Convective Instability in quasi 2D foams

1
Convective Instabilityin quasi 2D foams
Eric Janiaud, Stefan Hutzler, Denis
Weaire. Trinity College, Dublin
janiaude_at_tcd.ie
2
Convection in (3d) foams

• Add liquid on top of a foam
• if Qgt Threshold plastic flow of bubbles.

L. Alonso
3
Analogy with Thermal convection

• Driving force

???
Damping
4
Difference with Thermal convection

• Heat diffusion
• Gaussian
• continuous media
• Newtonian liquid

• Liquid diffusion
• non linear(chemistry)
• Discrete network
• Yield stressdilatency

Ra FArchimede/ Fviscosity
Nu Qconvection /Qno convection
?
Pr Dmvt / Dheat
Pe Tdiffusion / Tconvection
5
Issues

• Mix Rheology and drainage
• Onset
• dilatency, surfactants, bubble size, ?
  gradient...
• After the onset
• Shear bands, efficiency on liquid transport,
  size sorting...

6
From 3D to 2D...

• Decoration theorem

• Quasi 2D in a Hele-Shaw

Film
Vertex decorated
Pseudo Plateau Border
Drainage is possible !
No liquid flow between vertex
7
Quasi 2D foams in Hele-Shaw cell
8
What is the Volume fraction?

• Wetting Plateau border
• VR2L
• Film
• VL2e
• Perpendicular
• Plateau border
• VR2d
• Vertices
• VR3

Cox
Needs experiments and Evolver Simulations
9
Hele-Shaw Cell setup

• Sensitive to the wetting film
• Bidisperse foam
• Area 90 and 130 pixel

Q
Projector
10
Steady state Drainage

• Injection point
• Uniform free convection
• Local forced convection

What is the caracteristic length for roll?
What is the solution to the drainage equation?
11
Local injection
Q
12
Vertical Velocity
3 pictures
Velocity (pi/s)
Horizontal coordinate (pi)
Smooth profile No shear Band
13
Non uniform liquid Fraction
How to measure the volume fraction?
14
Image Analysis Vertices
Velocity tracking bubbles T1 neighbourhood
relations Local Volume fraction ration of
Pixel Stress/Strain field Vertex
position Capillary pressure curvature measurement
15
Plugin for ImageJ

• Public/free Java software
• developed by the NIH
• Object oriented
• easy implementation
• Already rich
• Multiplatform

16
Perspectives

• Forced 2D convection
• impose and measure ?
• measure the velocity field
• Free 2D convection
• homogenous liquid input !!!
• boundary conditions !!!
• destabilisation length?
• Back to 3D convection