Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-06-05T22:29:28.767Z Has data issue: false hasContentIssue false
  • English
  • Français

AC electrohydrodynamic instabilities in thin liquid films

Published online by Cambridge University Press:  17 July 2009

SCOTT A. ROBERTS  and
SATISH KUMAR
SCOTT A. ROBERTS
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
SATISH KUMAR*
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
*
†Email address for correspondence: kumar@cems.umn.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

When DC electric fields are applied to a thin liquid film, the interface may become unstable and form a series of pillars. In this paper, we apply lubrication theory to examine the possibility of using AC electric fields to exert further control over the size and shape of the pillars. For perfect dielectric films, linear stability analysis shows that the influence of an AC field can be understood by considering an effective DC field. For leaky dielectric films, Floquet theory is applied to carry out the linear stability analysis, and it reveals that high frequencies may be used to inhibit the accumulation of interfacial free charge, leading to a lowering of growth rates and wavenumbers. Nonlinear simulations confirm the results of the linear stability analysis while also uncovering additional mechanisms for tuning overall pillar height and width. The results presented here may be of interest for the controlled creation of surface topographical features in applications such as patterned coatings and microelectronics.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 631 , 25 July 2009 , pp. 255 - 279
Copyright
Copyright © Cambridge University Press 2009

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

Assender, H., Bliznyuk, V. & Porfyrakis, K. 2002 How surface topography relates to materials' properties. Science 297 (5583), 973–976.CrossRefGoogle ScholarPubMed
Bandyopadhyay, D. & Sharma, A. 2007 Electric field induced instabilities in thin confined bilayers. J. Colloid Interface Sci. 311 (2), 595–608.CrossRefGoogle ScholarPubMed
Benjamin, T. B. & Ursell, F. 1954 The stability of the plane free surface of a liquid in vertical periodic motion. Proc. R. Soc. London, Ser. A 225, 505–515.Google Scholar
Brenan, K. E., Campbell, S. L. V. & Petzold, L. R. 1996 Numerical Solution of Initial Value Problems in Differential-Algebraic Equations. SIAM Classics Series.CrossRefGoogle Scholar
Briskman, V. A. & Shaidurov, G. F. 1968 Parametric instability of a fluid surface in an alternating electric field. Dokl. Akad. Nauk 13 (6), 540–542.Google Scholar
Chou, S. Y. & Zhuang, L. 1999 Lithographically induced self-assembly of periodic polymer micropillar arrays. J. Vac. Sci. Technol., B 17 (6), 3197–3202.CrossRefGoogle Scholar
Chou, S. Y., Zhuang, L. & Guo, L. 1999 Lithographically induced self-construction of polymer microstructures for resistless patterning. Appl. Phys. Lett. 75 (7), 1004–1006.CrossRefGoogle Scholar
Conti, M., Donati, G., Cianciolo, G., Stefoni, S. & Samor, B. 2002 Force spectroscopy study of the adhesion of plasma proteins to the surface of a dialysis membrane: role of the nanoscale surface hydrophobicity and topography. J. Biomed. Mater. Res. 61 (3), 370–379.CrossRefGoogle Scholar
Craster, R. V. & Matar, O. K. 2005 Electrically induced pattern formation in thin leaky dielectric films. Phys. Fluids 17 (3), 032104.CrossRefGoogle Scholar
