© Imperial College LondonPage 1 Surfactant-Driven Thin Film Flows: Spreading, Fingering and Autophobing O. K. Matar  Department of Chemical Engineering.

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© Imperial College LondonPage 1 Surfactant-Driven Thin Film Flows: Spreading, Fingering and Autophobing O. K. Matar  Department of Chemical Engineering Imperial College London PASI on Interfacial Fluid Dynamics: From Theory to Applications Wednesday, 8 th August 2007 Correspondence to:

© Imperial College LondonPage 2 Outline Overview Previous work Models Predictions Open questions

© Imperial College LondonPage 3 Overview: Applications & Settings Engineering –Coatings –Paints –Adhesives –Foams –Reactors (falling film and spinning disc) –Heat exchangers and distillation columns Biology –Membranes –Lining of lungs –Tear films

© Imperial College LondonPage 4 Overview: Complex dynamics – examples I h min No h min Two fronts Fingering Instability time Hamraoui et al., 2004 Darhuber & Troian, 2003 Luckham et al., 2005

© Imperial College LondonPage 5 Autophobing & dewetting Two fronts Spreading Retraction Spreading and retraction of a drop of 0.4 cmc DTAB solution on a 100  m water film (Afsar-Siddiqui et al. 2004) Overview: Complex dynamics – examples II

© Imperial College LondonPage 6 Previous work –Spreading Grotberg et al. (1992) Starov et al. (1997) Dussaud, Matar & Troian (2005) –Fingering Marmur & Lelah (1981) Troian, Wu & Safran (1989) Frank & Garoff (1995a,b) He & Ketterson (1995) Afsar-Siddiqui, Luckham & Matar (2003a,b,c) Cazabat et al. ( ) Jensen & Naire (2005) –‘Running droplets’ Thiele et al. ( )

© Imperial College LondonPage 7 Previous work … –Dewetting & Autophobing Woodward & Schwartz (1996) Qu, Suter & Garoff (2002) Afsar-Siddiqui, Luckham & Matar (2004) Craster & Matar (2007) –Super-spreading Zhu et al. (1994) Stoebe et al. (1997) Churaev et. al. (2001) Chengara, Nikolov & Wasan (2002) Nikolov et al. (2002) Rafai et al. (2002) Kumar, Couzis & Maldarelli (2003)

© Imperial College LondonPage 8 Modelling Methodology: Problem Formulation I - Lubrication approximation. - Deposition is relatively thick. - Uncontaminated precursor layer. - Soluble surfactant. - Rapid vertical diffusion. - No adsorption of micelles at interfaces. - Micelles have same size. - Negligible intermolecular forces. - Non-linear equation of state. Assumptions: Schematic of surfactant-driven spreading problem Marangoni spreading Fingering

© Imperial College LondonPage 9 Modelling Methodology: Problem Formulation II Evolution equations for fingering problem Air-liquid interface (monomer) Bulk (monomer) Bulk (micelles) Air-liquid interface Fluxes + Sheludko E.O.S. Effects: Marangoni stresses Capillarity Diffusion (bulk and surface) Sorption kinetics Solubility Micellar formation and breakup Nonlinear E.O.S.

© Imperial College LondonPage 10 Modelling Methodology: Problem Formulation III Same as for fingering problem except: Introduce Disjoining pressure which should depend on surfactant adsorption  substrate wettability can be altered during spreading. Autophobing Assumptions:

© Imperial College LondonPage 11 Air-liquid interface Bulk (monomer) Bulk (micelles) Liquid-solid interface (monomer) Air-liquid interface (monomer) Modelling Methodology: Problem Formulation IV Evolution equations for autophobing problem

© Imperial College LondonPage 12 L-W apolar component Short-range polar component Disjoining pressure depends on surfactant concentration At long times For stability Modelling Methodology: Problem Formulation V

© Imperial College LondonPage 13 b =0.05, C = 10 -3, Pe s =10 4, Pe b,m =10 2,  =K s,b =1,  =100, M=3, n=10, t= R=1R=100 For relatively small R, micelles present at late times, confined to the drop. Tendency for two-front formation increases with increasing R and M. Large concentration gradients at edges of drop and secondary fronts. Fingering Results I: Base state Edmonstone, Craster & Matar, JFM, 2006

© Imperial College LondonPage 14 Fingering Results II b =0.05, C = 10 -3, Pe s =10 4, Pe b,m =10 2,  =K s,b =1,  =100, R=100, M=3, n=10, t=10 4. Initial perturbations random Organisation into fingers Target: the secondary front Primary front Secondary front Edmonstone, Craster & Matar, JFM, 2006

© Imperial College LondonPage 15 Fingering Results III Fingering occurs in M=3 case despite apparent absence of ‘h min ’ Pronounced fingering for intermediate M. Edmonstone, Craster & Matar, JFM, 2006

© Imperial College LondonPage 16 Fingering Results IV Hamraoui et al. (2004) Experiment Initial condition Numerical simulations Branching & tip-splitting Craster & Matar, Phys. Fluids, 2006

© Imperial College LondonPage 17 Fingering: Open questions Is this the best way of modelling the presence of micelles? What is the mechanism that drives the instability? How good is the agreement between theory and experiment?

© Imperial College LondonPage 18 Autophobing Results I:  LW = 4,  P = 4 Rim formation Craster & Matar, Langmuir, 2007

© Imperial College LondonPage 19 Autophobing Results II(a):  LW = 16,  P = Onset of retraction Early times Craster & Matar, Langmuir, 2007

© Imperial College LondonPage 20 Autophobing Results II(b):  LW = 16,  P = Dewetting Retraction Late times Craster & Matar, Langmuir, 2007

© Imperial College LondonPage 21 Autophobing Results III:  LW = 16,  P = Dewetting Retraction Above CMC Craster & Matar, Langmuir, 2007

© Imperial College LondonPage 22 Autophobing Results IV:  LW = -0.05,  P = 4 Film rupture Craster & Matar, Langmuir, 2007

© Imperial College LondonPage 23 Autophobing Results IV:  LW = -1.1,  P = Film rupture Craster & Matar, Langmuir, 2007

© Imperial College LondonPage 24 Autophobing: Open questions Is this the best of modelling the effect of surfactant on intermolecular interactions? Are we missing relevant physics? Should the structural component of  be taken into account (esp. for C > CMC)? How does this change the predictions and the agreement with experiments?

© Imperial College LondonPage 25 Superspreading Surfactant-assisted spreading on hydrophobic substrates Only certain surfactants act as “superspreaders” Effect strongest for C > CAC R ~ tvs.R ~ t 1/10 or R ~ t 1/4 Mechanism: –Marangoni flow? –Unusual structure of trisiloxanes? –Direct adsorption of micelles? –Intermolecular effects near the contact line?

© Imperial College LondonPage 26 Superspreading: Open questions What is the mechanism? What happens at the advancing contact line? Are structural disjoining pressures important (esp. for C > CMC)? If so, how do we build them into our lubrication theory-based models? What molecular level information do we need?

© Imperial College LondonPage 27 General open problem Molecular scale information Micro-scale experiments Macro-scale experiments Theory (e.g. statistical mechanics, DFT…) Dependence of  on surfactant Lubrication theories and simulations

© Imperial College LondonPage 28 Acknowledgements Collaborators –Richard Craster –Paul Luckham Students –Abia Afsar-Siddiqui –Mark Warner –Barry Edmonstone Funding agencies –EPSRC