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Investigating Convective Instability in Quasi-2D Foams: Mechanisms and Characterization

This study explores the dynamics of convective instability in quasi-2D foams, considering interactions between liquid and foam structures. By introducing liquid on top of foam, we examine conditions leading to plastic flow in bubbles and analyze factors such as density variations, viscosity, and capillary diffusion. Our findings draw parallels between foam behavior and thermal convection, addressing critical parameters like yield stress, shear bands, and drainability. We utilize innovative imaging techniques to measure local volume fraction and velocity fields, paving the way for future studies on foam rheology and dynamics.

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Investigating Convective Instability in Quasi-2D Foams: Mechanisms and Characterization

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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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