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