Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-28T11:27:36.168Z Has data issue: false hasContentIssue false
  • English
  • Français

Droplet breakup in a stagnation-point flow

Published online by Cambridge University Press:  26 August 2020

Alireza Hooshanginejad ,
Cari Dutcher Open the ORCID record for Cari Dutcher [Opens in a new window] ,
Michael J. Shelley  and
Sungyon Lee Open the ORCID record for Sungyon Lee [Opens in a new window]
Alireza Hooshanginejad
Affiliation:
Department of Mechanical Engineering, University of Minnesota, Minneapolis, ME55455, USA
Cari Dutcher
Affiliation:
Department of Mechanical Engineering, University of Minnesota, Minneapolis, ME55455, USA
Michael J. Shelley
Affiliation:
Center for Computational Biology, Flatiron Institute, Simons Foundation, New York, NY10010, USA Courant Institute of Mathematical Sciences, New York University, New York, NY10012, USA
Sungyon Lee*
Affiliation:
Department of Mechanical Engineering, University of Minnesota, Minneapolis, ME55455, USA
*
†Email address for correspondence: sungyon@umn.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We experimentally and theoretically investigate the dynamics of a partially wetting water droplet subject to a two-dimensional high-speed jet of air blowing perpendicularly to the substrate. When the jet velocity is above a critical value, the droplet evolves under wind and splits into two secondary drops. In addition to droplet splitting, we observe depinning of the droplet on one side when the jet is applied at a small distance from the initial centre of the droplet. In parallel with systematic experiments, we develop a mathematical model to compute the coupled evolution of the droplet and an idealised stagnation-point flow. Our simplified lubrication model yields a criterion for the critical jet velocity, as well as the time scale of the droplet breakup, in qualitative agreement with the experiments.

JFM classification

Drops and Bubbles: Drops Low-Reynolds-number flows: Lubrication theory Aerodynamics: High-speed flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 901 , 25 October 2020 , A19
Check for updates
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.)

