CHEMICALLY-DRIVEN HYDRODYNAMIC INSTABILITIES. Anne De Wit Nonlinear Physical Chemistry Unit Université Libre de Bruxelles

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1 CHEMICALLY-DRIVEN HYDRODYNAMIC INSTABILITIES Anne De Wit Nonlinear Physical Chemistry Unit Université Libre de Bruxelles 1

2 Scientific questions Chemical reactions can induce changes in viscosity or density which, in turn, can lead to hydrodynamic flows. Hence questions raised are: In which conditions can chemical reactions be at the very origin of hydrodynamic instabilities and not merely passive scalars? What are the properties of the patterns that can then arise? Influence on transport and yield of reaction? 2

3 Outline of the talk 1. A+B C reaction fronts 2. Chemically-driven viscous fingering 3. Buoyancy-driven flows around reaction fronts 3

4 Outline of the talk 1. A+B C reaction fronts 2. Chemically-driven viscous fingering 3. Buoyancy-driven flows around reaction fronts 4

5 1) Reaction-diffusion A+B C fronts position of reaction front x f = position of maximum production rate kab r=b o /A o

6 Reaction-diffusion profiles of an A+B->C front Galfi-Racz predictions (Phys. Rev. A 38, 3151 (1988)) Case 1: immobile RD front D a = D b r=b o /A o =1 Position of the reaction front x f = 0

7 Case 2: moving RD front D a D b or r=b o /A o 1 Galfi-Racz scalings: the front moves with x f ~ t 1/2 A o > B o : front moves to the right (i.e. invades B) Beta=A o2 D A /B o2 D B

8 Outline of the talk 1. A+B C reaction fronts 2. Chemically-driven viscous fingering 3. Buoyancy-driven flows around reaction fronts 8

9 Viscous fingering instability The viscous fingering instability is a hydrodynamical instability that occurs when a low viscosity fluid displaces a more viscous fluid in a porous medium. The interface between the two fluids is unstable and develops fingers of the more mobile solution that invade the less mobile one. Fingering affects both immiscible solutions in which case surface tension must be taken into account miscible solutions for which dispersion plays a key role

10 Miscible VF driven by an A+B C reaction Injection of a reactant A into another reactant B of the same viscosity. At the interface, production of a more viscous product C by a simple reaction A+B C B injected into A A injected into B CTAB (B) injected into NaSal (A) NaSal injected into CTAB Podgorski, Sostarecz, Zorman, Belmonte, Phys. Rev. E, 76, (2007) Radial injection

11 Rectilinear displacement in a Hele-Shaw cell (R. Maes, ULB) CTAB injected into NaSal B injected into A NaSal injected into CTAB A injected into B

12 Rectilinear displacement

13 TheoreDcal model Injection speed U Reaction A+B C Reactants of same viscosity Th. Gérard and A. De Wit, Phys. Rev. E., 79, (2009)

14 A B Symmetric case A o =B o D A =D B C A B A Reaction rate ab

15 A injected into B: larger c gradient hence larger viscosity gradient A C B Asymmetric case B o =2 A o D A =D B Fingering more intense where the less concentrated solution invades the more concentrated one (A into B here) A B A

16 B injected into A: larger c gradient hence larger viscosity gradient A B C Asymmetric case B o = A o D A > D B Fingering more intense where the slowest species invades the quickest one (B into A here) A B A

17 Rectilinear displacement Here D A > D B B injected into A: more intense fingering

18 Outline of the talk 1. A+B C reaction fronts 2. Chemically-driven viscous fingering 3. Buoyancy-driven flows around reaction fronts 18

19 Experiments in vertical Hele-Shaw cells Density varies with concentrations (with C. Almarcha, P. Trevelyan and P. Grosfils, ULB)

20 Experiments in verdcal Hele- Shaw cells (with C. Almarcha, P. Trevelyan and P. Grosfils, ULB) Acid-base neutralization reaction HCl 0.01M A+B C HCl+NaOH NaCl + H 2 O NaOH 0.01M Initial contact line Visualization by interferometry

21 No Rayleigh- Taylor instability as acid is lighter than base here

22 TheoreDcal model R b,c : Rayleigh numbers = t hyd / t chem

23 No Rayleigh- Taylor instability as acid is lighter than base here Source of the instability: the fast diffusion of acid towards the lower layer creates a depletion zone where locally one has heavy over light flows due to a diffusive-layer convection mechanism

24 Reactive system Non reactive system The chemical reaction breaks the symmetry of the hydrodynamic instability patterns

25 AcDve role of the color indicator (with A. D Onofrio et al., Buenos Aires) Same experiment in presence of a color indicator: bromocresol green Acid HCl 0.01M Instability also in the lower layer due to an active role of the color indicator g A. Zalts et al. Phys. Rev. E 77, (2008) Base NaOH 0.01M

26 Conclusions

27 1) Viscous fingering 27