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Spin coating of capillary tubes

Published online by Cambridge University Press:  20 January 2020

B. K. Primkulov
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, CambridgeMA 02139, USA
A. A. Pahlavan
Mechanical and Aerospace Engineering Department, Princeton University, Olden St., PrincetonNJ08544, USA
L. Bourouiba
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, CambridgeMA 02139, USA
J. W. M. Bush
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, CambridgeMA 02139, USA
R. Juanes*
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, CambridgeMA 02139, USA
Email address for correspondence:


We present the results of a combined experimental and theoretical study of the spin coating of the inner surface of capillary tubes with viscous liquids, and the modified Rayleigh–Plateau instability that arises when the spinning stops. We show that during the spin coating, the thinning of the film is governed by the balance of viscous and centrifugal forces, resulting in the film thickness scaling as $h\sim t^{-1/2}$. We demonstrate that the method enables us to reach uniform micrometre-scale films on the tube walls. Finally, we discuss potential applications with curable polymers that enable precise control of film geometry and wettability.

JFM Papers
© The Author(s), 2020. Published by Cambridge University Press

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Aussillous, P. & Quéré, D. 2000 Quick deposition of a fluid on the wall of a tube. Phys. Fluids 12 (10), 23672371.CrossRefGoogle Scholar
Bico, J. & Quéré, D. 2001 Falling slugs. J. Colloid Interface Sci. 243 (1), 262264.CrossRefGoogle Scholar
Blunt, M. J. 2001 Flow in porous media pore-network models and multiphase flow. Curr. Opin. Colloid Interface Sci. 6 (3), 197207.CrossRefGoogle Scholar
Bretherton, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10 (02), 166188.CrossRefGoogle Scholar
Cheng, H. 2007 Advanced Analytic Methods in Applied Mathematics, Science, and Engineering. LuBan Press.Google Scholar
Duclaux, V., Clanet, C. & Quéré, D. 2006 The effects of gravity on the capillary instability in tubes. J. Fluid Mech. 556, 217226.CrossRefGoogle Scholar
Eggers, J. & Villermaux, E. 2008 Physics of liquid jets. Rep. Prog. Phys. 71 (3), 036601.CrossRefGoogle Scholar
Emslie, A. G., Bonner, F. T. & Peck, L. G. 1958 Flow of a viscous liquid on a rotating disk. J. Appl. Phys. 29 (5), 858862.CrossRefGoogle Scholar
de Gennes, P.-G., Brochard-Wyart, F. & Quéré, D. 2004 Capillarity and Wetting Phenomena. Springer Science & Business Media.CrossRefGoogle Scholar
Goldsmith, H. L. & Spain, S. 1984 Margination of leukocytes in blood flow through small tubes. Microvasc. Res. 27 (2), 204222.CrossRefGoogle ScholarPubMed
Goren, S. L. 1962 The instability of an annular thread of fluid. J. Fluid Mech. 12 (02), 309319.CrossRefGoogle Scholar
Hoffman, R. L. 1975 A study of the advancing interface. I. Interface shape in liquid–gas systems. J. Colloid Interface Sci. 50 (2), 228241.CrossRefGoogle Scholar
Johnson, M., Kamm, R. D., Ho, L. W., Shapiro, A. & Pedley, T. J. 1991 The nonlinear growth of surface-tension-driven instabilities of a thin annular film. J. Fluid Mech. 233, 141156.CrossRefGoogle Scholar
Li, Z., Mak, S. Y., Sauret, A. & Shum, H. C. 2014 Syringe-pump-induced fluctuation in all-aqueous microfluidic system implications for flow rate accuracy. Lab on a Chip 14 (4), 744749.CrossRefGoogle ScholarPubMed
Morrow, N. R. & Mason, G. 2001 Recovery of oil by spontaneous imbibition. Curr. Opin. Colloid Interface Sci. 6 (4), 321337.CrossRefGoogle Scholar
Mugele, F. & Baret, J.-C. 2005 Electrowetting: from basics to applications. J. Phys.: Condens. Matter 17 (28), R705R774.Google Scholar
Odier, C., Levaché, B., Santanach-Carreras, E. & Bartolo, D. 2017 Forced imbibition in porous media: a fourfold scenario. Phys. Rev. Lett. 119 (20), 208005.CrossRefGoogle ScholarPubMed
Patzek, T. W. & Kristensen, J. G. 2001 Shape factor correlations of hydraulic conductance in noncircular capillaries: II. Two-phase creeping flow. J. Colloid Interface Sci. 236 (2), 305317.CrossRefGoogle Scholar
Plateau, J. 1873 Statique Expérimentale et Théorique des Liquides Soumis aux Seules Forces Moléculaires. Gauthier-Villars.Google Scholar
Pries, A. R., Neuhaus, D. & Gaehtgens, P. 1992 Blood viscosity in tube flow: dependence on diameter and hematocrit. Am. J. Phys. 263, H1770H1778.Google ScholarPubMed
Rayleigh, R. S. 1892 On the instability of cylindrical fluid surfaces. Phil. Mag. J. Sci. 34, 177180.CrossRefGoogle Scholar
Rossen, W. R. 2000 Snap-off in constricted tubes and porous media. Colloids Surf. A 166 (1-3), 101107.CrossRefGoogle Scholar
Scriven, L. E. 1988 Physics and applications of dip coating and spin coating. MRS Proc. 121, 717729.CrossRefGoogle Scholar
Taylor, G. I. 1961 Deposition of a viscous fluid on the wall of a tube. J. Fluid Mech. 10 (02), 161165.CrossRefGoogle Scholar
Walls, P. L. L., Dequidt, G. & Bird, J. C. 2016 Capillary displacement of viscous liquids. Langmuir 32 (13), 31863190.CrossRefGoogle ScholarPubMed
Washburn, E. W. 1921 The dynamics of capillary flow. Phys. Rev. 17 (3), 273283.CrossRefGoogle Scholar
Zeng, W., Jacobi, I., Beck, D. J., Li, S. & Stone, H. A. 2015 Characterization of syringe-pump-driven induced pressure fluctuations in elastic microchannels. Lab on a Chip 15 (4), 11101115.CrossRefGoogle ScholarPubMed
Zhao, B., Alizadeh Pahlavan, A., Cueto-Felgueroso, L. & Juanes, R. 2018 Forced wetting transition and bubble pinch-off in a capillary tube. Phys. Rev. Lett. 120 (8), 084501.CrossRefGoogle Scholar
Zhao, B., MacMinn, C. W. & Juanes, R. 2016 Wettability control on multiphase flow in patterned microfluidics. Proc. Natl Acad. Sci. USA 113 (37), 1025110256.CrossRefGoogle ScholarPubMed

Primkulov et al. supplementary movie 1

Video shows the viscous slug motion inside spinning capillary tubes. The capillary tubes are placed into slots 2, 4, 7, and 12. Orange liquid slugs are placed near the inner end of the tubes. As the system is spun, the slugs move outwards, depositing a film on the inner walls. Therefore, the length of the slugs diminishes as they move outwards.

Download Primkulov et al. supplementary movie 1(Video)
Video 23 MB

Primkulov et al. supplementary movie 2

Video shows the modified Rayleigh-Plateau instability of the micron-scale films that are generated with the spin-coating method. The timescale of the instability is uniform throughout the tube, which points at the uniform thickness of the film considering FIG.4(d).

Download Primkulov et al. supplementary movie 2(Video)
Video 126 KB