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Onset of thin film meniscus along a fibre

  • Shuo Guo (a1), Xianmin Xu (a2), Tiezheng Qian (a3), Yana Di (a2), Masao Doi (a4) and Penger Tong (a1)...


The dynamics of spreading of a macroscopic liquid droplet over a wetting surface is often described by a power-law relaxation, namely, the droplet radius increases as $t^{m}$ for time $t$ , which is known as Tanner’s law. Here we show, by both experiments and theory, that when the liquid spreading takes place between a thin soap film and a glass fibre penetrating the film, the spreading is significantly slowed down. When the film thickness $\ell$ becomes smaller than the fibre diameter $d$ , the strong hydrodynamic confinement effect of the soap film gives rise to a logarithmic relaxation with fibre creeping time $t$ . Such a slow dynamics of spreading is observed for hours both in the measured time-dependent height of capillary rise $h(t)$ on the fibre surface and viscous friction coefficient $\unicode[STIX]{x1D709}_{s}(t)$ felt by the glass fibre in contact with the soap film. A new theoretical approach based on the Onsager variational principle is developed to describe the dynamics of thin film spreading along a fibre. The newly derived equations of motion provide the analytical solutions of $h(t)$ and contact angle $\unicode[STIX]{x1D703}(t)$ , which are found to be in good agreement with the experimental results. Our work thus provides a common framework for understanding the confinement effect of thin soap films on the dynamics of spreading along a fibre.


