Abstract: The study of hydrodynamic instabilities in a stratified flow has gained significant attention in the scientific community for its applications in industries and environments [1, 2, 3]. Viscous fingering(VF) instability occurs when a less viscous fluid tries to push a more viscous one in the porous media or Hele-Shaw cell, where the flow equations are expressed by a simple empirical rule known as Darcy’s law. Far from Darcy’s flow regime, i.e., in a pressure-driven flow governed by the Navier-Stokes equations, if fluid flows in a channel uniformly in the vertical direction for a long time, the flow reaches a steady state with a fully developed parabolic velocity profile. Moreover, with this velocity profile that has a shear or a vertical gradient, if a less viscous fluid pushes a more viscous one, Kelvin-Helmholtz-type Instability (KHI) is encountered alongside the pure diffusive miscible VF [3]. Such KHI is found when a reactant A displaces another reactant fluid having the same viscosity following a simple A+ B→C reaction kinetics [4]. The governing equations become a set of coupled non-linear PDEs, which are solved using a diffuse interface finite volume method. Depending upon the product’s viscosity, K-H billows occur at either A-C or C-B reaction front [4]. The detailed modeling phenomena in comparison to the corresponding Darcy’s regime VF [6,7] will be discussed in this seminar.
REFERENCES
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[4] S. N. Maharana and M. Mishra. J. Fluid Mech. 925, A3, 2021.
[5] S. N. Maharana and M. Mishra. Phys. Fluids 34, pp. 012104, 2022.
[6] V. Sharma et. al J. Fluid Mech. (2019), vol. 862, pp. 624-638.
[7] P. Verma, V. Sharma and M. Mishra J. Fluid Mech. (2022), vol. 945, A19.