Fingering Dynamics in an Infinitely Fast Chemical Reaction Front in a Porous Medium

Viscous fingering (VF) instability is an archetype of pattern formation and is observed in diverse fields like enhanced oil recovery, chromatography separation, to name a few [1, 2]. It typically occurs when a less viscous fluid displaces another more viscous fluid in a porous medium deforming the interface into some rising and sinking fingers [1]. This hydrodynamic instability is a result of the competition of two forces due to convection and diffusion. When fluids are miscible and reactive, the chemical reaction influences the VF dynamics by modifying the viscosity profile. We consider an infinitely fast chemical reaction and model the dynamics using Darcys law and convection-diffusion-reaction equation incorporating instantaneous reaction term [3-5]. Moreover, the curvature of the interface plays an essential role in deciding the stability of the flow. A critical viscosity ratio exists for instability for radial flow, which does not appear in rectilinear flow [3]. We gain insight into VF dynamics by computing the onset of instability, when instability sets in. We obtain a transition in finger length for varying Peclet number (Pe) and viscosity ratios, which is not observed for slow or moderate reaction rates. References [1] G. M. Homsy, Annu. Rev. Fluid Mech., 19, (1987), 271-311. [2] H. E. Huppert, J. A. Neufeld, Annu. Rev. Fluid Mech., 46, (2014), 255-272. [3] S. H. Hejazi, P. M. J. Trevelyan, J. Azaiez, A. De Wit, J. Fluid Mech., 652, (2010), 501528. [4] V. Sharma, S. Pramanik, C.-Y. Chen, M. Mishra J. Fluid Mech., 862, (2019), 624-638. [5] Y. Nagatsu, A. De. Wit, Phys. Fluids 23(2009), 043103.