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![Page 1: Jordan Allen-Flowers Mitch Wilson Graduate Program in Applied Mathematics University of Arizona December 9,2009 Advisors: Dr. Alain Goriely, Robert Reinking.](https://reader035.fdocuments.us/reader035/viewer/2022062804/56649d2d5503460f94a04012/html5/thumbnails/1.jpg)
Analysis of a water drop on a hydrophobic surface
Jordan Allen-FlowersMitch Wilson
Graduate Program in Applied MathematicsUniversity of Arizona
December 9,2009Advisors: Dr. Alain Goriely, Robert Reinking
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OutlineIntroductionMethodsTheoryResults
Horizontal deformationContact time
Discussions Conclusions/Future Work
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IntroductionWater-drop phenomena
Hydrophobic surface
Three behaviors:Bouncing Crowning Splashing
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Research GoalsDiscover relationships between different
parametersHorizontal deformation Contact time
Compare to published results
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ApplicationsInkjet printingFluid transportBlood spatter at a crime sceneWater removal on leaves
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MethodsWater-drop system
Pipettes and syringesTest slidesPressure bulbs
Camera and softwareHigh-speed cameraPhotron Motion Tools, ImageJ software1000W lamp
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Theory: Maximum deformation
Weber number:
U is impact velocityD is drop diameterρ, σ are density and surface tensionRatio of kinetic energy to surface energyRanges from ~1 to ~50
DU
We2
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Three different scaling laws for maximal deformation:All kinetic energy is transformed to surface
energy
Kinetic energy is dissipated by viscosity
Gravity puddle approach
DUDWeDD ~)(~ max2/1
max
5/1max
5/1max ~(Re)~ DUDDD
2/1max
4/1max ~)(~ DUDWeDD
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Theory: Contact timeBalancing inertia and capillarity yields:
This can also be rewritten as:
But implies that τ is independent of U
2/32/13 ~)/(~ DD
)/()(~ 2/1 UDWe
UWe ~2/1
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Results- Horizontal Deformation
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More results for max deformation
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Results- Contact Time
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More results for contact time
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ConclusionsThe water-drop phenomena- quick, but
intricateOur data was consistent with the theory of
some authorsFuture work
Surface analysisDifferent liquidsPinch-off phenomenon
We would like to thank Dr. Alain Goriely and Rob Reinking, who made this research possible.
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ReferencesRein, M. 1993. "Phenomena of liquid drop impact on
solid and liquid surfaces" Fluid Dyn. Res. 12, 61-93.Okumura, K., Chevy F., Richard, D., Quere, D., Clanet, C.
2003. "Water spring: A model for bouncing drops" Europhys. Let. 62, 237-243.
Clanet, C., Beguin, C., Richard, D., Quere, D. 2004. "Maximal deformation of an impacting drop" J. Fluid Mech. 517, 199-208.
Richard, D., Clanet, C., Quere, D. 2002. "Contact time of a bouncing drop" Nature 417, 811.
Chandra, S., Avedisian, C.T. 1991. "On the collision of a droplet with a solid surface" Proc. Royal Soc. London A 432, 13.