Self-Organized Traveling Chemo-Hydrodynamic Fingers Triggered by a Chemical Oscillator

Abstract

Pulsatile chemo-hydrodynamic patterns due to a coupling between an oscillating chemical reaction and buoyancy-driven hydrodynamic flows can develop when two solutions of separate reactants of the Belousov−Zhabotinsky reaction are put in contact in the gravity field and conditions for chemical oscillations are met in the contact zone. In regular oscillatory conditions, localized periodic changes in the concentration of intermediate species induce pulsatile density gradients, which, in turn, generate traveling convective fingers breaking the transverse symmetry. These patterns are the self-organized result of a genuine coupling between chemical and hydrodynamic modes. SECTION: Liquids; Chemical and Dynamical Processes in SolutionO ut-of-equilibrium, breaking of symmetries and related spatiotemporal patterns have been much studied in hydrodynamic and reaction−diffusion (RD) systems. 1−3 At the intersection between these two fields, chemo-hydrodynamics focuses on analyzing patterns and instabilities that result from a nonlinear coupling of hydrodynamic and RD processes. 4 Related problems range from fingering instabilities of reactive interfaces 5,6 or traveling chemical fronts 4 to the spatiotemporal dynamics of chemicals advected in complex flow fields. 7,8 The reaction−diffusion−convection (RDC) interplay impacts numerous applications areas as diverse as combustion, 9 polymer processing, 10 extraction techniques 5,11 and CO 2 sequestration. 12 When chemicals are passively slaved to the flow, the convective motions develop independently of the presence of reactive processes. On the other hand, in presence of active chemistry, the reactions modify a physical property of the fluid like its density, viscosity, or surface tension for instance. Concentration gradients in RD processes can then trigger unfavorable mobility gradients, which in turn can yield convection. As an example, even when starting from an initially stable density stratification of a less dense reactive solution on top of a denser one in the gravity field, chemical processes can trigger buoyancy-driven convection. This occurs when the reaction produces either a denser product locally or when differential diffusion phenomena implying the various chemicals 6,13−16 or heat and mass 17 come into play. The hydrodynamic patterns are then typically convective fingers growing vertically. Simple A+B→ C reactions have been shown to be able to break the up−down symmetry of such convective fingers. 13 More complex reactions prone to produce spatiotemporal RD structures can induce other synergetic combinations of chemical and hydrodynamic modes. Typical examples of such intrinsic chemo-hydrodynamic scenarios include reaction-driven convection around a traveling chemical front stably stratified from both solutal and thermal perspectives 4,17,18 and buoyancy or Marangoni-induced convective cells following chemical waves in excitable and oscillatory systems. 19−23 In such cases, the chemical kinetics drives the source of the convective flows, and the velo...

Reaction-driven oscillating viscous fingering

“…10,11 It would be very nice to be able to couple viscous e ects with the canonical oscillating Belousov-Zhabotinky reaction around an A + B → oscillator con guration. 17 While coupling of BZ localized oscillations in this con guration has already been done successfully for buoyancy-driven e ects, 16,24 it still remains to see how to obtain large viscosity changes in the BZ system. We hope that the current work will trigger future e orts in this direction.…”

“…14,15 Chaos ARTICLE scitation.org/journal/cha Recently, special attention has been put on understanding how localized temporal oscillations of chemical concentrations can also actively couple to hydrodynamic ows to produce pulsatile ows. [16][17][18] Localized oscillations 19 or stationary Turing patterns 20,21 can be obtained in autocatalytic reactions around A + B → oscillator fronts when putting in contact two zones containing separate reactants A and B of an oscillatory reaction. 17,18,22,23 From the theoretical point of view, it has been shown that localized oscillations and Turing structures can interact with buoyancy-driven ows when the reactants A and B of the oscillatory Brusselator model are initially separated, meet by di usion, and produce the intermediate X and Y species locally, which changes the density.…”

“…18 Experimentally, interplay between the oscillating Belousov-Zhabotinsky (BZ) reaction and buoyancy-driven motions has been analyzed when two subsets of the reactants are put in contact along a horizontal line in the gravity eld. 16,24 With regard to the viscous ngering instability occurring when a less viscous solution displaces a more viscous one in a porous medium or Hele-Shaw cell (two glass plates separated by a thin gap), interplay with an oscillating reaction can be obtained only if the reaction induces su cient viscosity changes. Using pH-sensitive polymers, Escala et al have recently obtained a clock type change of viscosity thanks to a coupling with a pH clock reaction.…”

Back and forth invasion in the interaction of Turing and Hopf domains in a reactive microemulsion system

“…Experiments putting into contact active media have been recently reported where the reagents of the chemical oscillator, the Belousov-Zhabotinsky reaction, have been initially separated into two adjoined parts 8,9 . For instance the interaction of Turing and Hopf bifurcations can produce mixed states such as oscillatory Turing patterns or the coexistence of stable local domains supporting different a Université Libre de Bruxelles (ULB), Non-linear Physical Chemistry Unit, Service de Chimie Physique et Biologie Theorique, CP231, Campus Plaine, 1050, Brussels, Belgium; E-mail: jcarball@ulb.ac.be ‡ These authors contributed equally to this work dynamics but also more complex structures such as spatiotemporal chaos 1,3-5 .…”

Chemical convection in the methylene-blue–glucose system: Optimal perturbations and three-dimensional simulations

“…For compositional gradients parallel to gravity, let us mention the acidbase reaction with convection due to density effects [7][8][9][10], autocatalytic fronts [11,12], and, recently, oscillating chemical reactions [13]. For a compositional gradient perpendicular to gravity, different reaction schemes have been studied with buoyancy effects [14] as well as Marangoni effects occurring at an interface with another physical domain (e.g., an air layer) which is not involved in the chemical process [15,16].…”