Liquid foam and soap filmvibrations

F. Elias, C. Derec, C. Gay, V. Leroy

S. Hutzler, W. Drenckhan

To make a foam:To make a foam: water,air,soap.

water

air

Soap? Surfactant Soap? Surfactant moleculemolecule::

Hydrophobic tail

Hydrophilichead

Liquid Foams

Inside aInside asoap soap foamfoam::

Gas Bubblesseparated by aLiquid structured matrix

Internal structure

Liquid foam: poroelastic material with soft pores

Complex macroscopicproperties

Manipulate the foam with a wave -> new materials?

Why studying the Acoustics of Liquid Foams?

Measurements of(ultra)sound wave

velocity and attenuation over large range of

frequencies

characteristics of the foam (structure + composition)

Φ, <R>, …

?

Fundamental: investigate the dynamical properties of liquid foams

Probe the foam with ultrasounds.

! =Volume of the liquid phase

Volume of the foam

Average bubblesize

How does a foam modify the acoustic wave?

1. Acoustic properties of a liquid foam

2. Liquid foam in a standing wave

How does an acoustic wave change the foam?

Experimental studies

Setup :Setup :

1. Acoustic properties of a liquid foam; Preliminary results

c

L

S R

Source S :

Receptor R :

tf

time

1/f (f = 40 kHz)

Measurement of the flight time of an acoustic pulse in the foam

-> c =tf

L

<R> = 60 mm

v v stronglystrongly dependsdepends on on ΦΦ : :

Effective medium (Wood):

cg : sound velocity in thepure gas

0

100

200

300

0 0.1 0.2 0.3

c

(m/s)

!

Gaz: N2

Gaz: C2F6

344

170

!

2cg"g

"l

Φ = 1 v = vl = 1480 m/s

v

v vg

vg

UltrasoundsUltrasounds to to measuremeasure ΦΦ? ? MeasurementMeasurement withoutwithout contact: contact:

Dilatancy of foams

65 m

m

shear

Steps of shear rate

Rotorvelocity

Flight time of anacoustic pulse

50 100

Δtf

The foam is wetter in thesheared zon

Dilatancy : Φ increases when the shear rate increases.

0

0,5

1

1,5

2

2,5

3

3,5

0 1 2 3 4 5

y = 0,050535 + 0,77879x R2= 0,9988

Time of flight difference (

µs)

Plate velocity (rad/s)

0

1

2

3

Rotor velocity(rad/s)

Δtf (ms)

dilatance

tfcΦ

Emittertransducer

receiver

(S.P.L.Marze, A. Saint Jalmes, D. Langevin, Coll. Surf. A 2005)

A more complex problem… Acoustics of liquid foam in the literatureThe acoustic properties strongly depend on the liquid volume fraction (Φ)…

1 kHz

5 kHz

air+water+sulfone (3%) <R>= 1 mmair+water+??? <R> = 70-125 µmair+water+expandol(6%) <R> = 100-200 µmGillette <R> = 30 µm

chemical composition, mean radius, frequency

Φ Φ

… But it is not the only parameter

A broadband transducer emits a short pulse in air, which is reflected on thesample, and received by another transducer

Broadband characterisation:

emitter

FOAM

A0A

the complex impedance can be determined

From the reflection coefficient

Broadband characterisation:

mean reflection coefficient as a function of frequency

for v = 60 m/s

v = 55±10 m/s

Using shaving foam:

More experiments needed on foams with controlled physico-chemistry.

Allows to measure v but α is not easily measurable

γΔ

ε =dγdA

ε = 0ε ≠ 0 ε = ε’ + i ε’’

A

ω τ < 1ω τ > 1

Interfacial viscoelasticmodulus

area Surfacetension

The interfacial elasticity of the liquid matrix should be importantat high frequency

Soft elasticity of the liquid matrix:

τ

Soap film suspended on a vibrated frame

-> Dispersion relation?

air

air l = 2π / k

V

e

Inertia of theliquid film

Inertia of air

2 mm

Existing model:

Afenchenko et al, Phys. Fluids 10 (1998), 390

γ

Effect of the interfacial elasticity?

0

2

4

6

8

0 5 10 15 20

e = 3002 nme = 1312 nme = 830 nme = 607 nme = 432 nm

e = 342 nme = 299 nme = 245 nmv_modèle

et

with

-> Experiments: f = 300 Hz -> 10 kHz:

vexp > vtheory at high frequency

More experiments needed, and more theory.

Setup: Standing acoustic wave + « Bamboo » foam in a tube

Tube(plexyglas)

L = 2 m

35 mm

Loudspeaker

(f ~ 100 - 10 000 Hz)Soap films

Observation : white light illuminationlight reflected by soap films -> light interferences

2. What does an acoustic wave on a foam?Liquid Foam in a standing wave

Vibration of the soap films:Vibration of the soap films:

In the displacement antinodes:Vibration and swelling of the soapfilms

Soap filmundulation

VerticalTube

Counter-rotativevortices

Self-adaptationof the soapfilm localthickness

Visualisation of the standing wave:Visualisation of the standing wave:

820 Hz

1060 Hz

1300 Hz

1640 Hz

0

10

20

30

40

50

60

0 10 20 30 40 50 60

!

m

easure

d

(c

m)

! = c/f (cm)

λ = c/f(cm)

1

Conclusion

Bamboo foam in a standing wave

Acoustic properties of liquid foams

1- Strongly depends on the liquid content, but not only.2- Lack of theoretical modelling.3- Need experimental data with:

Large frequency range, Controlled bubble size (and polydispersity),

Controlled chemistry -> controlled interfacial viscoelasticity.

Acoustics: promising technique to probe the foam.

The response of the foam to an acoustic wave is complex!