Wetting as a Macroscopic and Microscropic ProcessJ.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

Capillary Rise

50nm x 900nm ChannelsHan et al 06

27mm Radius TubeStange et al 03

1 Million Orders of Magnitude!!

Polymer-Organic LED (P-OLED) Displays

Inkjet Printing of P-OLED Displays

Microdrop Impact & Spreading

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)

Flow Inside Solids – Marston et al 2010

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

)

θdU

Assumption:A unique angle for each speed

( )d f U

Drop Impact Experiments

10.18ms

10.25ms

)

Ud

-1(ms )U

d 30d Bayer & Megaridis 06

d ( )f U

Capillary Rise Experiments

Sobolev et al 01

Dynamic Wetting:An Interface Formation Process

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 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

* 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

nnf (r, t )=0

Interface Formation Modelling

A Finite Element Based Computational Framework

JES &YDS 2011, Viscous Flows in Domains with Corners, CMAMEJES & YDS 2012, Finite Element Framework for Simulating Dynamic Wetting Flows, Int. J. Num. Meth Fluids.JES & YDS, 2012, Finite Element Simulation of Dynamic Wetting Flows as an Interface Formation Process, to JCP.JES & YDS, 2012, The Dynamics of Liquid Drops and their Interaction with Surfaces of Varying Wettabilities, to PoF.

Mesh Resolution Critical

Arbitrary Lagrangian Eulerian Mesh Control

Drop Impact

Impact at Different Scales

Millimetre Drop

Microdrop

Nanodrop

Pyramidal (mm-sized) Drops

Experiment of Renardy et al, 03.

Microdrop Impact 25 micron water drop impacting at 5m/s on left: wettable substrate

right: nonwettable substrate

Microdrop Impact

60e

Velocity Scale

Pressure Scale

-15ms

Microdrop Impact

?

Hidden Dynamics

10t s 13.4t s

11.7t s 15t s15t s

10t s

Surfaces of Variable Wettability

2e1e

1

1.5

Flow Control on Patterned Surfaces

-14ms-15msJES & YDS 2012, to PoF

Dynamics of Flow Through a Capillary

Steady Propagation of a Meniscus

Flow Characteristics

‘Hydrodynamic Resist’

Smaller Capillaries

Washburn Model Basic Dynamic Wetting Models

Interface Formation Model and Experiments

EquilibriumDynamic

EquilibriumDynamic

EquilibriumDynamic

Meniscus

Meniscus shape unchanged by dynamic wetting

Meniscus shape dependent on speed of propagation.

Hydrodynamic Resist:Meniscus shape influenced by geometry

Summary: Dynamic Wetting Models

Capillary Rise: Models vs ExperimentsCompare to experiments of Joos et al 90 and

conventional Lucas-Washburn theory

Lucas-Washburn assumes:Poiseuille Flow ThroughoutSpherical Cap MeniscusFixed (Equilibrium) Contact Angle

h

Lucas-Washburn vs Full Simulation

R = 0.036cm; every 100secs

R = 0.074cm; every 50secs

Comparison to Experiment

Full Simulation Full Simulation

Washburn Washburn

JES & YDS 2012, to JCP

Wetting as a Microscopic Process:Flow through Porous Media

Problems and Issues

Problems and IssuesMicro: Pore scale dynamics of:

Menisci in wetting frontGanglia

Macro (Darcy-scale) dynamics of:Entire wetting frontGanglia in multiphase system

Multi-scale porosity:Motion on a microporous

substrate

Physical Reality

02 p 0u FtF

pu

0),r( tF

Kinematic boundary condition

Dynamic boundary condition

?

0u

Continuum ModelSimplest Case First: Full Displacement (no ganglia formation)

Wetting mode

Threshold modepu

02 p

2211| pApAp S

Wetting Front: Modes of Motion

1). T. Delker, D. B. Pengra & P.-z. Wong,Phys. Rev. Lett. 76, 2902 (1996).

2). M. Lago & M. Araujo, J. Colloid & Interf. Sci. 234, 35 (2001).

Some Unexplained Effects

) zg

Suggested Description

)1/(0 THRESHOLDFFudtdh

3

4

5

6

7

8

9

10

10 10 10 10 10 10 543210 t (s )

Z (cm )

)1/(111 )](1)[( ttAhHHh cc

2/3 of height in 2 mins)z

g

Washburnian

Non-Washburnian

1/3 of height in many hours

))

Developed Theory

3

4

5

6

7

8

9

10

10 10 10 10 10 10 543210 t (s )

Z (cm )

YDS & JES 2012, JFM; YDS & JES 2012, to PRE

)z

gRandom Fluctuations ‘Break’ Threshold Mode

Flow over a Porous Substrate

Wetting: Micro-Macro Coupling

Spreading on a Porous Medium

Current State of Modelling1) Contact Line Pinned 2) Shape Fixed as Spherical Cap

The RealityEquilibrium shape is history-dependent.

Spreading on a Porous Substrate

θD

θw U

θd

Spreading on a Porous Substrate

No equilibrium angle to perturb aboutFinal shape is history dependent

ApproachUse continuum limit (separation of scales)Consider flow near contact lineFind contact angles as a result:

2 2sin( ) / ; arctan p

W p D

p

UU U

U U

θD

θw

YDS & JES 2012, to JFM

Flow TransitionFormula is when contact lines coincide

Example:

Transition when

2 2sin( ) / ; arctan p

W p D

p

UU U

U U

0.5; 30 , 1642p W DUU

90p D WU U

Potential CollaborationDrop Impact

Microdrops on impermeable surfaces Drops on permeable/patterned surfaces

Capillary RiseInvestigation of ‘resist’ mechanism in micro/nano regimes

Flow with Forming/Disappearing InterfacesCoalescence, bubble detachment, jet break-up, cusp-formation, etc.

Porous MediaInvestigation of newly developed model

Thanks

Wetting: Statics

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

02 cos ep pR

eqh

R

eeqh

Wetting: Dynamics

Wetting: As a Microscopic Process

Macroscale

Microscale

MeniscusCapillary

tube

Wetting front

)

Dynamics: Classical ModellingIncompressible Navier Stokes

θe

Stress balanceKinematic condition

No-SlipImpermeability

Angle 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’

Flow Over Surfaces of Variable Wettability

Periodically Patterned Surfaces

• No slip – No effect.

Interface Formation vs MDS

Solid 2 less wettable

Qualitative agreement

JES & YDS 2007, PRE; JES &YDS 2009 EPJ

g

0p

0p

external pressure

0.0 1.0 2.0

0.0

0.5

1.0

W ashburn(no g ravity)

W ashburn D ynam ic ang le

s = 0 .9 ,

s = 0 .1 ,

h/h 0

(t / T )01/2

= 30*1

1 * = 60h (t )

An Illustrative Example

YDS & JES 2012, JFM