Curtis, A. & Wilkinson, C. 1997 Topographical control of cells. Biomaterials 18 (24), 1573–1583.CrossRefGoogle ScholarPubMed
DeAro, J. A., Weston, K. D., Buratto, S. K. & Lemmer, U. 1997 Mesoscale optical properties of conjugated polymers probed by near-field scanning optical microscopy. Chem. Phys. Lett. 277 (5–6), 532–538.CrossRefGoogle Scholar
delCampo, A., Lvarez, I., Filipe, S. & Wilhelm, M. 2007 3D microstructured surfaces obtained by soft-lithography using fast-crosslinking elastomeric precursors and 2d masters. Adv. Funct. Mater. 17 (17), 3590–3597.CrossRefGoogle Scholar
Deshpande, P., Pease, L. F., Chen, L., Chou, S. Y. & Russel, W. B. 2004 Cylindrically symmetric electrohydrodynamic patterning. Phys. Rev. E 70 (4), 041601.CrossRefGoogle ScholarPubMed
Devitt, E. B. & Melcher, J. R. 1965 Surface electrohydrodynamics with high-frequency fields. Phys. Fluids 8 (6), 1193–1195.CrossRefGoogle Scholar
Dickey, M. D., Gupta, S., Leach, K. A., Collister, E., Willson, C. G. & Russell, T. P. 2006 Novel 3-d structures in polymer films by coupling external and internal fields. Langmuir 22 (9), 4315–4318.CrossRefGoogle ScholarPubMed
Dickey, M., Raines, A., Collister, E., Bonnecaze, R., Sreenivasan, S. & Willson, C. 2007 High-aspect ratio polymeric pillar arrays formed via electrohydrodynamic patterning. J. Mater. Sci. 43 (1), 117–122.CrossRefGoogle Scholar
Edwards, W. S. & Fauve, S. 1994 Patterns and quasi-patterns in the faraday experiment. J. Fluid Mech. 278, 123–148.CrossRefGoogle Scholar
Faraday, M. 1831 On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Phil. Trans. R. Soc. Lond. 121, 299–340.Google Scholar
González, H., Castellanos, A., Barrero, A. & McCluskey, F. M. J. 1989 Stabilization of dielectric liquid bridges by electric fields in the absence of gravity. J. Fluid Mech. 206, 545–561.CrossRefGoogle Scholar
González, H., Garcia, F. J. & Castellanos, A. 2003 Stability analysis of conducting jets under ac radial electric fields for arbitrary viscosity. Phys. Fluids 15 (2), 395–407.CrossRefGoogle Scholar
González, H., Ramos, A. & Castellanos, A. 1997 Parametric instability of dielectric, slightly viscous liquid jets under ac electric fields. Phys. Fluids 9 (6), 1830–1837.CrossRefGoogle Scholar
González, H., Ramos, A. & Castellanos, A. 1999 Parametric instability of conducting, slightly viscous liquid jets under periodic electric fields. J. Electrostat. 47 (1–2), 27–38.CrossRefGoogle Scholar
Harrison, C., Stafford, C. M., Zhang, W. & Karim, A. 2004 Sinusoidal phase grating created by a tunably buckled surface. Appl. Phys. Lett. 85 (18), 4016–4018.CrossRefGoogle Scholar
Kim, D. & Lu, W. 2006 Three-dimensional model of electrostatically induced pattern formation in thin polymer films. Phys. Rev. B 73 (3), 035206.CrossRefGoogle Scholar
Kumar, K. & Bajaj, K. M. S. 1995 Competing patterns in the Faraday experiment. Phys. Rev. E 52 (5), R4606–R4609.CrossRefGoogle ScholarPubMed
Leach, K. A., Gupta, S., Dickey, M. D., Willson, C. G. & Russell, T. P. 2005 Electric field and dewetting induced hierarchical structure formation in polymer/polymer/air trilayers. Chaos 15 (4), 047506.CrossRefGoogle ScholarPubMed
Lee, B. S., Cho, H.-J., Lee, J.-G., Huh, N., Choi, J.-W. & Kang, I. S. 2006 a Drop formation via breakup of a liquid bridge in an ac electric field. J. Colloid Interface Sci. 302 (1), 294–307.CrossRefGoogle Scholar
