Sprittles presentation
-
Upload
jamessprittles -
Category
Technology
-
view
125 -
download
1
Transcript of Sprittles presentation
J.E. Sprittles (University of Oxford, U.K.)Y.D. Shikhmurzaev (University of Birmingham, U.K.)
European Coating Symposium, MonsSeptember 2013
Coating Phenomena
Impact of a solid on a liquidDuez et al 07
Dip coating experimentsCourtesy of Terry Blake
Impact of a liquid on a solidXu et al 05
Questions
?
1) Why is there still so much debate about wetting?
2) Are computational techniques essential?
3) Are the gas’ dynamics important?
4) How can we identify the ‘true’ physics?
Coating ExperimentsAdvantages:Flow is steady making
experimental analysis more tractable.
Parameter space is easier to map:Speeds over 6 ordersViscosities over 3 orders
appclU Liquid
GasSolid
The ‘apparent angle’
Coating ResultsApparent angle measured at resolution of 20microns for
water-glycerol solutions with μ=1, 10, 100 mPas.Increasing μ
clcl
UCa
You only observe the ‘apparent angle’. The actual one is fixed.Free surface bends below the experiment’s resolution (20μm)
Interpretation A: Static Contact Angle
erU
( )app r
The ‘actual angle’
Dynamics of angle cause change in apparent angleDynamic contact angle is a function of speed
Interpretation B: Dynamic Contact Angle
rU
d( )app r
Slip ModelsA: Equilibrium contact angleB: Slip - typically Navier-slip
eU ( )app r
l s
B: No-slip => No solution
Often, we have
Asymptotics for the Apparent Angle
2 2
22 2 20
2 2
ln
sin cos sin,
2sin 2 sin sin
( ) sin
app ds
g
l
Lg g Ca l
k K dg k
k K k
K
k
, 1slCaL
3 3 9 lnapp ds
LCa l
lnapp ds
Lg g Ca l
1d
In Cox 86, it was shown that in this case:
And for Voinov (76) has shown:
JES & YDS 2013, Finite Element Simulation of Dynamic Wetting Flows as an Interface Formation Process, Journal of Computational Physics, 233, 34-65
Computational Domain
U Gas
Liquid
x1x10x108x102
x104
Resolution:
Arbitrary Lagrangian Eulerian MeshBased on the ‘spine method’ of Scriven and co-workers
Microdrop simulationwith impact, spreading and rebound
Free Surface Profiles With: 67 , 1nme sl
Computations vs Asymptotics
Ca=0.5
Ca=0.05
Ca=0.005
Solid line: ComputationsDashed line: Asymptotic (Cox’s) result
Limitations of Cox’s FormulaChen, Rame & Garoff 95:
“Aspects of the unique hydrodynamics acting in the inner region, not included in the model, project out and become visible in the imaged region.”
0.1Ca 0.5Ca
( )r m
app
( )r m
app
2) Are computational techniques essential?
Yes! To accurately capture high-speed coating flows.
Slip Model vs ExperimentsGas’ viscosity leads to air entrainment at a finite speed.
Decreasing viscosity ratio
Hydrodynamic Assist
U, cm/s
dθ
Blake et al 99
-1(ms )U
app
app
Vary Flow Rate
30d
UEffect is not due to free surface bending(Wilson et al 06)
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-solidLiquid-solidinterfaceinterface
SolidSolid
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 upt
s s1 1 1 2 2 2
1 3 2
v e v e 0cos
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
f ftp
t
In the bulk (Navier Stokes):
At contact lines:
On free surfaces:Interface Formation Model
θd
e2
e1
nnf (r, t )=0
Interface Formation Modelling
*2 || ||
s 2 22
s 2 222 2
2|| || || 2
21,2 1,2 1,2
1n [ u ( u) ] (I nn) u U2
(u v ) n
( v )
1v (u U )2( )
s se
s sss e
s
s s
t
a b
Liquid-solid interface
Interface Formation vs ExperimentsApparent angle = Dynamic actual angle
1) Why is there still a debate about wetting?
Fundamentally different models describe experiments(with reasonable parameter values).
