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Three-dimensional backflow at liquid–gas interface induced by surfactant

Published online by Cambridge University Press:  15 July 2020

Hongyuan Li Open the ORCID record for Hongyuan Li [Opens in a new window] ,
Zexiang Li ,
Xiangkui Tan ,
Xiangyu Wang ,
Shenglin Huang Open the ORCID record for Shenglin Huang [Opens in a new window] ,
Yaolei Xiang ,
Pengyu Lv  and
Huiling Duan Open the ORCID record for Huiling Duan [Opens in a new window]
Hongyuan Li
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, BIC-ESAT, College of Engineering, Peking University, Beijing100871, PR China
Zexiang Li
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, BIC-ESAT, College of Engineering, Peking University, Beijing100871, PR China
Xiangkui Tan
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, BIC-ESAT, College of Engineering, Peking University, Beijing100871, PR China
Xiangyu Wang
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, BIC-ESAT, College of Engineering, Peking University, Beijing100871, PR China
Shenglin Huang
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, BIC-ESAT, College of Engineering, Peking University, Beijing100871, PR China
Yaolei Xiang
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, BIC-ESAT, College of Engineering, Peking University, Beijing100871, PR China
Pengyu Lv*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, BIC-ESAT, College of Engineering, Peking University, Beijing100871, PR China
Huiling Duan*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, BIC-ESAT, College of Engineering, Peking University, Beijing100871, PR China CAPT, HEDPS and IFSA Collaborative Innovation Center of MoE, Peking University, Beijing100871, PR China
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

A liquid–gas interface (LGI) on submerged microstructure surfaces has the potential to achieve large slip velocities, which is significant for underwater applications such as drag reduction. However, surfactants adsorbing on the LGI can cause surface tension gradient against the mainstream, which weakens the flow near the LGI and severely limits drag reduction. The mechanism of the effect of surfactants on two-dimensional flows has already been proposed, while the effect of surfactants on the three-dimensional flow near the LGI is still not clear. In our study, we specifically design an experimental system to directly observe a three-dimensional backflow at the LGI. The formation as well as the behaviour of the backflow are demonstrated to be significantly influenced by the surfactant. Combining experimental measurements, theoretical analyses and numerical simulations, we reveal the underlying mechanism of the backflow, which is a competition between the mainstream and the Marangoni flows generated by the interfacial concentration gradients of surfactant simultaneously in streamwise and spanwise directions, reflecting the three-dimensional feature of the backflow. In addition, a kinematic similarity is obtained to characterize the backflow. The current work provides a model system for investigating the three-dimensional backflow at the LGI with surfactants, which is significant for practical applications such as drag reduction and superhydrophobicity.

