J.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)

Wetting: Dynamics

Capillary Rise 50nm x 900nm Channels Han et al 06 27mm Radius Tube Stange 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 Angle Required as a boundary condition for the free surface shape. r t

Speed-Angle Formulae R σ1σ1 σ 3 - σ 2 Young Equation Dynamic Contact Angle Formula ) U Assumption: A unique angle for each speed

Drop Impact Experiments ) Bayer & Megaridis 06

Capillary Rise Experiments Sobolev et al 01

Physics of Dynamic Wetting Make a dry solid wet. Create a new/fresh liquid-solid interface. Class of flows with forming interfaces. Forming interface Formed interface Liquid-solidinterface Solid

Relevance of the Young Equation R σ 1e σ 3e - σ 2e 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) θeθe θdθd Static situationDynamic wetting σ1σ1 σ 3 - σ 2 R

In the bulk: On liquid-solid interfaces: At contact lines: On free surfaces: Interface Formation Model θdθd e2e2 e1e1 n n f (r, t )=0 Interface Formation Modelling

JES &YDS 2011, Viscous Flows in Domains with Corners, CMAME JES & 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

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 Velocity Scale Pressure Scale

Microdrop Impact ?

Hidden Dynamics

Surfaces of Variable Wettability 1 1.5

Flow Control on Patterned Surfaces JES & YDS 2012, to PoF

Steady Propagation of a Meniscus

Flow Characteristics

‘Hydrodynamic Resist’ Smaller Capillaries

Washburn Model Basic Dynamic Wetting Models Interface Formation Model and Experiments Equilibrium Dynamic Equilibrium Dynamic Equilibrium Dynamic 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 Experiments Compare to experiments of Joos et al 90 and conventional Lucas-Washburn theory Lucas-Washburn assumes: Poiseuille Flow Throughout Spherical Cap Meniscus Fixed (Equilibrium) Contact Angle

Lucas-Washburn vs Full Simulation R = 0.036cm; every 100secs R = 0.074cm; every 50secs

Comparison to Experiment Full Simulation Washburn JES & YDS 2012, to JCP

Wetting as a Microscopic Process: Flow through Porous Media

Problems and Issues

Micro: Pore scale dynamics of: Menisci in wetting front Ganglia Macro (Darcy-scale) dynamics of: Entire wetting front Ganglia in multiphase system Multi-scale porosity: Motion on a microporous substrate

Physical Reality

Kinematic boundary condition Dynamic boundary condition ? Continuum Model Simplest Case First: Full Displacement (no ganglia formation)

Wetting mode Threshold mode 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 ) z g

Suggested Description 2/3 of height in 2 mins ) z g Washburnian Non- Washburnian 1/3 of height in many hours ) )

Developed Theory YDS & JES 2012, JFM; YDS & JES 2012, to PRE ) z g Random Fluctuations ‘Break’ Threshold Mode

Flow over a Porous Substrate

Wetting: Micro-Macro Coupling Spreading on a Porous Medium

Current State of Modelling 1) Contact Line Pinned 2) Shape Fixed as Spherical Cap

The Reality Equilibrium shape is history-dependent.

Spreading on a Porous Substrate θDθD θwθw U θdθd

No equilibrium angle to perturb about Final shape is history dependent Approach Use continuum limit (separation of scales) Consider flow near contact line Find contact angles as a result: θDθD θwθw U YDS & JES 2012, to JFM

Flow Transition Formula is when contact lines coincide Example: Transition when

Potential Collaboration Drop Impact Microdrops on impermeable surfaces Drops on permeable/patterned surfaces Capillary Rise Investigation of ‘resist’ mechanism in micro/nano regimes Flow with Forming/Disappearing Interfaces Coalescence, bubble detachment, jet break-up, cusp-formation, etc. Porous Media Investigation of newly developed model

Wetting: Statics

) Young Laplace Contact Line Contact Angle

Wetting: Statics

Wetting: Dynamics

Wetting: As a Microscopic Process Macroscale Microscale Meniscus Capillary tube Wetting front

) Dynamics: Classical Modelling Incompressible Navier Stokes Stress balance Kinematic condition No-Slip Impermeability 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’

Periodically Patterned Surfaces No slip – No effect.No slip – No effect.

Interface Formation vs MDS Solid 2 less wettable Qualitative agreement JES & YDS 2007, PRE; JES &YDS 2009 EPJ

g external pressure h (t ) An Illustrative Example YDS & JES 2012, JFM