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Hydrodynamic dispersion and diffusivity contrast govern the stability of a reaction front in porous media

Gourab Chakraborty, Vinod Narayanan, and Uddipta Ghosh*

  • *Contact author: uddipta.ghosh@iitgn.ac.in
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Phys. Rev. Fluids 11, 083904 – Published 17 August, 2026

DOI: https://doi.org/10.1103/fd77-rd4d

Abstract

Viscous fingering instabilities occurring at reactive mixing interfaces prevailing in porous media are often driven by concentration-dependent viscosity of the constituent fluids and play a vital role in several environmental and industrial processes. The stability of such reaction fronts is usually modeled at the Darcy scale, often under the pretense of a constant and identical molecular diffusivity of both the reactants and the product. However, at the Darcy scale, evolution of mixing interfaces is generally governed by hydrodynamic dispersion rather than molecular diffusion, while the diffusion coefficients of the various species involved are often distinct. Yet, their impact on the stability of a reaction front remains hitherto unexplored. As such, in this article we perform a linear stability analysis to unravel the role of dispersion on the stability of a bimolecular reaction front with regards to viscous fingering, where all species have distinct molecular diffusivities. The dispersion tensor is assumed to be linearly dependent on the local Darcy velocity, and the viscosity is assumed to vary exponentially with species concentrations. The stability of the front is analyzed using a transient approach where an initial value problem (IVP) is solved for the perturbations. A second approach using a quasi-steady-state approximation (QSSA) is also adopted as a reference case. We show that although the results from QSSA and IVP eventually converge at sufficiently large times, significant differences persist during the early stages, depending on the precise nature of viscosity variation. In particular, the results from the IVP approach show that both longitudinal and transverse dispersion tend to suppress the growth of perturbations. We further establish that the stability characteristics of the front become independent of the ratio between diffusion-to-advection timescales (the Péclet number) when hydrodynamic dispersion is taken into account. We demonstrate that diffusivity contrast between the product and the reactants may suppress or promote instability. Notably, it is shown that enhanced diffusivity of the product in scenarios where it is the most viscous element may stabilize an otherwise unstable front. The results shown here may be relevant to applications such as contaminant remediation, enhanced oil recovery, and carbon sequestration.

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Phys. Rev. Fluids 11, 083904– Published 17 August, 2026
  • Received 29 January 2026
  • Accepted 24 July 2026
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