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Transcript of J.E. Sprittles (University of Birmingham / Oxford, U.K.) Y.D. Shikhmurzaev(University of Birmingham,...
![Page 1: J.E. Sprittles (University of Birmingham / Oxford, U.K.) Y.D. Shikhmurzaev(University of Birmingham, U.K.) Seminar at KAUST, February 2012.](https://reader036.fdocuments.us/reader036/viewer/2022062223/551ac41d550346b2288b554d/html5/thumbnails/1.jpg)
Dynamic Wetting Processes:Modelling and SimulationJ.E. Sprittles (University of Birmingham / Oxford, U.K.)Y.D. Shikhmurzaev (University of Birmingham, U.K.)
Seminar at KAUST, February 2012
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‘Impact’ A few years after completing my PhD.....
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Wetting: Statics
Non-Wettable (Hydrophobic)Wettable (Hydrophilic)e e
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Wetting: Dynamics
( )h t
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Wetting: As a Microscopic Process
Macroscale
Microscale
MeniscusCapillary
tube
Wetting front
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Wetting: Micro-Macro
Spreading on a Porous Medium
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Processes with Wetting at their Core
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Capillary Rise
50nm x 900nm ChannelsHan et al 06
27mm Radius TubeStange et al 03
1 Million Orders of Magnitude!!
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Curtain Coating
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Curtain Coating Optimization
Increased Coating Speed
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Harnessing Instabilities: Spinning Disk Atomizer
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Polymer-Organic LED (P-OLED) Displays
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Inkjet Printing of P-OLED Displays
Microdrop Impact & Spreading
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Additive Manufacturing
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Modelling
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Why bother?1 - Recover Hidden Information
2 - Map Regimes of Spreading
3 – Experiment
Millimetres in Milliseconds - Rioboo et al (2002)
Microns in Microseconds - Dong et al (2002)
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Wetting: Statics
)
0 1 12e ep p r
1 3 2cose e e e Young
Laplace
1e
θs
e
1e
2ep 0pr
1e
1e
3e
R
Contact Line
Contact Angle
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Wetting: Statics
R2 cos e
eqh Rg
2 cos eeqgh
R
0
2 cos ep pR
eqh
eqh
R
e
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)
Dynamics: Classical ModellingIncompressible Navier Stokes
θe
Stress balance
Kinematic condition
No-Slip
ImpermeabilityAngle
Prescribed
No Solution!
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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.Léger (1986), D.Kröner (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.Ramé (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.O’Rear (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)
‘Moving Contact Line Problem’
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r
Pasandideh-Fard et al 1996
Dynamic Contact AngleRequired as a boundary condition for the free surface shape.
r
t
d( )d f t
d e
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Speed-Angle Formulae
dθ = ( )f U
e1 3 2cose e e e
R
σ1
σ3 - σ2
Young Equation Dynamic Contact Angle Formula
)
θd
U
Assumption:A unique angle for each speed
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Capillary Rise Experiments
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The Interface Formation Model
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Physics of Dynamic Wetting
Make a dry solid wet.
Create a new/fresh liquid-solid interface.
Class of flows with forming interfaces.
Forminginterface
Formed interface
Liquid-solidinterface
Solid
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Relevance of the Young Equation
U
1 3 2cose e e e 1 3 2cos d
R
σ1e
σ3e - σ2e
Dynamic contact angle results from dynamic surface tensions.
The angle is now determined by the flow field.
Slip created by surface tension gradients (Marangoni effect)
θe θd
Static situation Dynamic wetting
σ1
σ3 - σ2
R
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2u 1u 0, u u up
t
s s1 1 1 2 2 2
1 3 2
v e v e 0
cos
s s
d
s1
*1
*1
s 1 11
s 1 111 1
1 1|| ||
v 0
n [( u) ( u) ] n n
n [( u) ( u) ] (I nn) 0
(u v ) n
( v )
(1 4 ) 4 (v u )
s se
s sss e
s
ff
t
p
t
* 12 || ||2
s 2 22
s 2 222 2
12|| || || 2 22
21,2 1,2 1,2
n [ u ( u) ] (I nn) (u U )
(u v ) n
( v )
v (u U ) , v U
( )
s se
s sss e
s s
s s
t
a b
In the bulk:
On liquid-solid interfaces:
At contact lines:
On free surfaces:
Interface Formation Model
θd
e2
e1
n
nf (r, t )=0
Interface Formation Modelling
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Comparison With Experiments
0.0001 0.0010 0.0100 0.1000 1.0000
0
30
60
90
120
150
180
d
Ca
0.0001 0.0010 0.0100 0.1000 1.0000
0
30
60
90
120
150
180
d
Ca
Perfect wetting (Hoffman 1975; Ström et al. 1990; Fermigier & Jenffer 1991)
Partial wetting (□: Hoffman 1975;
: Burley & Kennedy 1976; , ,: Ström et al. 1990)
The theory is in good agreement with all experimental data published in the literature.
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A Computational Framework
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Graded Mesh – For Both Models
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Arbitrary Lagrangian-Eulerian(Free surface nodes follow the fluid’s path; bulk’s don’t)
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Oscillating Drops: Code ValidationFor Re=100, f2 = 0.9
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Oscillating Drops: Code Validation
a
b
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Drop Impact
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Impact at Different Scales
Millimetre Drop
Microdrop
Nanodrop
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Pyramidal (mm-sized) Drops
Experiment Renardy et al.
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Microdrop Impact
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Microdrop Impact and Spreading
60e
Velocity Scale
Pressure Scale
-15ms
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Typical Microdrop Experiment (Dong et al 07)
?
?
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Recovering Hidden Information
10t s 13.4t s
11.7t s 15t s15t s
10t s
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Flow Over Surfaces of Variable Wettability
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Periodically Patterned Surfaces
• No slip – No effect.
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Interface Formation vs Molecular Dynamics
Solid 2 less wettableSolid 2 less wettable
Qualitative agreementQualitative agreement
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Surfaces of Variable Wettability
2 110e
1 60e 2e
1e
1
1.5
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Flow Control on Patterned Surfaces
-14ms -15ms
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Capillary Rise
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Capillary Rise
R
h 2eqh Rg
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Flow Characteristics
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‘Hydrodynamic Resist’
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Dynamic Wetting Models
Washburn Model Basic Dynamic Wetting Models
Interface Formation Model and Experiments
Meniscus shape unchanged by dynamic wetting
Meniscus shape dependent on speed of propagation.
Meniscus shape influenced by geometry
EquilibriumDynamic
EquilibriumDynamic
EquilibriumDynamic
Meniscus
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Wetting Fronts Propagating Through Porous Media
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Wetting Fronts in Porous Media
Threshold ModeWetting Mode
Wetting Front
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Capillary Rise through Packed Beads
Circles: Experimental data from Delker et al 1996Line: Developed theory
) zWashburnian
z (cm)
t (s)
Non-Washburnian
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Flow over a Porous Substrate
![Page 57: J.E. Sprittles (University of Birmingham / Oxford, U.K.) Y.D. Shikhmurzaev(University of Birmingham, U.K.) Seminar at KAUST, February 2012.](https://reader036.fdocuments.us/reader036/viewer/2022062223/551ac41d550346b2288b554d/html5/thumbnails/57.jpg)
![Page 58: J.E. Sprittles (University of Birmingham / Oxford, U.K.) Y.D. Shikhmurzaev(University of Birmingham, U.K.) Seminar at KAUST, February 2012.](https://reader036.fdocuments.us/reader036/viewer/2022062223/551ac41d550346b2288b554d/html5/thumbnails/58.jpg)
Thanks