JFM classification

Convection: Marangoni convection Interfacial Flows (free surface): Capillary flows Micro-/Nano-fluid dynamics: Microfluidics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 899 , 25 September 2020 , A8
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Adrian, R. J. & Westerweel, J. 2010 Particle Image Velocimetry. Cambridge University Press.Google Scholar
Alharbi, A. Y. & Sick, V. 2010 Investigation of boundary layers in internal combustion engines using a hybrid algorithm of high speed micro-PIV and PTV. Exp. Fluids 49, 949–959.CrossRefGoogle Scholar
Bolognesi, G., Cottin-Bizonne, C. & Pirat, C. 2014 Evidence of slippage breakdown for a superhydrophobic microchannel. Phys. Fluids 26, 082004.CrossRefGoogle Scholar
Brinded, K. A., Tiller, P. R. & Lane, S. J. 1993 Triton X-100 as a reference compound for ammonia high-resolution chemical ionization mass spectrometry and as a tuning and calibration compound for thermospray. Rapid Commun. Mass Sp. 7, 1059–1061.CrossRefGoogle Scholar
Chang, C. H. & Franses, E. I. 1995 Adsorption dynamics of surfactants at the air/water interface: a critical review of mathematical models, data, and mechanisms. Colloids Surf. A 100, 1–45.CrossRefGoogle Scholar
Choi, C. H. & Kim, C. J. 2006 Large slip of aqueous liquid flow over a nanoengineered superhydrophobic surface. Phys. Rev. Lett. 96, 066001.CrossRefGoogle Scholar
Crowdy, D. G. 2016 Analytical formulae for longitudinal slip lengths over unidirectional superhydrophobic surfaces with curved menisci. J. Fluid Mech. 791, R7.CrossRefGoogle Scholar
Diddens, C., Tan, H. S., Lv, P. Y., Versluis, M., Kuerten, J. G. M., Zhang, X. H & Lohse, D. 2017 Evaporating pure, binary and ternary droplets: thermal effects and axial symmetry breaking. J. Fluid Mech. 823, 470–497.CrossRefGoogle Scholar
Dong, J., Chen, S., Corti, D. S., Franses, E. I., Zhao, Y., Ng, H. T. & Hanson, E. 2011 Effect of Triton X-100 on the stability of aqueous dispersions of copper phthalocyanine pigment nanoparticles. Rapid Commun. Mass Sp. 362, 33–41.Google ScholarPubMed
Eckmann, D. M. & Cavanagh, D. P. 2003 Bubble detachment by diffusion-controlled surfactant adsorption. Colloids Surf. A 227, 21–33.CrossRefGoogle Scholar
Fainerman, V. B., Lylyk, S. V., Aksenenko, E. V., Liggieri, L., Makievski, A. V., Petkov, J. T. & Miller, R. 2009 Adsorption layer characteristics of Triton surfactants. Part 2. Dynamic surface tension and adsorption. Colloids Surf. A 334, 8–15.CrossRefGoogle Scholar
Hourlier-Fargette, A., Antkowiak, A., Chateauminois, A. & Neukirch, S. 2017 Role of uncrosslinked chains in droplets dynamics on silicone elastomers. Soft Matt. 13, 3484–3491.CrossRefGoogle ScholarPubMed
Huang, S., Lv, P. & Duan, H. 2019 Morphology evolution of liquid-gas interface on submerged solid structured surfaces. Extreme. Mech. Lett. 27, 34–51.CrossRefGoogle Scholar
Joseph, P., Cottin-Bizonne, C., Benoit, J. M., Ybert, C., Journet, C., Tabeling, P.& Bocquet, L. 2006 Slippage of water past superhydrophobic carbon nanotube forests in microchannels. Phys. Rev. Lett. 97, 156104.CrossRefGoogle ScholarPubMed
Kähler, C. J., Scholz, U. & Ortmanns, J. 2006 Wall-shear-stress and near-wall turbulence measurements up to single pixel resolution by means of long-distance micro-PIV. Exp. Fluids 41, 327–341.CrossRefGoogle Scholar
Kähler, C. J., Scharnowski, S. & Cierpka, C. 2012 On the uncertainty of digital PIV and PTV near walls. Exp. Fluids 52, 1641–1656.CrossRefGoogle Scholar
