Dr James Sprittles Mathematics Institute, University of Warwick Science of Inkjet and Printed Drops,...
Preview:
Citation preview
- Slide 1
- Dr James Sprittles Mathematics Institute, University of Warwick
Science of Inkjet and Printed Drops, November 2014
- Slide 2
- Slide 3
- 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
- Slide 4
- Microdrop Spreading WettableNon-Wettable
- Slide 5
- Microdrop Spreading Velocity Scale Pressure Scale
- Slide 6
- 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?
- Slide 7
- Slide 8
- Gas Cushion Dynamics van Dam & Le Clerc 2004, PoF
- Slide 9
- Gas Cushion Dynamics
- Slide 10
- De Ruiter et al 2012, PRL Bouwhuis et al 2012, PRL Gas
Film
- Slide 11
- Influence of the Ambient Gas
- Slide 12
- Ambient gas pressure is key to the drops behaviour What
physical mechanism causes this and how does it enter a mathematical
model?
- Slide 13
- Gas Effects: Which Mechanism? Wetting Gas Film Impact
- Slide 14
- Slide 15
- 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
- Slide 16
- Air Entrainment Courtesy of Jacco Snoeijer, University of
Twente Critical speed of wetting => gas pulled into the
liquid
- Slide 17
- 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
- Slide 18
- Different Ambient Gases Benkreira & Ikin 2010, Dynamic
Wetting and Gas Viscosity Effects, Chemical Engineering
Science
- Slide 19
- Slide 20
- The Classical Model
- Slide 21
- 1) Impact Phase When will the gas film rupture? Never! Gas
Film
- Slide 22
- 2) Wetting Phase No Solution!! Moving contact line problem
- Slide 23
- 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)
- Slide 24
- L.E.Scriven (1971), C.Huh (1971), A.W.Neumann (1971), S.H.
Davis (1974), E.B.Dussan (1974), E.Ruckenstein (1974), A.M.Schwartz
(1975), M.N.Esmail (1975), L.M.Hocking (1976), O.V.Voinov (1976),
C.A.Miller (1976), P.Neogi (1976), S.G.Mason (1977), H.P.Greenspan
(1978), F.Y.Kafka (1979), L.Tanner (1979), J.Lowndes (1980), D.J.
Benney (1980), W.J.Timson (1980), C.G.Ngan (1982), G.F.Telezke
(1982), L.M.Pismen (1982), A.Nir (1982), V.V.Pukhnachev (1982),
V.A.Solonnikov (1982), P.-G. de Gennes (1983), V.M.Starov (1983),
P.Bach (1985), O.Hassager (1985), K.M.Jansons (1985), R.G.Cox
(1986), R.Lger (1986), D.Krner (1987), J.-F.Joanny (1987),
J.N.Tilton (1988), P.A.Durbin (1989), C.Baiocchi (1990), P.Sheng
(1990), M.Zhou (1990), W.Boender (1991), A.K.Chesters (1991),
A.J.J. van der Zanden (1991), P.J.Haley (1991), M.J.Miksis (1991),
D.Li (1991), J.C.Slattery (1991), G.M.Homsy (1991), P.Ehrhard
(1991), Y.D.Shikhmurzaev (1991), F.Brochard-Wyart (1992),
M.P.Brenner (1993), A.Bertozzi (1993), D.Anderson (1993), R.A.Hayes
(1993), L.W.Schwartz (1994), H.-C.Chang (1994), J.R.A.Pearson
(1995), M.K.Smith (1995), R.J.Braun (1995), D.Finlow (1996), A.Bose
(1996), S.G.Bankoff (1996), I.B.Bazhlekov (1996), P.Seppecher
(1996), E.Ram (1997), R.Chebbi (1997), R.Schunk (1999),
N.G.Hadjconstantinou (1999), H.Gouin (10999), Y.Pomeau (1999),
P.Bourgin (1999), M.C.T.Wilson (2000), D.Jacqmin (2000), J.A.Diez
(2001), M.&Y.Renardy (2001), L.Kondic (2001), L.W.Fan (2001),
Y.X.Gao (2001), R.Golestanian (2001), E.Raphael (2001), A.ORear
(2002), K.B.Glasner (2003), X.D.Wang (2003), J.Eggers (2004),
V.S.Ajaev (2005), C.A.Phan (2005), P.D.M.Spelt (2005), J.Monnier
(2006) Wetting Models: Liquid Phase L.E.Scriven (1971)
- Slide 25
- 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)
- Slide 26
- Slide 27
- 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.
- Slide 28
- 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
- Slide 29
- Dynamic Wetting Model Simplest possible dynamic wetting model:
Navier-slip on the liquid-solid interface with Fixed equilibrium
contact angle
- Slide 30
- 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
- Slide 31
- Multiscale Mesh: For Coating Flows Gas Liquid x1 x10 8 2 4
Resolution: Bulk Scale Slip Lengths
- Slide 32
- Sprittles 2014, Air Entrainment in Dynamic Wetting: Knudsen
Effects and the Influence of Ambient Air Pressure, Submitted
- Slide 33
- Free Surface Profiles Consider silicone oil with as a base
state Gas Liquid
- Slide 34
- Effect of Gas Pressure Maxwell-slip at solid and liquid is
critical
- Slide 35
- Flow Field Atmospheric Pressure Reduced PressureAtmospheric
Pressure Velocity Continuous Maxwell Slip
- Slide 36
- Comparison to Experiment
- Slide 37
- Gas Films Dynamics Liquid Gas
- Slide 38
- Gas Films Dynamics Liquid Gas
- Slide 39
- 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
- Slide 40
- Implications for Drop Impact Xu et al 05: threshold pressure
required to suppress splashing
- Slide 41
- Threshold Pressures Threshold Pressure vs Impact Speed for
Different Gases Air Helium Krypton SF 6
- Slide 42
- Non-Equilibrium Gas Effects Note where &
- Slide 43
- Open Problems Alternative flow configurations. Theory-driven
experimental analysis. Navier-Stokes Boltzmann Coupling: Continuum
Mechanics Navier Stokes ? Statistical Mechanics Boltzmann
Equation
- Slide 44
- Slide 45
- Impact Phenomena Classical Model Maxwell-Slip Model Knudsen
Effects Drop actually impacts solid!
- Slide 46
- Slide 47
- 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
- Slide 48
- Formation of Drops Compound Drops: Mr J.A. Simmons Drop
Breakup: Dr Y. Li
- Slide 49
- (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
- Slide 50
- Slide 51
- (Lack of) Influence of Inertia Bulk flow cant be responsible
for the effect. Re = 0 Re = 100
- Slide 52
- A Local Knudsen Number Dependence of film height on capillary
number