© imperial college londonpage 1 surfactant-driven thin film flows: spreading, fingering and...

© Imperial College London

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: [email protected]


Outline

• Overview

• Previous work

• Models

• Predictions

• Open questions


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


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


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


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)


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)


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


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.


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:



Bulk (monomer)

Bulk (micelles)

Liquid-solid interface

(monomer)


(monomer)

Modelling Methodology: Problem Formulation IVEvolution equations for autophobing problem


L-W apolar component

Short-range polar component

Disjoining pressure

depends on

surfactant

concentration

At long times

For stability

Modelling Methodology: Problem Formulation V


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


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


JFM, 2006


Fingering Results III

• Fingering occurs in M=3 case despite apparent absence of ‘hmin’

• Pronounced fingering for intermediate M.


JFM, 2006


Fingering Results IV

Hamraoui et al. (2004)

Experiment

Initial condition

Numerical simulations

Branching

& tip-splitting

Craster & Matar,

Phys. Fluids, 2006


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?


Autophobing Results I: LW = 4, P = 4

Rim formation

Craster & Matar,

Langmuir, 2007


Autophobing Results II(a): LW = 16, P = -0.75Onset of retractionEarly times

Craster & Matar,

Langmuir, 2007


Autophobing Results II(b): LW = 16, P = -0.75

Dewetting

Retraction Late times

Craster & Matar,

Langmuir, 2007


Autophobing Results III: LW = 16, P = -0.75

Dewetting

Retraction Above CMC

Craster & Matar,

Langmuir, 2007


Autophobing Results IV: LW = -0.05, P = 4Film rupture

Craster & Matar,

Langmuir, 2007


Autophobing Results IV: LW = -1.1, P = -0.75Film rupture

Craster & Matar,

Langmuir, 2007


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?


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?


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?


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


Acknowledgements

• Collaborators– Richard Craster– Paul Luckham

• Students– Abia Afsar-Siddiqui– Mark Warner– Barry Edmonstone

• Funding agencies– EPSRC

© imperial college londonpage 1 surfactant-driven thin film flows: spreading, fingering and...

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