Karatay, E., Haase, A. S., Visser, C. W., Sun, C., Lohse, D., Tsai, P. A. & Lammertink, R. G. 2013 Control of slippage with tunable bubble mattresses. Proc. Natl Acad. Sci. USA 110, 8422–8426.CrossRefGoogle ScholarPubMed
Kashaninejad, N., Nguyen, N. T. & Chan, W. K. 2012 Eccentricity effects of microhole arrays on drag reduction efficiency of microchannels with a hydrophobic wall. Phys. Fluids 24, 112004.CrossRefGoogle Scholar
Landel, J. R., Peaudecerf, F. J., Temprano-Coleto, F., Gibou, F., Goldstein, R. E. & Luzzatto-Fegiz, P. 2019 A theory for the slip and drag of superhydrophobic surfaces with surfactant. J. Fluid Mech. 883, A18.Google ScholarPubMed
Lauga, E. & Stone, H. A. 2003 Effective slip in pressure-driven stokes flow. J. Fluid Mech. 489, 55–77.CrossRefGoogle Scholar
Lee, C., Choi, C. H. & Kim, C. J. 2008 Structured surfaces for a giant liquid slip. Phys. Rev. Lett. 101, 064501.CrossRefGoogle ScholarPubMed
Lee, C., Choi, C. H. & Kim, C. J. 2016 Superhydrophobic drag reduction in laminar flows: a critical review. Exp. Fluids 57, 176.CrossRefGoogle Scholar
Lin, S. Y., McKeigue, K. & Maldarelli, C. 2003 Diffusion-controlled surfactant adsorption studied by pendant drop digitization. AIChE J. 36, 1785–1795.CrossRefGoogle Scholar
Lindken, R., Rossi, M., Große, S. & Westerweel, J. 2009 Micro-particle image velocimetry (${\rm \mu }$PIV): recent developments, applications, and guidelines. Lab on a Chip 9, 2551–2567.CrossRefGoogle Scholar
Lv, P. Y., Xiang, Y. L., Xue, Y. H., Lin, H. & Duan, H. L. 2017 Morphological bubble evolution induced by air diffusion on submerged hydrophobic structures. Phys. Fluids 29, 032001.CrossRefGoogle Scholar
Marin, A., Karpitschka, S., Noguera-Marán, D., Cabrerizo-Válchez, M. A., Rossi, M., Kähler, C. J. & Valverde, M. A. R. 2019 Solutal marangoni flow as the cause of ring stains from drying salty colloidal drops. Phys. Rev. Fluids 4, 041601.CrossRefGoogle Scholar
Mathai, V., Calzavarini, E., Brons, J., Sun, C. & Lohse, D. 2016 Microbubbles and microparticles are not faithful tracers of turbulent acceleration. Phys. Rev. Lett. 117, 024501.CrossRefGoogle Scholar
Oliveira, J. L. G., Van der Geld, C. W. M. & Kuerten, J. G. 2015 Lagrangian velocity and acceleration statistics of fluid and inertial particles measured in pipe flow with 3D particle tracking velocimetry. Intl J. Multiphase Flow 73, 97–107.CrossRefGoogle Scholar
Ou, J., Perot, B. & Rothstein, J. P. 2004 Laminar drag reduction in microchannels using ultrahydrophobic surfaces. Phys. Fluids 16, 4635–4643.CrossRefGoogle Scholar
Peaudecerf, F. J., Landel, J. R., Goldstein, R. E. & Luzzatto-Fegiz, P. 2017 Traces of surfactants can severely limit the drag reduction of superhydrophobic surfaces. Proc. Natl Acad. Sci. USA 114, 7254–7259.CrossRefGoogle ScholarPubMed
Pereira, R., Ashton, I., Sabbaghzadeh, B., Shutler, J. D. & Upstill-Goddard, R. C. 2018 Reduced air–sea CO$_2$ exchange in the Atlantic Ocean due to biological surfactants. Nat. Geosci. 11, 492–496.CrossRefGoogle Scholar
Philip, J. R. 1972 Flows satisfying mixed no-slip and no-shear conditions. Z. Angew. Math. Phys. 23, 353–372.CrossRefGoogle Scholar
Pirman, D. A., Kiss, A., Heeren, R. M. & Yost, R. A. 2012 Identifying tissue-specific signal variation in MALDI mass spectrometric imaging by use of an internal standard. Anal. Chem. 85, 1090–1096.CrossRefGoogle ScholarPubMed
