Reaction Induced Kelvin-Helmholtz Roll-ups

  • Maharana, Surya (IIT Ropar, India)
  • Mishra, Manoranjan (IIT Ropar, India)

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Chemo-hydrodynamic instabilities in reactive porous media flows (in Darcy’s regime) have become a ubiquitous topic for their applicability in industries and environments [1]. It has been more than four decades, and instabilities such as Saffman–Taylor, and Rayleigh–Taylor instability are known to be induced by a chemical reaction. However, we have recently identified Kelvin-Helmholtz (K-H) instability as a Chemo-hydrodynamic instability that a chemical reaction can induce [2]. In a system away from Darcy’s regime, i.e., in a pressure-driven channel-flow governed by the Navier-Stokes equations, such K-H billows are found when a reactant A displaces another reactant fluid having the same viscosity following a simple A+ B→C reaction kinetics. Depending upon the product’s viscosity, K-H billows occur at either A-C or C-B reaction front [3]. To compare the non-reactive experiments [4] and see whether such K-H billows can be generated by the reaction if modifies the viscosity only at a particular transversal region instead of the entire channel height [2,3] we solve the same problem on a two-layer configuration. Indeed, the inflection points at A-C or C-B reaction front of the base velocity profiles explain why K-H billows occur at either A-C or C-B reaction front. This will be discussed in the talk. Moreover, it is noticed that the disturbance is amplified by phase locking of the multiple streamlines across the channel height. Further, the onset times of instability (t_on) are found through direct numerical simulations for various governing non-dimensional parameters such as the mobility ratio (R_c), Damköholer number (Da), Péclet number (Pe), and Reynolds number (Re). The plane spanned by t_on and R_c , shows that when Da, Pe, and Re are fixed, there are certain ranges of the mobility ratio (R_c) for which the flow remains stable within a finite desirable time. Thus, confirming the existence of a critical R_c value for the instability. Nevertheless, how this chemo-hydrodynamic K-H instability enhances the transverse spreading of the product fluid at an intermediate time shows the existence of a convection-dominated regime. A detailed parametric investigation will be presented on these flow dynamics. [1] A. De Wit. Ann. Rev. Fluid Mech. 52, 531, 2020. [2] S. N. Maharana and M. Mishra. J. Fluid Mech. 925, A3, 2021. [3] S. N. Maharana and M. Mishra. Phys. Fluids 34, pp. 012104, 2022. [4] X. Hu and T. Cubaud. . Phys. Rev. Lett. 121, pp 044502, 2018.