Hostname: page-component-77f85d65b8-6pvrj Total loading time: 0 Render date: 2026-03-26T08:13:52.575Z Has data issue: false hasContentIssue false
  • English
  • Français

Drag reduction on drop during impact on multiscale superhydrophobic surfaces

Published online by Cambridge University Press:  08 April 2020

Grégoire Martouzet ,
Choongyeop Lee ,
Christophe Pirat ,
Christophe Ybert Open the ORCID record for Christophe Ybert [Opens in a new window]  and
Anne-Laure Biance Open the ORCID record for Anne-Laure Biance [Opens in a new window]
Grégoire Martouzet
Affiliation:
Université de Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622, VILLEURBANNE, France
Choongyeop Lee
Affiliation:
Department of Mechanical Engineering, Kyung Hee University, Yongin17104, Republic of Korea
Christophe Pirat
Affiliation:
Université de Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622, VILLEURBANNE, France
Christophe Ybert
Affiliation:
Université de Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622, VILLEURBANNE, France
Anne-Laure Biance*
Affiliation:
Université de Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622, VILLEURBANNE, France
*
†Email address for correspondence: anne-laure.biance@univ-lyon1.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

Liquid drop impact dynamics depends on the liquid–substrate interaction. In particular, when liquid–solid friction is decreased, the spreading of the impacting drop lasts longer. We characterise this effect by using two types of superhydrophobic surfaces, with similar wetting properties but different friction coefficients. It is found that, for large enough impact velocities, a reduced friction delays the buildup of a viscous boundary layer, and leads to an increase of the time required to reach the maximal radius of the impacting drop. An asymptotic analysis is carried out to quantify this effect, and agrees well with the experimental findings. Interestingly, this novel description complements the general picture of drop impact on solid surfaces, and more generally addresses the issue of drag reduction in the presence of slippage for non-stationary flows.

JFM classification

Drops and Bubbles: Drops Flow Control: Drag reduction Interfacial Flows (free surface): Capillary flows

Information

Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 892 , 10 June 2020 , R2
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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.)