+ Viscous bending
Influence of Gas PressureSplashing in DropImpact:Xu, Zhang & Nagel 05
Air Entrainment Speedin Dip CoatingBenkreira & Ikin 10
(Lack of) Influence of Inertia Bulk flow can’t be responsible for the effect.
Re = 0
Re = 100
Rarefied Gas DynamicsSlip at solid-gas interface is due to finite mean free path.Mean free path (hence Kn) depends on gas density.
1KnL
U
uKn u Uy
Gas Dynamics Near Contact Line
U
Atmospheric pressure: mean free path ~ 0.1 microns
/u U
s
s
0.1 m
Gas Dynamics Near Contact LineAt Reduced Pressure: mean free path~ 10microns
/u U
s
U
s
0.1 m 10 m
Delayed Air EntrainmentMean free paths (mfp) are:Atmospheric pressure: mfp ~ 0.1 micronsReduced pressure (10mbar): mfp ~ 10 microns
cCa
( )mfp m
3) Are the gas’ dynamics important?
Yes, its behaviour is key to air entrainment
Microdrop Impact
JES & YDS 2012, The Dynamics of Liquid Drops and their Interaction with Solids of Varying Wettability, Physics of Fluids, 24, 082001.
Coalescence of Liquid DropsDeveloped framework can be adapted for coalescence.
Thoroddsen’s Group: Ultra high-speed imaging
Nagel’s Group:Sub-optical electrical measurements r
Thoroddsen et al 2005
dSimulation
Experiment
Coalescence: Models vs ExperimentsBridge radius versus time: 2mm drops of 220cP water-glycerol.
Interface formation
Conventional
Nagel’sElectrical Measurements
Thoroddsen’sOpticalExperiments
/r R
/t R
4) How can we identify the ‘true’ physics?
By accessing smaller spatio-temporal scales
JES & YDS 2012, Coalescence of Liquid Drops: Different Models vs Experiments, Physics of Fluids, 24, 122105
Microscale Dynamic WettingUltra high speed imaging of microfluidic wetting phenomenon, with Dr E. Li & Professor S.T. Thoroddsen
FundingFundingThis presentation is based on work supported by:
Computations vs Experiments1.5, 10, 104 mPa s Water-glycerol solutions of
& Asymptotics
Asymptotic Formula for Actual Angle in IFM
2 1 0
22
2 2 2 2 20
2 2 2 2
2 22
2 ( , )cos cos
.
sin cos ( ) sin cos ( )( , )
sin cos ( ) sin cos ( )
, ( ) sin
s se e d
e d se
d d dd
d d d d
d
V u k
V V
V ScCa
K k Ku k
K k K
K
When there is no ‘hydrodynamic assist’, for small capillary numbers the actual angle is dynamic:
Moffat 64
IFM vs Experiments
Shikhmurzaev 93
Shikhmurzaev 93 + Cox 86
& AsymptoticsActual angle varies and free surface bends.
‘Hydrodynamic Resist’
Smaller Capillaries
U
d
R
New effect: contact angle depends on capillary size
( m)R
Sobolev et al 01
d
1/3U
Fibre Coating: Effect of Geometry
app
d
Simpkins & Kuck 03
app
4mmd U
2mmd
U
Drop Spreading: Effect of Impact Speed
10.18ms
10.25ms
)
U
app
-1(ms )U
appBayer & Megaridis 06
30d
CoalescenceConventional model: singular as initial cusp is rounded in zero time -> infinite velocities
Interface formation: singularity-free as cusp is rounded in finite time that it takes internal interface to disappear
Forming interface
d
Instant rounding
Infinite bridge speed
90d180d
drdt
r
Gradual rounding
Finite bridge speed
Coalescence: Free surface profiles
Interface formation theory
Conventional theory
Water-Glycerolmixture of 230cP
Time: 0 < t < 0.1
0.01 - 0.360.03 - 0.3650.1 - 0.370.6 - 0.391 - 0.43 - 0.426 - 0.4410 - 0.45
Wetting6 (1489) running 1166,2277 and 0.1microns – saved previous t_info – running for current info
Microdrop Impact 25 micron water drop impacting at 5m/s on left: wettable substrate right: nonwettable substrate