Light Propagation in

FoamsMirFaez Miri

Insitute for Advanced Studies in Basic Sciences, Zanjan, Iran

Multiple Scattering

wet foamGillette shaving cream dry foam

Foams

Durian et. al., PRA 1991, 44, R7902 Physics of Foams, Weaire and Hutzler

Metallic Foams

• Drainage– gravity– pressure gradient

• Coarsening– diffusion of gas

F

V

• DWS (Diffusing Wave Spectroscopy)

• In soft materials, the speckles fluctuate due to the microscopic motion in the media.

• Local dynamic properties can be studied by intensity autocorrelation function.

])6(2exp[)( 210,1 τττ −≈Bg

)6sinh(6)(,1 τ

ττΓ

Γ≈Tg

0

2 1)(τ∗=Γ

lL

For Brownian particles

• These shapes are identical to those obtained for diffusing Brownian particles,despite the absence of any such motion.

A) Transmitted lightexponential in

B) Backscattered light exponential in tt

DWS results for foamDurian et. al., Science, 1991, 687, vol 252

• coarsening

• capillary waves ?

• Brownian motion of the bubbles ?

ztd α 45.0=z

Durian et. al., PRA 1991, 44, R7902

rearrangement

1.02 ±=

−

γα γtRdl ∝∗

301

Rrt ∝

dr∝

30

1∗∝

ltR

Durian et. al., PRA 1991, 44, R7902Durian et. al., Science, 1991, 687, vol 252

reflectance r

1. MirFaez Miri and Holger Stark, Phys. Rev. E 68 (2003) 031102.

2. MirFaez Miri and Holger Stark, Europhysics Letters, 65 (2004) 567.

n=1.34 (water)

( )( )2 2,1.81,0.4

μ η

=

4. MirFaez Miri, Ebrahim Madadi, and Holger Stark,

Phys. Rev. E 72, (2005) 031111.

NEW!

fresnel‘s formula =r (i )

)(.

).)(.()( ∗∗∗

∧∗

∧

∗ −+= ppsspp rrrrEE

bEbErrir

θcos1−=

∗∗ sll

iifitiir

2sin)(0cos)()2cos()(cos

=

+−= πθ

Hs 7.0* =l

4. MirFaez Miri, Ebrahim Madadi, and Holger Stark,

Phys. Rev. E 72, (2005) 031111.

* / al

M.U. Vera, A. Saint-Jalmes & D.J. Durian,Appl. Optics (2001)

FUTURE

TOPOLOGY1.MirFaez Miri and Nicolas Rivier, The equilibrium state of 2D foams, Europhysics Letters, 54 (2001) 112.

2. MirFaez Miri and Nicolas Rivier, Universality in two-dimensional cellular structures evolving by cell division and disappearance, Phys. Rev. E 73, (2006) 031101.

OPTICS3. MirFaez Miri and Holger Stark, Persistent random walk in a honeycomb structure: Light transport in foams,

Phys. Rev. E 68 (2003) 031102.

4. MirFaez Miri and Holger Stark, The role of liquid films for light propagation in dry foams, EurophysicsLetters, 65 (2004) 567.

5. MirFaez Miri and Holger Stark, Modelling light transport in dry foams by a coarse-grained persistent random walk, J. Phys. A. 38, (2005). 3743

6. MirFaez Miri, Ebrahim Madadi, and Holger Stark, Diffusive Transport of Light in a Kelvin Foam, Phys. Rev. E 72, (2005) 031111.

7. M. Schmeideberg, MirFaez Miri and Holger Stark, Photon Channeling in Foams, Eur. Phys. J. E 18, (2005) 123.

8. MirFaez Miri, Zeinab Sadjadi, and Ebrahim Fouladvand, Persistent random walk on

A site-disordered one-dimensional lattice, Phys. Rev. E 73, 031115 (2006)