j.e. sprittles (university of birmingham / oxford, u.k.) y.d. shikhmurzaev(university of birmingham,...
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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
‘Impact’ A few years after completing my PhD.....
Wetting: Statics
Non-Wettable (Hydrophobic)Wettable (Hydrophilic)e e
Wetting: Dynamics
( )h t
Wetting: As a Microscopic Process
Macroscale
Microscale
MeniscusCapillary
tube
Wetting front
Wetting: Micro-Macro
Spreading on a Porous Medium
Processes with Wetting at their Core
Capillary Rise
50nm x 900nm ChannelsHan et al 06
27mm Radius TubeStange et al 03
1 Million Orders of Magnitude!!
Curtain Coating
Curtain Coating Optimization
Increased Coating Speed
Harnessing Instabilities: Spinning Disk Atomizer
Polymer-Organic LED (P-OLED) Displays
Inkjet Printing of P-OLED Displays
Microdrop Impact & Spreading
Additive Manufacturing
Modelling
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)
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
Wetting: Statics
R2 cos e
eqh Rg
2 cos eeqgh
R
0
2 cos ep pR
eqh
eqh
R
e
)
Dynamics: Classical ModellingIncompressible Navier Stokes
θe
Stress balance
Kinematic condition
No-Slip
ImpermeabilityAngle
Prescribed
No Solution!
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’
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
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
Capillary Rise Experiments
The Interface Formation Model
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
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
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
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.
A Computational Framework
Graded Mesh – For Both Models
Arbitrary Lagrangian-Eulerian(Free surface nodes follow the fluid’s path; bulk’s don’t)
Oscillating Drops: Code ValidationFor Re=100, f2 = 0.9
Oscillating Drops: Code Validation
a
b
Drop Impact
Impact at Different Scales
Millimetre Drop
Microdrop
Nanodrop
Pyramidal (mm-sized) Drops
Experiment Renardy et al.
Microdrop Impact
Microdrop Impact and Spreading
60e
Velocity Scale
Pressure Scale
-15ms
Typical Microdrop Experiment (Dong et al 07)
?
?
Recovering Hidden Information
10t s 13.4t s
11.7t s 15t s15t s
10t s
Flow Over Surfaces of Variable Wettability
Periodically Patterned Surfaces
• No slip – No effect.
Interface Formation vs Molecular Dynamics
Solid 2 less wettableSolid 2 less wettable
Qualitative agreementQualitative agreement
Surfaces of Variable Wettability
2 110e
1 60e 2e
1e
1
1.5
Flow Control on Patterned Surfaces
-14ms -15ms
Capillary Rise
Capillary Rise
R
h 2eqh Rg
Flow Characteristics
‘Hydrodynamic Resist’
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
Wetting Fronts Propagating Through Porous Media
Wetting Fronts in Porous Media
Threshold ModeWetting Mode
Wetting Front
Capillary Rise through Packed Beads
Circles: Experimental data from Delker et al 1996Line: Developed theory
) zWashburnian
z (cm)
t (s)
Non-Washburnian
Flow over a Porous Substrate
Thanks
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