Line Tension

1
Line Tension

• Aart Gieske
• 17 December 2007
• Colloids and Interfaces

2
Outline

• Introduction
• Experimental determination of line tension
• Theoretical vs. Experimental values
• Line tension near wetting
• Boundary tension
• Summary
• References

3
Introduction

• Line tension exists along the three phase contact
  line
• First described by Gibbs

vapour
liquid
substrate
Image adapted from http//www.biomachinations.com/
?cat10
4
Relevance of line tension

• Wetting effects
• Stability of foams and emulsions
• Adhesion/release of droplets to/from surfaces
• Adhesion of biological cells to surfaces

Image http//www.whatsnextnetwork.com/technology
/index.php/2006/11/03/p3883more3883
5
Line tension dimensional analysis
6
Thermodynamic definition
vapour
liquid
?
R
substrate
7
Thermodynamic definition
8
Physical origin of line tension

• Interaction between molecules and substrate
• Surface potential V(l)
• De Feijter and Vrij dependence of line tension
  on
• interaction
  potential

V(l)
Line tension can be positive or Negative,
depending on V(l)
s sl slv
ssv
l
lmin
9
Experimental determination of line tension
z
vapour
liquid
R
?
r
substrate
10
Experimental determination of line tension
z0
z
y
sv
r
sl
vapour
liquid
R
?
r
x
substrate
11
Experimental determination of line tension
For macroscopically large droplets r? No
line tension t0
Youngs Law
12
Experimental determination of line tension
contact angle for large droplets (Youngs Law)
13
Experimental determination of line tension
Adapted from Wang et al.
-0.5 x 10-9 N lt t lt 0.3 x 10-9 N
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Theoretical determination of line tension

• Simplification by mean field theory
• Calculation of density profiles
• Local methods
• Intermolecular forces only modelled at the three
  phase confluence zone
• Non-local methods
• Excess energy from a larger region is studied
• Membrane method
• Method of two interacting dividing surfaces

15
Experiment vs. Theory

• Diverse experimental results
• Predominantly positive line tensions
• 2 classes of results
• - t 10-9 N ? droplets in µm range
• - t 10-6 N ? droplets in mm range
• Diverse theoretical results
• Most results t 10-12 10-10 N
• Much smaller order of magnitude!

16
Experiment vs. Theory

• Problems with experimental results
• Young equation only applicable for equilibrium
  conditions
• Hysteresis
• Heterogeneity of solid surface, impurities,
  etc...
• Problems with theoretical results
• Mean field approximation and other
  simplifications, depending on the model

17
Line tension near wetting

• Line tension is undefined
• beyond the wetting point
• What happens near at
• the wetting point?
• 1st order vs. critical wetting
• Experimental findings vs.
• Theory

T
cp
vapour-substrate
W
µ µcoex
liquid-substrate
µ
µw
µc
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Line tension near wetting
t
T
cp
?
vapour-substrate
W
µ µcoex
liquid-substrate
0
µ
µw
µc
T
Tw
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Line tension near wetting

• Indekeu method interface displacement model

1st order wetting transition
Interface displacement profile at wetting
transition
V(l)
vapour
liquid
l1
l (x)
x
l
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Prewetting

• Along the prewetting line ? 2 surface phases
  coexist
• ? Gthin, Gthick and substrate

T
?
cp
pwcp
vapour-substrate
?thick
W
µ µcoex
?thin
liquid-substrate
µ
µpw
µcoex
µw
µc
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Prewetting Boundary tension
T

• Analogous to line tension
• Boundary tension between surface phases along
  prewetting line

cp
pwcp
vapour-substrate
W
µ µcoex
liquid-substrate
µ
µw
µc
22
Line tension Boundary tension
t
T
c
pwcp
boundary tension
line tension
vapour-substrate
W
µ µcoex
liquid-substrate
0
µ
µw
µc
T
Tw
Tpwcp
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Summary

• Dimensions are energy over length
• Line tension plays more important roles in
  smaller systems
• No consesus has been reached between experimental
  findings and theoretical predictions
• The behaviour of line tension near wetting is not
  fully understood

24
References

• Blokhuis, E.M. Liquid drops at surfaces Surface
  and Interfacial Tension 2003 p. 149-193
• Blokhuis, E.M. Wetting lecture notes MSc
  college Colloids and Interfaces, 2007-2008
• Indekeu, J.O. Physica A 1992 183 p. 439-461
• Neumann, A.W. Amirfazli, A. Advances in
  Colloids and Interface Science 2004 110 p.
  121-141
• Wang, J.Y. Beteleu, S. Law, B.M. Physical
  Review Letters 1999 83 p. 3677-3680

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Questions?