FOAM DRAINAGE part 3

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Suzanna Bailey
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1 FOAM DRAINAGE part 3 gas effect : coupling coarsening and drainage () C 2 F 6 :almost «insoluble», so no coarsening N 2 : much more soluble, significantly faster coarsening Free-drainage, liquid fraction at a given position : Free-drainage, height of drained liquid : ε / ε C 2 F 6 L / L f N 2 wet dry C 2 F 6.2. N 2 Time (s) t(s) strong effect of the gas on the drainage speed!

gas effect : coupling coarsening and drainage (2) coarsening time : drainage time : R 2 τc 2Df( ε) µ H R ε τd 2 τ c/ τd 4 µ H ε D R f( ε) t c / t d >> : low coarsening during drainage t c / t d << :

2 gas effect : coupling coarsening and drainage (2) coarsening time : drainage time : R 2 τc 2Df( ε) µ H R ε τd 2 τ c/ τd 4 µ H ε D R f( ε) t c / t d >> : low coarsening during drainage t c / t d << : strong coarsening DURING drainage coupling between both effects acceleration of drainage In the extreme case : all drainage is controlled by coarsening + no more dependance with ε gas effect : coupling coarsening and drainage (3) Height effect : τ c/ τd 4 µ H ε D R f( ε) Drainage time for different liquid fractions : t c / t d << : no more dependence on ε foam sample height t c / t d >> : dependence with ε Note that one can already reduce coarsening with only traces of an insoluble gas added to a soluble one

3 Container shape effect the sample cross-section A is not always constant : conservation equation : ε + t (uε) + z (uε) A A z = a special case : drainage in an Eiffel Tower... liquid fraction profiles : A = cst Eiffel tower A(z) = A exp(z/ z ) z, g height with that shape, one should get no vertical gradients during drainage... dry wet dry wet Bulk viscosity effect: Newtonian and Non-Newtonian fluids newtonian fluids (glycerol-based) : PB resistance R pb when viscosity µ, as M µ r M = µ s R pb.7 v = R pb ρgd µ 2 ε R pb.4.2 glycerol Xanthan carbopol shear viscosity (mpa.s) shear-thinning fluids : same as Newtonian, as soon as one uses an effective viscosity : the one associated to the shear rate occuring inside the foam

4 Non-gravitational drainage () on ground : gravity B = > capillarity the flow is mainly controlled by gravity +. g - = + ε ε ε τ ε λ 3/ 2 λ 2 hypothesis valid for dry foams Experimental limits for wet foams : convective instability A forced-drainage in microgravity? B << the flow is then only due to capillary effects wet Liquid dry Parabolic flights? 2 sec. of µg at each parabola 3 parabolas / flight 3 flights / session

$liquid fraction,24,2,6,2,8 very high liquid fractions ε time t = 4s t = 7s t = s t = 3s t = 5s t = 7s front position (m),8,4 Q,6 A t /2,4 2 3 4 5 6 7 8 9 R (mm),4$

5 Continuous flowrate, injected in point : Non-gravitational drainage (2) 3D foam, in a flat cell isotropic propagation? Liquid limits at different times : 4s 7s s 5s Dry foam (white) Non-gravitational drainage (3) liquid profiles :,28 Front behavior : Theory : R /6 / 2 f = K Q t ε, liquid fraction,24,2,6,2,8 very high liquid fractions ε time t = 4s t = 7s t = s t = 3s t = 5s t = 7s front position (m),8,4 Q,6 A t /2, R (mm), Q (ml/min) µg time (s) A, Q /6 agreement with the g= drainage equations at low ε still some agreement with the g= drainage equations at high ε no convective instabilities in micro-gravity...

Thin film drainage Reynolds equation for thin film drainage

zones black film coloured film «marginal regeneration» (Mysels)

Aradian thesis) horizontal film held on a support (suction by

The dimple is finally «sucked» into the PB : In a symmetric way

6 Thin film drainage Reynolds equation for thin film drainage speed (large thickness, without disjoining forces) : V = 3 2h p 2 3µ R Almost never work! vertical film on a frame : for very mobile surfaces turbulent zones black film coloured film «marginal regeneration» (Mysels) (Drawings from A. Aradian thesis) horizontal film held on a support (suction by PBs) : Thin film drainage (2) Large film diameter : «dimple» The dimple is finally «sucked» into the PB : In a symmetric way : signature of low surface mobility In a single point : signature of high surface mobility small film diameter : no dimples, no circulation, flat thin film

of the interfacial mobility (also similar experiments by E. Janiaud, F.

7 Flow in a single PB O. Pitois, C. Fritz, M. Adler, MLV (O. Pitois, C. Fritz, M. Adler, Coll. Surf. A, 25) Measurements of PB cross section, as a function of Q Measurements of the pressure drop over a single PB : Effect of the interfacial mobility (also similar experiments by E. Janiaud, F. Elias, Paris 6) Flow in PBs between glass plates W. Drenckhan, TCD Measurements of the PB size vs Q : for different surface properties. µ r M = µ With this setup : mostly high values of M s M = M =

$4.2 time.2.4.6.8 bottom position top Time = Time = and assuming mass conservation, one can recovers the liquid fraction evolution ε (z, t).$ important results to remember (ask me for complete references on these results) - take care of the effect of coarsening during drainage!

important results to remember (ask me for complete references on these results) - take care of the effect of coarsening during drainage!

8 «If you were a bubble, in a draining foam» During drainage : the bubble move upward Following the position of markers in the foam : time = FOAM normalized displacement time bottom position top Time = Time = and assuming mass conservation, one can recovers the liquid fraction evolution ε (z, t). important results to remember (ask me for complete references on these results) - take care of the effect of coarsening during drainage! - First steps of drainage of a thin film towards its equlibrium value is quite complex (dimples, marginal regeneration, ). Many dynamic effects, which also depends on the film size. - Experiments on isolated structures (like single PB, 2 PBs, single thin film) are usually consistent with macroscopic measurements in foams, and are quite useful. - Experiments in microgravity : a lot of fun!

THE PHYSICS OF FOAM. Boulder School for Condensed Matter and Materials Physics. July 1-26, 2002: Physics of Soft Condensed Matter. 1.

THE PHYSICS OF FOAM. Boulder School for Condensed Matter and Materials Physics. July 1-26, 2002: Physics of Soft Condensed Matter. 1. THE PHYSICS OF FOAM Boulder School for Condensed Matter and Materials Physics July 1-26, 2002: Physics of Soft Condensed Matter 1. Introduction Formation Microscopics 2. Structure Experiment Simulation