© imperial college londonpage 1 surfactant-driven thin film flows: spreading, fingering and...
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© Imperial College LondonPage 1
Surfactant-Driven Thin Film Flows: Spreading, Fingering and
Autophobing
O. K. MatarDepartment of Chemical Engineering
Imperial College London
PASI on Interfacial Fluid Dynamics: From Theory to Applications
Wednesday, 8th August 2007
Correspondence to: o.matar@imperial.ac.uk
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Outline
• Overview
• Previous work
• Models
• Predictions
• Open questions
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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
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Overview: Complex dynamics – examples I
hmin
No hmin
Two fronts
Fingering
Instability
time Hamraoui et al., 2004
Hamraoui et al., 2004
Darhuber & Troian, 2003Luckham et al., 2005
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Autophobing & dewetting
Two fronts
Spreading Retraction
Spreading and retraction of a drop of 0.4 cmc DTAB solution
on a 100m water film (Afsar-Siddiqui et al. 2004)
Overview: Complex dynamics – examples II
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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. (1996-2004)• Jensen & Naire (2005)
– ‘Running droplets’• Thiele et al. (2004-2005)
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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)
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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
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Modelling Methodology: Problem Formulation IIEvolution 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.
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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:
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Air-liquid interface
Bulk (monomer)
Bulk (micelles)
Liquid-solid interface
(monomer)
Air-liquid interface
(monomer)
Modelling Methodology: Problem Formulation IVEvolution equations for autophobing problem
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L-W apolar component
Short-range polar component
Disjoining pressure
depends on
surfactant
concentration
At long times
For stability
Modelling Methodology: Problem Formulation V
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b =0.05, C = 10-3, Pes=104, Peb,m=102, =Ks,b=1, =100, M=3, n=10, t=0-1000.
R=1 R=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
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Fingering Results IIb =0.05, C = 10-3, Pes=104, Peb,m=102, =Ks,b=1, =100, R=100, M=3, n=10, t=104.
• Initial perturbations random
• Organisation into fingers • Target: the secondary front
Primary
front
Secondary
front
Edmonstone, Craster & Matar,
JFM, 2006
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Fingering Results III
• Fingering occurs in M=3 case despite apparent absence of ‘hmin’
• Pronounced fingering for intermediate M.
Edmonstone, Craster & Matar,
JFM, 2006
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Fingering Results IV
Hamraoui et al. (2004)
Experiment
Initial condition
Numerical simulations
Branching
& tip-splitting
Craster & Matar,
Phys. Fluids, 2006
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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?
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Autophobing Results I: LW = 4, P = 4
Rim formation
Craster & Matar,
Langmuir, 2007
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Autophobing Results II(a): LW = 16, P = -0.75Onset of retractionEarly times
Craster & Matar,
Langmuir, 2007
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Autophobing Results II(b): LW = 16, P = -0.75
Dewetting
Retraction Late times
Craster & Matar,
Langmuir, 2007
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Autophobing Results III: LW = 16, P = -0.75
Dewetting
Retraction Above CMC
Craster & Matar,
Langmuir, 2007
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Autophobing Results IV: LW = -0.05, P = 4Film rupture
Craster & Matar,
Langmuir, 2007
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Autophobing Results IV: LW = -1.1, P = -0.75Film rupture
Craster & Matar,
Langmuir, 2007
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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?
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Superspreading
• Surfactant-assisted spreading on hydrophobic substrates• Only certain surfactants act as “superspreaders”• Effect strongest for C > CAC• R ~ t vs. R ~ t1/10 or R ~ t1/4
• Mechanism: – Marangoni flow?– Unusual structure of trisiloxanes?– Direct adsorption of micelles?– Intermolecular effects
near the contact line?
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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?
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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
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