Prsentation PowerPoint

1
Sylvie Cohen-Addad, Reinhard Höhler,
Yacine Khidas
Interplay between interfacial rheology, bubble
rearrangements and the slow macroscopic
rheological response of aqueous foams
We have studied the slow linear viscoelastic
response of wet aqueous foams by macroscopic
creep compliance measurements, combined to a
diffusing-wave spectroscopy investigation of the
local dynamics. The data strongly suggest that
this rheological response arises from two
distinct relaxation mechanisms The first is due
to the coarsening induced bubble rearrangements
and governs the steady state creep, the second
results from the interplay between surface
tension and surface viscosity of the gas-liquid
interfaces and gives rise to a transient
relaxation.
Slow linear viscoelastic relaxations in
coarsening foams
Possible origins of the low frequency dissipation
Introduction

• At the film scale
• Fluid transport in films and Plateau borders
• Intrinsic surface viscosity of the gas-liquid
  interfaces
• Resistance to diffusion from the surfactant
• Buzza, Lu, Cates 1995 Edwards, Wasan 1996

Gillette foam Age ? 100 min
Cohen-Addad, Hoballah, Höhler PRE 1998
Data from Gopal, Durian PRL 2003

• At the mesoscopic scale
• Dissipation may be due to elastic energy
  irreversibly lost upon local structural
  rearrangements.
• Sollich et al PRL 1997 Hébraud et al PRL 1998
• Coarsening unjams foams.
• Gopal, Durian 2003

Linear elasticity described by Princen law
Surface tension
T1 rearrangement
Can coarsening induced rearrangements explain the
low frequency dissipation ?

• Static shear modulus
• Princen, Kiss 1986 Mason, Bibette, Weitz 1995
  Saint-Jalmes, Durian 1999

Mean bubble diameter
A simple mesoscopic steady creep model
Experiment Creep rheometry in situ DWS light
scattering
Response to a step stress
Samples
s 0

• Hypotheses
• The sample is subjected to constant shear
  stress s far below the yield stress.
• The stress is relaxed locally upon randomly
  dispersed coarsening induced rearrangements.
• Rearrangements have a characteristic volume V
  and occur at a rate R per units of volume and
  time.

• 92 gas volume fraction
• Different coarsening rates

Yield stress
time t
Fast
Intermediate
Applied stress s
Slow
time
Shear compliance J(t) g/s
DJ
Origin of the long time relaxation
Origin of the short time relaxation Scaling with
bubble size
Dt
Jeo
h1
time
J1
J1
Jeo Jo J1
Increase of compliance expected due to temporary
local loss of rigidity
DJ/Jeo ? R V Dt
Predicted creep rate R can be measured by
Diffusing Wave Spectroscopy R 1/(to Vo) V
should be of the order a few (bubble diameters)3
Volume fraction rearranged during a small time
interval Dt
J1 ? d same scaling as Princen law. h1 ? d-1
as predicted by Buzza et al. if dilatational
surface viscosity dominates the
dissipation. Characteristic time
scale t1 J1 h1 independent of d !

• Measured volume of a rearranged zone V ? (3
  d)3
• Agreement with the model

2D model of transient structural relaxation
Conclusions and outlook

• The viscoelastic dissipation in the linear
  regime, at low frequency, may indeed be explained
  by two well defined processes (no glassy dynamics
  !)

L
Forces acting on a Plateau border Edwards,
Brenner, Wasan (1991)
Creep deformation

• In the limit of long times, dissipation arises
  from elastic energy lost upon coarsening induced
  bubble rearrangements.
• At times of the order of a few seconds,
  dissipation arises from a structural relaxation
  which is governed by the interfacial rheology.

Surface tension
Dilatational surface viscosity
0
Time
Calculated relaxation time t1 ? k / T

• The contribution of the rearrangements to the
  slow rheological response is well modelised by a
  mesoscopic approach based on coarsening dynamics.
  A full understanding will require to consider
  film interfacial properties.

• Ultimate goal Understanding the link between
  local physico-chemical processes and macroscopic
  foam rheology.

Gillette t1 ? 5 s ? k ? 0.15 kg s-1 AOK
foams (sodium a- olefine sulfonate PEO
Dodecanol) t1 ? 3 s ? k ? 0.05 kg s-1
Consistent with values reported for
similar mixed surfactant systems Djabbarah,
Wasan 1982
This work was presented at the 5th European
Conference in foam, emulsions and applications,
Champs-sur-Marne, France, July 2004. Relevant
publication Cohen-Addad, Höhler, Khidas, Phys.
Rev. Lett. 92, 2004