Prosser, A. J. & Franses, E. I. 2001 Adsorption and surface tension of ionic surfactants at the air-water interface: review and evaluation of equilibrium models. Colloids Surf. A 178, 1–40.CrossRefGoogle Scholar
Raffel, M., Willert, C. E., Scarano, F., Kähler, C. J., Wereley, S. T. & Kompenhans, J. 2018 Particle Image Velocimetry: A Practical Guide. Springer.CrossRefGoogle Scholar
Rosen, M. J. & Kunjappu, J. T. 2012 Surfactants and Interfacial Phenomena. Wiley.CrossRefGoogle Scholar
Rothstein, J. P. 2010 Slip on superhydrophobic surfaces. Annu. Rev. Fluid Mech. 42, 89–109.CrossRefGoogle Scholar
Samimy, M. & Lele, S. K. 1991 Motion of particles with inertia in a compressible free shear layer. Phys. Fluids A 3, 1915–1923.CrossRefGoogle Scholar
Schäffel, D., Koynov, K., Vollmer, D., Butt, H. J. & Schönecker, C. 2016 Local flow field and slip length of superhydrophobic surfaces. Phys. Rev. Lett. 116, 134501.CrossRefGoogle ScholarPubMed
Schönecker, C., Baier, T. & Hardt, S. 2014 Influence of the enclosed fluid on the flow over a microstructured surface in the Cassie state. J. Fluid Mech. 740, 168–195.CrossRefGoogle Scholar
Song, D., Song, B., Hu, H., Du, X., Du, P., Choi, C. H. & Rothstein, J. P. 2018 Effect of a surface tension gradient on the slip flow along a superhydrophobic air-water interface. Phys. Rev. Fluids 3, 033303.CrossRefGoogle Scholar
Stanislas, M., Okamoto, K., Kähler, C. J. & Westerweel, J. 2005 Main results of the second international PIV challenge. Exp. Fluids 39, 170–191.CrossRefGoogle Scholar
Tagawa, Y., Takagi, S. & Matsumoto, Y. 2014 Surfactant effect on path instability of a rising bubble. J. Fluid Mech. 738, 124–142.CrossRefGoogle Scholar
Thermo Scientific. 2018 Fluoro-Max Fluorescent Beads. Available at: https://assets.fishersci.com/TFS-Assets/CDD/Specification-Sheets/PS-10017619-MTL-FLUORO-GRRDBL-EN.pdf.Google Scholar
Truesdell, R., Mammoli, A., Vorobieff, P., van Swol, F. & Brinker, C. J. 2006 Drag reduction on a patterned superhydrophobic surface. Phys. Rev. Lett. 97, 044504.CrossRefGoogle ScholarPubMed
Tsai, W. T. & Liu, K. K. 2003 An assessment of the effect of sea surface surfactant on global atmosphere-ocean CO$_2$ flux. J. Geophys. Res. 108 (C4), 3127.CrossRefGoogle Scholar
Tsai, P., Peters, A. M., Pirat, C., Wessling, M., Lammertink, R. G. & Lohse, D. 2009 Quantifying effective slip length over micropatterned hydrophobic surfaces. Phys. Fluids 21, 112002.CrossRefGoogle Scholar
Wassmuth, F., Laidlaw, W. G. & Coombe, D. A. 1990 Interfacial instabilities: the Linde instability. Chem. Engng Sci. 45, 3483–3490.CrossRefGoogle Scholar
Westerweel, J., Geelhoed, P. F. & Lindken, R. 2004 Single-pixel resolution ensemble correlation for micro-PIV applications. Exp. Fluids 37, 375–384.CrossRefGoogle Scholar
Yu, H. T., Lu, Z. Y., Lohse, D. & Zhang, X. H. 2015 Gravitational effect on the formation of surface nanodroplets. Langmuir 31, 12628–12634.CrossRefGoogle ScholarPubMed
Zhu, Y. D., Yuan, H. J., Zhang, C. H. & Lee, C. B. 2013 Image-preprocessing method for near-wall particle image velocimetry (PIV) image interrogation with very large in-plane displacement. Meas. Sci. Technol. 24, 125302.CrossRefGoogle Scholar

Li et al. supplementary movie 1

The flow field above the liquid-gas interface in the plane of z=45 μm by μPIV.
Download Li et al. supplementary movie 1(Video)
Video 1 MB

Li et al. supplementary movie 2

The flow field above the liquid-gas interface in the plane of z=30 μm by μPIV

Download Li et al. supplementary movie 2(Video)
Video 1 MB