Lee, S. H., Kim, P., Jeong, H. E. & Suh, K. Y. 2006 b Electrically induced formation of uncapped, hollow polymeric microstructures. J. Micromech. Microengng 16 (11), 2292–2297.CrossRefGoogle Scholar
Lei, X., Wu, L., Deshpande, P., Yu, Z., Wu, W., Ge, H. & Chou, S. Y. 2003 100 nm period gratings produced by lithographically induced self-construction. Nanotechnology 14 (7), 786–790.CrossRefGoogle Scholar
Lin, Z., Kerle, T., Baker, S. M., Hoagland, D. A., Schaffer, E., Steiner, U. & Russell, T. P. 2001 Electric field induced instabilities at liquid/liquid interfaces. J. Chem. Phys. 114 (5), 2377–2381.CrossRefGoogle Scholar
Lin, Z., Kerle, T., Russell, T. P., Schaffer, E. & Steiner, U. 2002 Structure formation at the interface of liquid/liquid bilayer in electric field. Macromolecules 35 (10), 3971–3976.CrossRefGoogle Scholar
Melcher, J. R. & Smith, C. V. 1969 Electrohydrodynamic charge relaxation and interfacial perpendicular-field instability. Phys. Fluids 12 (4), 778–790.CrossRefGoogle Scholar
Melcher, J. R. & Warren, E. P. 1966 Continuum feedback control of a Rayleigh–Taylor type instability. Phys. Fluids 9 (11), 2085–2094.CrossRefGoogle Scholar
Morariu, M. D., Voicu, N. E., Schaffer, E., Lin, Z., Russell, T. P. & Steiner, U. 2003 Hierarchical structure formation and pattern replication induced by an electric field. Nat. Mater. 2 (1), 48–52.CrossRefGoogle ScholarPubMed
Nabetani, Y., Yamasaki, M., Miura, A. & Tamai, N. 2001 Fluorescence dynamics and morphology of electroluminescent polymer in small domains by time-resolved SNOM. Thin Solid Films 393 (1–2), 329–333.CrossRefGoogle Scholar
Pease, L. F. & Russel, W. B. 2002 Linear stability analysis of thin leaky dielectric films subjected to electric fields. J. Non-Newtonian Fluid Mech. 102 (2), 233–250.CrossRefGoogle Scholar
Pease, L. F. & Russel, W. B. 2003 Electrostatically induced submicron patterning of thin perfect and leaky dielectric films: a generalized linear stability analysis. J. Chem. Phys. 118 (8), 3790–3803.CrossRefGoogle Scholar
Pease, L. F. & Russel, W. B. 2004 Limitations on length scales for electrostatically induced submicrometer pillars and holes. Langmuir 20 (3), 795–804.CrossRefGoogle ScholarPubMed
Pease, L. F. & Russel, W. B. 2006 Charge driven, electrohydrodynamic patterning of thin films. J. Chem. Phys. 125 (18), 184716.CrossRefGoogle ScholarPubMed
Ranucci, C. S. & Moghe, P. V. 2001 Substrate microtopography can enhance cell adhesive and migratory responsiveness to matrix ligand density. J. Biomed. Mater. Res. 54 (2), 149–161.3.0.CO;2-O>CrossRefGoogle ScholarPubMed
Reynolds, J. M. 1965 Stability of an electrostatically supported fluid column. Phys. Fluids 8 (1), 161–170.CrossRefGoogle Scholar
Roberts, S. A. 2009 Stability of microscale fluid interfaces: a study of fluid flows near soft substrates and pattern formation under electrostatic fields. PhD thesis, University of Minnesota (in preparation).Google Scholar
Robinson, J. A., Bergougnou, M. A., Cairns, W. L., Castle, G. S. P. & Inculet, I. I. 2000 Breakdown of air over a water surface stressed by a perpendicular alternating electric field, in the presence of a dielectric barrier. IEEE Trans. Ind. Appl. 36 (1), 68–75.CrossRefGoogle Scholar
Robinson, J. A., Bergougnou, M. A., Castle, G. S. P. & Inculet, I. I. 2001 The electric field at a water surface stressed by an AC voltage. IEEE Trans. Ind. Appl. 37 (3), 735–742.CrossRefGoogle Scholar