References

REFERENCES

Basu, S., Nandakumar, K. & Masliyah, J. H. 1997 A model for detachment of a partially wetting drop from a solid surface by shear flow. J. Colloid Interface Sci. 190 (1), 253–257.CrossRefGoogle Scholar
Bertozzi, A. L. 1998 The mathematics of moving contact lines in thin liquid films. Not. Am. Math. Soc. 45 (6), 689–697.Google Scholar
Constantin, P., Dupont, T. F., Goldstein, R. E., Kadanoff, L. P., Shelley, M. J. & Zhou, S. 1993 Droplet breakup in a model of the hele-shaw cell. Phys. Rev. E 47, 4169–4181.Google Scholar
Dimitrakopoulos, P. 2007 Deformation of a droplet adhering to a solid surface in shear flow: onset of interfacial sliding. J. Fluid Mech. 580, 451–466.CrossRefGoogle Scholar
Dimitrakopoulos, P. & Higdon, J. J. L. 1997 Displacement of fluid droplets from solid surfaces in low-Reynolds-number shear flows. J. Fluid Mech. 336, 351–378.CrossRefGoogle Scholar
Dimitrakopoulos, P. & Higdon, J. J. L. 1998 On the displacement of three-dimensional fluid droplets from solid surfaces in low-Reynolds-number shear flows. J. Fluid Mech. 377, 189–222.CrossRefGoogle Scholar
Ding, H. & Spelt, P. 2007 Inertial effects in droplet spreading: a comparison between diffuse-interface and level-set simulations. J. Fluid Mech. 576, 287–296.CrossRefGoogle Scholar
Durbin, P. A. 1988 On the wind force needed to dislodge a drop adhered to a surface. J. Fluid Mech. 196, 205–222.CrossRefGoogle Scholar
Dussan, V. E. B. 1979 On the spreading of liquids on solid surfaces: static and dynamic contact lines. Annu. Rev. Fluid Mech. 11, 371–400.CrossRefGoogle Scholar
Dussan, V. E. B. 1985 On the ability of drops or bubbles to stick to non-horizontal surfaces of solids. Part 2. small drops or bubbles having contact angles of arbitrary size. J. Fluid Mech. 151, 1–20.Google Scholar
Dussan, V. E. B. 1987 On the ability of drops or bubbles to stick to surfaces of solids. Part 3. the influences of the motion of the surrounding fluid on dislodging drops. J. Fluid Mech. 174, 381–397.CrossRefGoogle Scholar
Dussan, V. E. B. & Chow, R. T. -P. 1983 On the ability of drops or bubbles to stick to non-horizontal surfaces of solids. J. Fluid Mech. 137, 1–29.CrossRefGoogle Scholar
ElSherbini, A. I. & Jacobi, A. M. 2004 a Liquid drops on vertical and inclined surfaces: I. An experimental study of drop geometry. J. Colloid Interface Sci. 273 (2), 556–565.CrossRefGoogle ScholarPubMed
ElSherbini, A. I. & Jacobi, A. M. 2004 b Liquid drops on vertical and inclined surfaces: II. A method for approximating drop shapes. J. Colloid Interface Sci. 273 (2), 566–575.CrossRefGoogle Scholar
Espín, L. & Kumar, S. 2017 Droplet wetting transitions on inclined substrates in the presence of external shear and substrate permeability. Phys. Rev. Fluids 2, 014004.CrossRefGoogle Scholar
Fry, H. 2012 A study of droplet deformation. PhD thesis, University College London.Google Scholar
Hiemenz, K. 1911 Die grenzschicht an einem in den gleichförmigen flüssigkeitsstrom eingetauchten geraden kreiszylinder. Dingl. Polytech. J. 326, 321–410.Google Scholar
Hooshanginejad, A. & Lee, S. 2017 Droplet depinning in a wake. Phys. Rev. Fluids. 2, 031601(R).CrossRefGoogle Scholar
Howarth, L. 1935 On the calculation of the steady flow in the boundary layer near the surface of a cylinder in a stream. Aeronautical Research Committee Reports and Memoranda No. 1632.Google Scholar
von Kármán, T. 1921 Über laminaire und turbulente reibung ber laminaire und turbulente reibung. Z. Angew. Math. Mech. 1, 233–252.CrossRefGoogle Scholar
Krechetnikov, R. 2010 On application of lubrication approximations to nonunidirectional coating flows with clean and surfactant interfaces. Phys. Fluids 22 (9), 092102.CrossRefGoogle Scholar
McKinley, I. S. & Wilson, S. K. 2001 The linear stability of a ridge of fluid subject to a jet of air. Phys. Fluids 13, 872–883.CrossRefGoogle Scholar
McKinley, I. S., Wilson, S. K. & Duffy, B. R. 1999 Spin coating and air-jet blowing of thin viscous drops. Phys. Fluids 11, 30–47.CrossRefGoogle Scholar
Milne, A. J. B., Defez, M., Cabrerizo-Vílchez, M. & Amirfazli, A. 2014 Understanding (sessile/constrained) bubble and drop oscillations. Adv. Colloid Interface Sci. 203, 22–36.CrossRefGoogle ScholarPubMed
Moore, M. N. J., Ristroph, L., Childress, S., Zhang, J. & Shelley, M. J. 2013 Self-similar evolution of a body eroding in a fluid flow. Phys. Fluids 25, 116602.CrossRefGoogle Scholar
Moriarty, J. A., Schwartz, L. W. & Tuck, E. O. 1991 Unsteady spreading of thin liquid films with small surface tension. Phys. Fluids 3 (733), 733–742.CrossRefGoogle Scholar
Park, J. & Kumar, S. 2017 Droplet sliding on an inclined substrate with a topographical defect. Langmuir 33, 7352–7363.CrossRefGoogle Scholar
Pohlhausen, K. 1921 Zur näherungsweisen integration der differentialgleichung der laminaren grenzschicht. Z. Angew. Math. Mech. 1, 252–268.Google Scholar
Prandtl, L. 1904 In Verhandlungen des dritten internationalen Mathematiker-Kongresses in Heidelberg, Germany, A. Krazer, ed., Teubner, Leipzig, Germany (1905), p. 484. English trans. in Early Developments of Modern Aerodynamics, J. A. K. Ackroyd, B. P. Axcell & A. I. Ruban, eds., Butterworth-Heinemann, Oxford, UK (2001), p. 77.Google Scholar
Ren, W., Trinh, P. H. & Weinan, E. 2015 On the distinguished limits of the Navier slip model of the moving contact line problem. J. Fluid Mech. 772, 107–126.CrossRefGoogle Scholar
Schlichting, H. 1960 Boundary Layer Theory. McGraw-Hill.Google Scholar
Schmucker, J. A. 2013 Experimental investigation of wind-forced drop stability. PhD dissertation, Texas A & M University, Department of Aerospace Engineering.Google Scholar
Schwartz, L. W. & Eley, R. R. 1998 Simulation of droplet motion on low-energy and heterogeneous surfaces. J. Colloid Interface Sci. 202 (1), 173–188.CrossRefGoogle Scholar
Schwartz, L. W., Roy, R. V., Eley, R. R. & Princen, H. M. 2004 Surfactant-driven motion and splitting of droplets on a substrate. J. Engng Maths 50, 157–175.CrossRefGoogle Scholar
Smith, F. T., Brighton, P. W. M., Jackson, P. S. & Hunt, J. C. R. 1981 On boundary-layer flow past two-dimensional obstacles. J. Fluid Mech. 113, 123–152.Google Scholar
Smith, F. T., Li, L. & Wu, G. X. 2003 Air cushioning with a lubrication/inviscid balance. J. Fluid Mech. 482, 291–318.CrossRefGoogle Scholar