Article purchase

Temporarily unavailable

References

Bartolo, D., Eouamrirene, F., Verneuil, E., Buguin, A., Silberzan, P. & Moulinet, S. 2006 Bouncing or sticky droplets: impalement transitions on superhydrophobic micropatterned surfaces. Eur. Phys. Lett. 74, 299–305.CrossRefGoogle Scholar
Bayer, I. S. & Megaridis, C. M. 2006 Contact angle dynamics in droplets impacting on flat surfaces with different wetting characteristics. J. Fluid Mech. 558, 415–449.CrossRefGoogle Scholar
Biance, A.-L., Pirat, C. & Ybert, C. 2011 Drop fragmentation due to hole formation during Leidenfrost impact. Phys. Fluids 23 (2), 022104.CrossRefGoogle Scholar
Bird, J. C., Dhiman, R., Kwon, H.-M. & Varanasi, K. K. 2013 Reducing the contact time of a bouncing drop. Nature 503 (7476), 385–388.CrossRefGoogle ScholarPubMed
Callies, M. & Quéré, D. 2005 On water repellency. Soft Matt. 1 (1), 55–61.CrossRefGoogle Scholar
Choi, C.-H. & Kim, C.-J. 2006 Large slip of aqueous liquid flow over a nanoengineered superhydrophobic surface. Phys. Rev. Lett. 96 (6), 066001.CrossRefGoogle Scholar
Clanet, C., Beguin, C., Richard, D. & Quere, D. 2004 Maximal deformation of an impacting drop. J. Fluid Mech. 517, 199–208.CrossRefGoogle Scholar
Deng, T., Varanasi, K. K., Hsu, M., Bhate, N., Keimel, C., Stein, J. & Blohm, M. 2009 Nonwetting of impinging droplets on textured surfaces. Appl. Phys. Lett. 94, 133109.CrossRefGoogle Scholar
Duez, C., Ybert, C., Clanet, C. & Bocquet, L. 2007 Making a splash with water repellency. Nat. Phys. 3 (3), 180–183.CrossRefGoogle Scholar
Duez, C., Ybert, C., Clanet, C. & Bocquet, L. 2010 Wetting controls separation of inertial flows from solid surfaces. Phys. Rev. Lett. 104 (8), 084503.CrossRefGoogle ScholarPubMed
Eggers, J., Fontelos, M. A., Josserand, C. & Zaleski, S. 2010 Drop dynamics after impact on a solid wall: theory and simulations. Phys. Fluids 22, 062101.CrossRefGoogle Scholar
Fujioka, H. & Wei, H.-H. 2018 Letter: new boundary layer structures due to strong wall slippage. Phys. Fluids 30 (12), 121702.Google Scholar
Gie, G.-M. & Kelliher, J. P. 2012 Boundary layer analysis of the Navier–Stokes equations with generalized navier boundary conditions. J. Differ. Equ. 253 (6), 1862–1892.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 (15), 156104.CrossRefGoogle ScholarPubMed
Josserand, C., Lemoyne, L., Troeger, R. & Zaleski, S. 2005 Droplet impact on a dry surface: triggering the splash with a small obstacle. J. Fluid Mech. 524, 47–56.CrossRefGoogle Scholar
Josserand, C. & Thoroddsen, S. T. 2016 Drop impact on a solid surface. Annu. Rev. Fluid Mech. 48 (1), 365–391.CrossRefGoogle Scholar
Laan, N., de Bruin, K. G., Bartolo, D., Josserand, C. & Bonn, D. 2014 Maximum diameter of impacting liquid droplets. Phys. Rev. A 2, 044018.Google Scholar
Lagubeau, G., Fontelos, M. A., Josserand, C., Maurel, A., Pagneux, V. & Petitjeans, P. 2012 Spreading dynamics of drop impacts. J. Fluid Mech. 713, 50–60.CrossRefGoogle Scholar
Lastakowski, H., Boyer, F., Biance, A.-L., Pirat, C. & Ybert, C. 2014 Bridging local to global dynamics of drop impact onto solid substrates. J. Fluid Mech. 747, 103–118.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. & Kim, C.-J. 2011 Influence of surface hierarchy of superhydrophobic surfaces on liquid slip. Langmuir 27, 4243–4248.CrossRefGoogle ScholarPubMed
Lee, J. B., Laan, N., de Bruin, K. G., Skantzaris, G., Shahidzadeh, N., Derome, D., Carmeliet, J. & Bonn, D. 2016 Universal rescaling of drop impact on smooth and rough surfaces. J. Fluid Mech. 786, R4.CrossRefGoogle Scholar
Liu, Y., Moevius, L., Xu, X., Qian, T., Yeomans, J. M. & Wang, Z. 2014 Pancake bouncing on superhydrophobic surfaces. Nat. Phys. 10 (7), 515–519.CrossRefGoogle ScholarPubMed
Luu, L.-H. & Forterre, Y. 2013 Giant drag reduction in complex fluid drops on rough hydrophobic surfaces. Phys. Rev. Lett. 110 (18), 184501.CrossRefGoogle ScholarPubMed
Matthews, M. T. & Hill, J. M. 2008 A note on the boundary layer equations with linear slip boundary condition. Appl. Maths Lett. 21 (8), 810–813.CrossRefGoogle Scholar
Reyssat, M., Pein, A., Marty, F., Chen, Y. & Quere, D. 2006 Bouncing transitions on microtextured materials. Eur. Phys. Lett. 74, 306–312.CrossRefGoogle Scholar
Reyssat, M., Richard, D., Clanet, C. & Quere, D. 2010 Dynamical superhydrophobicity. Faraday Discuss. 146, 19–33.CrossRefGoogle ScholarPubMed
Richard, D. & Quere, D. 2000 Bouncing water drops. Eur. Phys. Lett. 50, 769–775.CrossRefGoogle Scholar
Roisman, I. V. 2009 Inertia dominated drop collisions. II. An analytical solution of the Navier–Stokes equations for a spreading viscous film. Phys. Fluids 21 (5), 052104.CrossRefGoogle Scholar
Roisman, I. V., Berberovic, E. & Tropea, C. 2009 Inertia dominated drop collisions. I. On the universal flow in the lamella. Phys. Fluids 21, 052103.CrossRefGoogle Scholar
Rothstein, J. P. 2010 Slip on superhydrophobic surfaces. Annu. Rev. Fluid Mech. 42, 89–109.CrossRefGoogle Scholar
de Ruiter, J., Lagraauw, R., van den Ende, D. & Mugele, F. 2015 Wettability-independent bouncing on flat surfaces mediated by thin air films. Nat. Phys. 11 (1), 48–53.CrossRefGoogle Scholar
Schroll, R. D., Josserand, C., Zaleski, S. & Zhang, W. W. 2010 Impact of a viscous liquid drop. Phys. Rev. Lett. 104, 034504.CrossRefGoogle ScholarPubMed
Sun, G., Gao, T., Zhao, X. & Zhang, H. 2010 Fabrication of micro/nano dual-scale structures by improved deep reactive ion etching. J. Micromech. Microengng 20 (7), 075028.CrossRefGoogle Scholar
Tsai, P., Hendrix, M. H. W., Dijkstra, R. M., Shui, L. & Lohse, D. 2011 Microscopic structure influencing macroscopic splash at high Weber number. Soft Matt. 7 (24), 11325–11333.CrossRefGoogle Scholar
Tsai, P., Pacheco, S., Pirat, C., Lefferts, L. & Lohse, D. 2009 Drop impact upon micro- and nanostructured superhydrophobic surfaces. Langmuir 25, 12293–12298.CrossRefGoogle ScholarPubMed
Vadillo, D. C., Soucemarianadin, A., Delattre, C. & Roux, D. C. D. 2009 Dynamic contact angle effects onto the maximum drop impact spreading on solid surfaces. Phys. Fluids 21 (12), 122002.CrossRefGoogle Scholar
Wachters, L. H. & Westerling, N. A. 1966 Heat transfer from a hot wall to impinging water drops in spheroidal state. Chem. Engng Sci. 21, 1047–1056.CrossRefGoogle Scholar
Yarin, A. L. 2006 Drop impact dynamics: splashing, spreading, receding, bouncing.... Annu. Rev. Fluid Mech. 38, 159–192.CrossRefGoogle Scholar
Ybert, C., Barentin, C., Cottin-Bizonne, C., Joseph, P. & Bocquet, L. 2007 Achieving large slip with superhydrophobic surfaces: scaling laws for generic geometries. Phys. Fluids 19 (12), 123601.CrossRefGoogle Scholar