysis using electrohydrodynamic instabilities. Microfluid. Nanofluid, 2(5), 399–415 (2006)

    Google Scholar 

  32. R.M. Thaokar, V. Kumaran, Electrohydrodynamic instability of the interface between two fluids confined in a channel. Phys. Fluids 17(8), 084104 (2005)

    ADS  MATH  Google Scholar 

  33. R.V. Craster, O.K. Matar, Electrically induced pattern formation in thin leaky dielectric films. Phys. Fluids 17(3), 032104 (2005)

    ADS  MATH  Google Scholar 

  34. A. Nurocak, A. K. Uguz, Effect of the direction of the electric field on the interfacial instability between a passive fluid and a viscoelastic polymer. Eur. Phys. J. Special Topics 219(1), 99–110 (2013)

    ADS  Google Scholar 

  35. D. T. Papageorgiou, P. G. Petropoulos, Generation of interfacial instabilities in charged electrified viscous liquid films.J. Eng. Math. 50(2), 223–240 (2004)

    MathSciNet  MATH  Google Scholar 

  36. L. Haiwang, W. Teck Neng, N. Nam-Trung, Electrohydrodynamic and shear-stress interfacial instability of two streaming viscous liquid inside a microchannel for tangential electric fields. Micro Nanosyst. 4(1), 14–24 (2012)

  37. K. Zakaria, H. Kamel, Y. Gamiel, Instability of a viscous liquid sheet under the influence of a tangential electric field. Alex. Eng. J. 61(7), 5169–5181 (2022)

    Google Scholar 

  38. K. Savettaseranee, D.T. Papageorgiou, P.G. Petropoulos, B.S. Tilley, The effect of electric fields on the rupture of thin viscous films by van der Waals forces. Phys. Fluids 15(3), 641–652 (2003)

    ADS  MATH  Google Scholar 

  39. C. J. Petrie, M. M. Denn, Instabilities in polymer processing. AlChe J. 22(2), 209–236 (1976)

    Google Scholar 

  40. S. Y. Chou, L. Zhuang, L. Guo, Lithographically induced self-construction of polymer microstructures for resistless patterning. Appl. Phys. Lett. 75(7), 1004–1006 (1999)

    ADS  Google Scholar 

  41. K. Gautam, P.A.L. Narayana, K. C. Sahu, Linear instability driven by an electric field in two-layer channel flow of Newtonian and Herschel-Bulkley fluids. J. Nonnewton. Fluid Mech. 285, 104400 (2020)

    MathSciNet  Google Scholar 

  42. Z. G. Su, T. F. Li, K. Luo, H. L. Yi, Nonlinear behavior of electrohydrodynamic flow in viscoelastic fluids. Phys. Rev. Fluids 6(9), 093701 (2021)

    ADS  Google Scholar 

  43. S. Moravec, D. Liepsch, Flow investigations in a model of a three-dimensional human artery with Newtonian and non-Newtonian fluids. Biorheology 20(6), 745–759 (1983)

    Google Scholar 

  44. D. Liepsch, S. T. Moravec, Pulsatile flow of non-Newtonian fluid in distensible models of human arteries. 21(4), 571–586 (1984)

    Google Scholar 

  45. H. A. Stone, Introduction to fluid dynamics for microfluidic flows, CMOS Biotechnol. 5–30 (2007)

  46. H. Bruus, Theoretical microfluidics. (Oxford University Press, 2007), p 18

  47. R. Gupta, D.F. Fletcher, B.S. Haynes, Taylor flow in microchannels: a review of experimental and computational work. J. Comput. Multiph. Flows. 2(1), 1–31 (2010)

    Google Scholar 

  48. A. Günther, K. F. Jensen, Multiphase microfluidics: from flow characteristics to chemical and materials synthesis. Lab Chip 6(12), 1487–1503 (2006)

    Google Scholar 

  49. L. E. Johns, R. Narayanan, Interfacial Instability. (Springer Science and Business Media, 2007)

  50. D. T. Papageorgiou, Film flows in the presence of electric fields. Annu. Rev. Fluid Mech. 51, 155–187 (2019)

    ADS  MathSciNet  MATH  Google Scholar 

  51. D. Picchi, I. Barmak, A. Ullmann, N. Brauner, Stability of stratified two-phase channel flows of Newtonian/non-Newtonian shear-thinning fluids. Int. J. Multiph. Flow 99, 111–131 (2018)

    MathSciNet  Google Scholar 

  52. C. Nouar, I. Frigaard, Stability of plane Couette-Poiseuille flow of shear-thinning fluid. Phys. Fluids 21(6), 064104 (2009)

    ADS  MATH  Google Scholar 

  53. K. C. Sahu, P. Valluri, P. D. M. Spelt, O. K. Matar, Linear instability of pressure-driven channel flow of a Newtonian and a Herschel-Bulkley fluid. Phys. Fluids 19(12), 122101 (2007)

    ADS  MATH  Google Scholar 

  54. W. Guo, G. Labrosse, R. Narayanan, The application of the Chebyshev-spectral method in transport phenomena. (Springer Science & Business Media, 2013)

  55. X. S. Jiang, L. H. Qi, J. Luo, X. H. Zeng, Influences of disturbance frequency on the droplet generation for microdroplet deposition manufacture. Proc. Inst. Mech. Eng. B J. Eng. Manufact. 223(12), 1529–1539 (2009)

  56. C. S. Yih, Instability due to viscosity stratification. J. Fluid Mech. 27(2), 337–352 (1967)

    ADS  MATH  Google Scholar 

Download references

Acknowledgements

We acknowledge financial support provided by TÜBİTAK through project No. 116M374.

Author information

Authors and Affiliations

  1. Department of Chemical Engineering, Boğaziçi University, Istanbul, 34342, Turkey

    S. Ilke Kaykanat & A. Kerem Uguz

Authors
  1. S. Ilke Kaykanat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Kerem Uguz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to S. Ilke Kaykanat or A. Kerem Uguz.

Additional information

IMA10 - Interfacial Fluid Dynamics and Processes. Guest editors: Rodica Borcia, Sebastian Popescu, Ion Dan Borcia.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kaykanat, S.I., Uguz, A.K. Effect of parallel electric field on the linear stability between a Newtonian and a power-law fluid in a microchannel. Eur. Phys. J. Spec. Top. 232, 385–394 (2023). https://doi.org/10.1140/epjs/s11734-023-00788-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjs/s11734-023-00788-7

Search

Navigation