Robinson, J. A., Bergougnou, M. A., Castle, G. S. P. & Inculet, I. I. 2002 A nonlinear model of AC-field-induced parametric waves on a water surface. IEEE Trans. Ind. Appl. 38 (2), 379–388.CrossRefGoogle Scholar
Russel, W. B., Saville, D. A. & Schowalter, W. R. 1989 Colloidal Dispersions. Cambridge University Press.CrossRefGoogle Scholar
Sato, M. 1984 The production of essentially uniform-sized liquid droplets in gaseous or immiscible liquid media under applied A.C. potential. J. Electrostat. 15 (2), 237–247.CrossRefGoogle Scholar
Saville, D. A. 1997 Electrohydrodynamics: the Taylor–Melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29 (1), 27–64.CrossRefGoogle Scholar
Schäffer, E., Thurn-Albrecht, T., Russell, T. P. & Steiner, U. 2000 Electrically induced structure formation and pattern transfer. Nature 403 (6772), 874–877.CrossRefGoogle ScholarPubMed
Schäffer, E., Thurn-Albrecht, T., Russell, T. P. & Steiner, U. 2001 Electrohydrodynamic instabilities in polymer films. Europhys. Lett. 53 (4), 518–524.CrossRefGoogle Scholar
Shankar, V. & Sharma, A. 2004 Instability of the interface between thin fluid films subjected to electric fields. J. Colloid Interface Sci. 274 (1), 294–308.CrossRefGoogle ScholarPubMed
Taylor, G. I. & McEwan, A. D. 1965 The stability of a horizontal fluid interface in a vertical electric field. J. Fluid Mech. 22 (1), 1–15.CrossRefGoogle Scholar
Thaokar, R. M. & Kumaran, V. 2005 Electrohydrodynamic instability of the interface between two fluids confined in a channel. Phys. Fluids 17 (8), 084104.CrossRefGoogle Scholar
Topaz, C. M., Porter, J. & Silber, M. 2004 Multifrequency control of faraday wave patterns. Phys. Rev. E 70 (6), 066206.CrossRefGoogle ScholarPubMed
Tsai, I. Y., Kimura, M., Stockton, R., Green, J. A., Puig, R., Jacobson, B. & Russell, T. P. 2004 Fibroblast adhesion to micro- and nano-heterogeneous topography using diblock copolymers and homopolymers. J. Biomed. Mater. Res. A 71A (3), 462–469.CrossRefGoogle Scholar
Verma, R., Sharma, A., Kargupta, K. & Bhaumik, J. 2005 Electric field induced instability and pattern formation in thin liquid films. Langmuir 21 (8), 3710–3721.CrossRefGoogle ScholarPubMed
Voicu, N. E., Harkema, S. & Steiner, U. 2006 Electric-field-induced pattern morphologies in thin liquid films. Adv. Funct. Mater. 16 (7), 926–934.CrossRefGoogle Scholar
Voicu, N. E., Saifullah, M. S. M., Subramanian, K. R. V., Welland, M. E. & Steiner, U. 2007 TiO2 patterning using electro-hydrodynamic lithography. Soft Matter. 3, 554–557.CrossRefGoogle ScholarPubMed
Wu, L. & Chou, S. Y. 2003 Dynamic modelling and scaling of nanostructure formation in the lithographically induced self-assembly and self-construction. Appl. Phys. Lett. 82 (19), 3200–3202.CrossRefGoogle Scholar
Wu, N., Pease, L. F. & Russel, W. B. 2005 Electric-field-induced patterns in thin polymer films: weakly nonlinear and fully nonlinear evolution. Langmuir 21 (26), 12290–12302.CrossRefGoogle ScholarPubMed
Wu, N. & Russel, W. B. 2005 Dynamics of the formation of polymeric microstructures induced by electrohydrodynamic instability. Appl. Phys. Lett. 86 (24), 241912.CrossRefGoogle Scholar
Yeo, L. Y., Lastochkin, D., Wang, S.-C. & Chang, H.-C. 2004 A new AC electrospray mechanism by Maxwell–Wagner polarization and capillary resonance. Phys. Rev. Lett. 92 (13), 133902.CrossRefGoogle ScholarPubMed
Yih, C.-S. 1968 Stability of a horizontal fluid interface in a periodic vertical electric field. Phys. Fluids 11 (7), 1447–1449.CrossRefGoogle Scholar