FORCED COALESCENCE OF MICRONSIZE DROPS

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Role of Bubble Surface Mobility for the Foam-Wall
Friction Experiment and Modeling
N. D. Denkov Laboratory of Chemical Physics
Engineering Faculty of Chemistry, Sofia
University, Sofia, Bulgaria
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Why studying foam-wall friction?

• Wall-slip is usually significant (including
  rheo-experiments).
• The research problem is closely related to
  bubble in capillary problem (Bretherton).
• Very convenient for studying the effect of bubble
  surface mobility.

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Background
Constitutive rheological relation for
foams ?0 - yield stress (elastic origin) ?V
- rate-dependent stress (viscous
dissipation) - shear rate 1/s
Princen, 1985
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Theoretical studies Schwartz Princen,
Hansen Kraynik n 2/3 (for small
oscillations) Kraynik m 2/3 (adapting the
Brethertons solution)
Experimental measurements Princen n 1/2
(for continuous shear of emulsions) Mason n
between 1/2 and 0.9 (emulsions with small
droplets)
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Contents
1. Experimental methods ? Parallel-plates
rheometry (wall-slip and inside-foam shear). ?
Microscope observation of dynamic wetting
films. ? Oscillating drop method (solution
surface properties).
2. Experimental results ? Viscous friction in
the wall-slip region. ? Viscous friction in
sheared foam.
3. Theoretical model of foam-wall friction ?
Viscous friction in the wetting film and in the
transition region. ? Role of surface mobility.
4. Conclusions.
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1. Experimental methods Viscous friction between
foam and smooth wall
Perfect slip at low velocity The viscous stress
on the wall can be measured The role of surface
mobility can be studied
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Microscope observation of dynamic wetting films
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Characterizing the surface properties of
surfactant solutions
Oscillating Drop Method
Drop oscillations Frequency - 0.125 Hz Area
amplitude - 2
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2. Experimental results Foam-wall friction
Effect of bubble surface mobility
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Role of Surface Dilatational Modulus
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Effect of solution viscosity
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Scaling of the data with solution viscosity
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Thickness and shape of dynamic wetting films
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Profile of the upper film surface and film
thickness
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Film thickness vs. Capillary number
Capillary number
n 0.60
n 0.65
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Viscous friction inside sheared foam
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Effect of solution viscosity on viscous friction
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Scaling of the data with solution viscosity
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Effect of bubble surface mobility
1 wt Na Laurate 1 wt K Soap
3 wt Betaine 0 to 70 Glycerol
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Role of Surface Dilatational Modulus
Note ES is measured at oscillation frequency of
0.125 Hz n is given at air volume fraction ?
90
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3. Theoretical modeling of foam-wall friction
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Set of Equations to be Solved
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Numerical Results - Friction Force
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Relative contribution of the friction in the PB
region into the total friction force
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Effect of surface mobility
L
u(x)
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Effect of surface mobility on Film thickness
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• Experiments on viscous friction in foams
• Two cases (mobile and immobile) are distinguished
  again
• Effect of solution viscosity - scaling with Can
• Viscous friction inside sheared foams is still
  poorly understood

N. D. Denkov, V. Subramanian, D. Gurovich, A.
Lips, Wall Slip and Viscous Dissipation in
Sheared Foams Effect of Surface Mobility,
Colloids Surfaces A, in press.
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Acknowledgements

• Sofia University, Sofia, Bulgaria
• Dr. S. Tcholakova numerical calculations
• Mr. K. Golemanov experiments with wetting films

• Unilever RD, Edgewater, USA
• Dr. K. P. Ananth - useful discussions on
  surfactant properties
• Mr. P. Singh - help in rheological measurements
• Mr. C. Ho - measurements of surface dilatational
  modulus

Prof. H. Stone and Dr. H. Princen - for the
useful discussions on foam and emulsion rheology
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Method for Bubble size determination P. Garrett
et al., 1993
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2 wt K Soap solution
2 mm gap
3 mm gap
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Possible origin of different viscous dissipation
indexes, n, in emulsions and foams
Foams ?DR ? 100 s gt ?C Emulsions
?DR ? 50 ms ? ?C