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Convective Instability in quasi 2D foams

Convective Instability in quasi 2D foams. Eric Janiaud, Stefan Hutzler, Denis Weaire. Trinity College, Dublin. janiaude@tcd.ie. Convection in (3d) foams. Add liquid on top of a foam : if Q> Threshold: plastic flow of bubbles. L. Alonso. Gravity thought density variation.

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Convective Instability in quasi 2D foams

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  1. Convective Instabilityin quasi 2D foams Eric Janiaud, Stefan Hutzler, Denis Weaire. Trinity College, Dublin janiaude@tcd.ie

  2. Convection in (3d) foams • Add liquid on top of a foam : • if Q> Threshold: plastic flow of bubbles. L. Alonso

  3. Gravity thought density variation Gravity thought density variation + d + d Viscosity: energy dissipated in T1 Capillary diffusion: reduces density variation Plastic yield stress: capillary stress balances non uniform hydrostatic pressure Analogy with Thermal convection Driving force:  Damping:

  4. Heat diffusion Gaussian continuous media Newtonian liquid Liquid diffusion non linear(chemistry) Discrete network Yield stress+dilatency Difference with Thermal convection Ra = FArchimede/ Fviscosity Nu = Qconvection /Qno convection ? Pr = Dmvt / Dheat Pe = Tdiffusion / Tconvection

  5. Issues MixRheology and drainage Onset: dilatency, surfactants, bubble size,  gradient... After the onset : Shear bands, efficiency on liquid transport, size sorting...

  6. Decoration theorem: Quasi 2D in a Hele-Shaw: From 3D to 2D... 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 V~R2L • Film V~L2e • “Perpendicular” Plateau border V~R2d • Vertices V~R3 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. Q Q 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

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