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Bonn, D., Eggers, J., Indekeu, J., Meunier, J. & Rolley, E. 2009 Wetting and spreading. Rev. Mod. Phys. 81, 739805.10.1103/RevModPhys.81.739
Clanet, C. & Quéré, D. 2002 Onset of menisci. J. Fluid Mech. 460, 131149.10.1017/S002211200200808X
Decker, E. L. & Garoff, S. 1997 Contact angle hysteresis: the need for new theoretical and experimental models. J. Adhes. 63, 159185.
de Gennes, P. G., Brochard-Wyart, F. & Quéré, D. 2004 Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. Springer.10.1007/978-0-387-21656-0
de Gennes, P. G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827863.10.1103/RevModPhys.57.827
Di, Y., Xu, X. & Doi, M. 2016 Theoretical analysis for meniscus rise of a liquid contained between a flexible film and a solid wall. Europhys. Lett. 113, 36001.10.1209/0295-5075/113/36001
Doi, M. 2011 Onsager’s variational principle in soft matter. J. Phys.: Condens. Matter 23, 284118.
Doi, M. 2013 Soft Matter Physics. Oxfort University Press.10.1093/acprof:oso/9780199652952.001.0001
Doi, M. 2015 Onsager principle as a tool for approximation. Chin. Phys. B 24, 020505.
Dussan, E. B. V. & Davis, S. H. J. 1974 On the motion of a fluid–fluid interface along a solid surface. Fluid Mech. 65, 7195.10.1017/S0022112074001261
Guan, D., Wang, Y. J., Charlaix, E. & Tong, P. 2016a Asymmetric and speed-dependent capillary force hysteresis and relaxation of a suddenly stopped moving contact line. Phys. Rev. Lett. 116, 066102.10.1103/PhysRevLett.116.066102
Guan, D., Wang, Y. J., Charlaix, E. & Tong, P. 2016b Simultaneous observation of asymmetric speed-dependent contact force hysteresis and slow relaxation of a suddenly stopped moving contact line. Phys. Rev. E 94, 042802.
Guo, S., Gao, M., Xiong, X., Wang, Y., Wang, X., Sheng, P. & Tong, P. 2013 Direct measurement of friction of a fluctuating contact line. Phys. Rev. Lett. 111, 026101.10.1103/PhysRevLett.111.026101
Guo, S., Lee, C. H., Sheng, P. & Tong, P. 2015 Measurement of contact-line dissipation in a nanometer-thin soap film. Phys. Rev. E 91, 012404.
Guo, S., Xiong, X., Xu, Z., Sheng, P. & Tong, P. 2014 Measurement of the friction coefficient of a fluctuating contact line using an AFM-based dual-mode mechanical resonator. Chin. Phys. B 23, 116802.
Huibers, P. D. T. & Shah, D. O. 1997 Multispectral determination of soap film thickness. Langmuir 13, 59955998.10.1021/la960738n
James, D. 1974 The meniscus on the outside of a small circular cylinder. J. Fluid Mech. 63 (4), 657664.10.1017/S0022112074002126
Kaz, D. M., McGorty, R., Mani, M., Brenner, M. P. & Manoharan, V. N. 2012 Physical ageing of the contact line on colloidal particles at liquid interfaces. Nat. Mater. 11 (2), 138142.10.1038/nmat3190
Landau, L. D. & Lifshitz, E. M. 1986 Fluid Mechanics, 2nd edn. Butterworth-Heinemann.
Leger, L. & Joanny, J.-F. 1992 Liquid spreading. Rep. Prog. Phys. 55, 431486.10.1088/0034-4885/55/4/001
Lo, L. 1983 The meniscus on a needle – a lesson in matching. J. Fluid Mech. 132, 6578.10.1017/S0022112083001470
Ma, H., Jimenez, J. & Rajagopalan, R. 2000 Brownian fluctuation spectroscopy using atomic force microscopes. Langmuir 16, 22542261.10.1021/la991059q
Man, X. & Doi, M. 2016 Ring to mountain transition in deposition pattern of drying droplets. Phys. Rev. Lett. 116, 066101.10.1103/PhysRevLett.116.066101
Pagonabarraga, I. 2012 Adsorbed colloids relax slowly. Nat. Mater. 11 (2), 99100.10.1038/nmat3235
Poulin, P., Nallet, F., Cabane, B. & Bibette, J. 2015 Evidence for Newton black films between adhesive emulsion droplets. Phys. Rev. Lett. 77, 32483251.10.1103/PhysRevLett.77.3248
Quéré, D., Di Meglio, J. & Brochard-Wyart, F. 1988 Wetting of fibers: theory and experiments. Rev. Phys. Appl. 23, 10231030.10.1051/rphysap:019880023060102300
Quéré, D. 2008 Wetting and roughness. Annu. Rev. Mater. Res. 38, 7199.10.1146/annurev.matsci.38.060407.132434
Ramiasa, M., Ralston, J., Fetzer, R. & Sedev, R. 2014 The influence of topography on dynamic wetting. Adv. Colloid Interface Sci. 206, 275293.10.1016/j.cis.2013.04.005
Reif, F. 1985 Fundamentals of Statistical and Thermal Physics. McGraw-Hill.
Snoeijer, J. H. & Andreotti, B. 2013 Moving contact lines: scales, regimes, and dynamical transitions. Annu. Rev. Fluid Mech. 45, 269292.10.1146/annurev-fluid-011212-140734
Tanner, L. H. 1979 The spreading of silicone oil drops on horizontal surfaces. J. Phys. D: Appl. Phys. 12, 14731484.10.1088/0022-3727/12/9/009
Wang, Y.-J., Guo, S., Chen, H.-Y. & Tong, P. 2016 Understanding contact angle hysteresis on an ambient solid surface. Phys. Rev. E 93, 052802.
Xiong, X., Guo, S., Xu, Z., Sheng, P. & Tong, P. 2009 Development of an atomic-force-microscope-based hanging-fiber rheometer for interfacial microrheology. Phys. Rev. E 80, 061604.
Xu, X., Di, Y. & Doi, M. 2016 Variational method for liquids moving on a substrate. Phys. Fluids 28, 087101.10.1063/1.4959227
Yazdanpanah, M. M., Hosseini, M., Pabba, S., Berry, S. M., Dobrokhotov, V. V., Safir, A., Keynton, R. S. & Cohn, R. W. 2008 Micro-Wilhelmy and related liquid property measurements using constant-diameter nanoneedle-tipped atomic force microscope probes. Langmuir 24, 1375313764.10.1021/la802820u
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