On the spreading of impacting drops

Research output: Contribution to journalArticleAcademicpeer-review

64 Citations (Scopus)
1 Downloads (Pure)

Abstract

The energy budget and dissipation mechanisms during droplet impact on solid surfaces are studied numerically and theoretically. We find that for high impact velocities and negligible surface friction at the solid surface (i.e. free slip), approximately one-half of the initial kinetic energy is transformed into surface energy, independent of the impact parameters and the detailed energy loss mechanism(s). We argue that this seemingly universal rule is related to the deformation mode of the droplet and is reminiscent of pipe flow undergoing a sudden expansion, for which the head loss can be calculated by multiplying the kinetic energy of the incoming flow by a geometrical factor. For impacts on a no-slip surface also dissipation in the shear boundary layer at the solid surface is important. In this case the geometric head loss acts as a lower bound on the total dissipation (i.e. the spreading on a no-slip surface approaches that on a free-slip surface when the droplet viscosity is sent to zero). This new view on the impact problem allows for simple analytical estimates of the maximum spreading diameter of impacting drops as a function of the impact parameters and the properties of the solid surface. It bridges the gap between previous momentum balance approaches and energy balance approaches, which hitherto did not give consistent predictions in the low viscosity limit. Good agreement is found between our models and experiments, both for impacts on ‘slippery’ or lubricated surfaces (e.g. Leidenfrost droplet impacts and head-on droplet–droplet collisions) and for impacts on no-slip surfaces.
Original languageEnglish
Pages (from-to)636-655
Number of pages20
JournalJournal of fluid mechanics
Volume805
DOIs
Publication statusPublished - 2016

Fingerprint

slip
solid surfaces
dissipation
Kinetic energy
energy dissipation
kinetic energy
viscosity
energy budgets
pipe flow
impact velocity
Viscosity
surface energy
Pipe flow
boundary layers
Energy balance
friction
Interfacial energy
shear
Energy dissipation
momentum

Keywords

  • METIS-320669
  • IR-103892

Cite this

@article{587a3e9fc47d47de9a08213af5bb24c5,
title = "On the spreading of impacting drops",
abstract = "The energy budget and dissipation mechanisms during droplet impact on solid surfaces are studied numerically and theoretically. We find that for high impact velocities and negligible surface friction at the solid surface (i.e. free slip), approximately one-half of the initial kinetic energy is transformed into surface energy, independent of the impact parameters and the detailed energy loss mechanism(s). We argue that this seemingly universal rule is related to the deformation mode of the droplet and is reminiscent of pipe flow undergoing a sudden expansion, for which the head loss can be calculated by multiplying the kinetic energy of the incoming flow by a geometrical factor. For impacts on a no-slip surface also dissipation in the shear boundary layer at the solid surface is important. In this case the geometric head loss acts as a lower bound on the total dissipation (i.e. the spreading on a no-slip surface approaches that on a free-slip surface when the droplet viscosity is sent to zero). This new view on the impact problem allows for simple analytical estimates of the maximum spreading diameter of impacting drops as a function of the impact parameters and the properties of the solid surface. It bridges the gap between previous momentum balance approaches and energy balance approaches, which hitherto did not give consistent predictions in the low viscosity limit. Good agreement is found between our models and experiments, both for impacts on ‘slippery’ or lubricated surfaces (e.g. Leidenfrost droplet impacts and head-on droplet–droplet collisions) and for impacts on no-slip surfaces.",
keywords = "METIS-320669, IR-103892",
author = "S. Wildeman and C.W. Visser and Chao Sun and Detlef Lohse",
year = "2016",
doi = "10.1017/jfm.2016.584",
language = "English",
volume = "805",
pages = "636--655",
journal = "Journal of fluid mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",

}

On the spreading of impacting drops. / Wildeman, S.; Visser, C.W.; Sun, Chao; Lohse, Detlef.

In: Journal of fluid mechanics, Vol. 805, 2016, p. 636-655.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - On the spreading of impacting drops

AU - Wildeman, S.

AU - Visser, C.W.

AU - Sun, Chao

AU - Lohse, Detlef

PY - 2016

Y1 - 2016

N2 - The energy budget and dissipation mechanisms during droplet impact on solid surfaces are studied numerically and theoretically. We find that for high impact velocities and negligible surface friction at the solid surface (i.e. free slip), approximately one-half of the initial kinetic energy is transformed into surface energy, independent of the impact parameters and the detailed energy loss mechanism(s). We argue that this seemingly universal rule is related to the deformation mode of the droplet and is reminiscent of pipe flow undergoing a sudden expansion, for which the head loss can be calculated by multiplying the kinetic energy of the incoming flow by a geometrical factor. For impacts on a no-slip surface also dissipation in the shear boundary layer at the solid surface is important. In this case the geometric head loss acts as a lower bound on the total dissipation (i.e. the spreading on a no-slip surface approaches that on a free-slip surface when the droplet viscosity is sent to zero). This new view on the impact problem allows for simple analytical estimates of the maximum spreading diameter of impacting drops as a function of the impact parameters and the properties of the solid surface. It bridges the gap between previous momentum balance approaches and energy balance approaches, which hitherto did not give consistent predictions in the low viscosity limit. Good agreement is found between our models and experiments, both for impacts on ‘slippery’ or lubricated surfaces (e.g. Leidenfrost droplet impacts and head-on droplet–droplet collisions) and for impacts on no-slip surfaces.

AB - The energy budget and dissipation mechanisms during droplet impact on solid surfaces are studied numerically and theoretically. We find that for high impact velocities and negligible surface friction at the solid surface (i.e. free slip), approximately one-half of the initial kinetic energy is transformed into surface energy, independent of the impact parameters and the detailed energy loss mechanism(s). We argue that this seemingly universal rule is related to the deformation mode of the droplet and is reminiscent of pipe flow undergoing a sudden expansion, for which the head loss can be calculated by multiplying the kinetic energy of the incoming flow by a geometrical factor. For impacts on a no-slip surface also dissipation in the shear boundary layer at the solid surface is important. In this case the geometric head loss acts as a lower bound on the total dissipation (i.e. the spreading on a no-slip surface approaches that on a free-slip surface when the droplet viscosity is sent to zero). This new view on the impact problem allows for simple analytical estimates of the maximum spreading diameter of impacting drops as a function of the impact parameters and the properties of the solid surface. It bridges the gap between previous momentum balance approaches and energy balance approaches, which hitherto did not give consistent predictions in the low viscosity limit. Good agreement is found between our models and experiments, both for impacts on ‘slippery’ or lubricated surfaces (e.g. Leidenfrost droplet impacts and head-on droplet–droplet collisions) and for impacts on no-slip surfaces.

KW - METIS-320669

KW - IR-103892

U2 - 10.1017/jfm.2016.584

DO - 10.1017/jfm.2016.584

M3 - Article

VL - 805

SP - 636

EP - 655

JO - Journal of fluid mechanics

JF - Journal of fluid mechanics

SN - 0022-1120

ER -