Dr James Sprittles Mathematics Institute, University of Warwick Science of Inkjet and Printed Drops,...
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Capillary Microflows in a Non-Equilibrium Gas Dr James Sprittles Mathematics Institute, University of Warwick Science of Inkjet and Printed Drops, November 2014
Dr James Sprittles Mathematics Institute, University of Warwick Science of Inkjet and Printed Drops, November 2014
Dr James Sprittles Mathematics Institute, University of Warwick
Science of Inkjet and Printed Drops, November 2014
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Microdrop Spreading Sponsored by Kodak European Research. To
study dynamics of drop ejected from inkjet printers. Focus on
models used for spreading dynamics. Contact angle dynamics,
liquid-solid slip, etc. Computational framework developed for
models. Gas dynamics neglected as: & Consider impact of water
drop at
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Microdrop Spreading WettableNon-Wettable
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Microdrop Spreading Velocity Scale Pressure Scale
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Microdrop Spreading ? 25 m water drop impacting at 5m/s.
Experiments: Dong et al 06 Do you see a gas bubble trapped under
the drops?
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Gas Cushion Dynamics van Dam & Le Clerc 2004, PoF
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Gas Cushion Dynamics
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De Ruiter et al 2012, PRL Bouwhuis et al 2012, PRL Gas
Film
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Influence of the Ambient Gas
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Ambient gas pressure is key to the drops behaviour What
physical mechanism causes this and how does it enter a mathematical
model?
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Gas Effects: Which Mechanism? Wetting Gas Film Impact
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Coating Experiments Advantages: Flow is steady making
experimental analysis more tractable. Parameter space is easier to
map: Speeds over 6 orders Viscosities over 3 orders Liquid
GasSolid
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Air Entrainment Courtesy of Jacco Snoeijer, University of
Twente Critical speed of wetting => gas pulled into the
liquid
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Effect of Gas Pressure on Wetting Speed Benkreira & Khan
2008, Air Entrainment in Dip Coating Under Reduced Pressures,
Chemical Engineering Science Reduced Gas Pressure Increased Coating
Speed
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Different Ambient Gases Benkreira & Ikin 2010, Dynamic
Wetting and Gas Viscosity Effects, Chemical Engineering
Science
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The Classical Model
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1) Impact Phase When will the gas film rupture? Never! Gas
Film
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2) Wetting Phase No Solution!! Moving contact line problem
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Wetting Models: Liquid Phase A. A `slip condition: Slip region
of size ~ l B. Dynamic contact angle formula: No-slip ( u=0) u=U A.
Classical formulation B. Dynamic contact angle must be specified.
has no solution. (Navier slip) (Youngs equation)
Wetting Models: Gas Phase A. A `slip condition: Slip region of
size ~ l No-slip ( u=0) A. Classical formulation has no solution
(Navier slip)
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Non-Equilibrium Gas Dynamics Slip at solid-gas interface is due
to finite mean free path. Mean free path (hence Kn) depends on gas
density/pressure.
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Find where & At the gas-solid boundary we have: Whilst at
the gas-liquid free-surface: turns off free-surface Maxwell-slip
Maxwell Slip Conditions
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Dynamic Wetting Model Simplest possible dynamic wetting model:
Navier-slip on the liquid-solid interface with Fixed equilibrium
contact angle
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JES & YDS 2012, Finite Element Framework for Simulating
Dynamic Wetting Flows, International Journal for Numerical Methods
in Fluids. JES & YDS, 2013, Finite Element Simulation of
Dynamic Wetting Flows as an Interface Formation Process, Journal of
Computational Physics
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Multiscale Mesh: For Coating Flows Gas Liquid x1 x10 8 2 4
Resolution: Bulk Scale Slip Lengths
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Sprittles 2014, Air Entrainment in Dynamic Wetting: Knudsen
Effects and the Influence of Ambient Air Pressure, Submitted
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Free Surface Profiles Consider silicone oil with as a base
state Gas Liquid
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Effect of Gas Pressure Maxwell-slip at solid and liquid is
critical
A Local Knudsen Number Calculating a local Knudsen number based
on gas films height. 0.4310.011 0.470.160.1 0.860.01213
1.290.009460
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Implications for Drop Impact Xu et al 05: threshold pressure
required to suppress splashing
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Threshold Pressures Threshold Pressure vs Impact Speed for
Different Gases Air Helium Krypton SF 6
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Non-Equilibrium Gas Effects Note where &
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Open Problems Alternative flow configurations. Theory-driven
experimental analysis. Navier-Stokes Boltzmann Coupling: Continuum
Mechanics Navier Stokes ? Statistical Mechanics Boltzmann
Equation
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Impact Phenomena Classical Model Maxwell-Slip Model Knudsen
Effects Drop actually impacts solid!
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1. Model: Prevents film ever breaking + 2. Computation: Poor
resolution of film initiates mesh- dependent breakup Failure of
Commercial Software 6 different answers! Hysing et al, 2009,
IJNMF
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Formation of Drops Compound Drops: Mr J.A. Simmons Drop
Breakup: Dr Y. Li
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(Post-Impact) Coalescence of Liquid Drops Coalescence of Liquid
Drops: Different Models vs Experiments, Physics of Fluids 2012
Experiments: Dr J.D. Paulsen Our Simulation: Green Lines
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(Lack of) Influence of Inertia Bulk flow cant be responsible
for the effect. Re = 0 Re = 100
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A Local Knudsen Number Dependence of film height on capillary
number
