Effects of Diffusion in Viscous Fingering Instabilities in Porous Medium Flows

Various fingering instabilities are observed in porous medium flows like enhanced oil recovery, CO2 sequestration, contaminant transport in aquifers [1] due to variation in fluid viscosity, density or the permeability of the porous medium. The finger like patterns ubiquitous during the displacement of a more viscous fluid by a less viscous one is a hydrodynamic instability called viscous fingering (VF) [1, 2]. A competition between the forces due to convection and diffusion results in different VF dynamics, wherein diffusion is known to stabilize the flow. An experimental observation of diffusion dominating convection during the later stages of the instability is reported by Chui et al. [2]. However, the effects of diffusion are expected to be strong when concentration gradients are high which occurs during initial stages of flow. Through state-of-the-art experiments, we report a diffusion driven zone during initial stages of the flow. We consider a radial displacement of miscible fluids using a point source as well as a finite source [3] in which the injected less viscous fluid is also present in a circle of finite radius inside the Hele-Shaw cell. The results are supported by performing non-linear simulations. References [1] G. M. Homsy, Annu. Rev. Fluid Mech., 19, (1987), 271-311. [2] J.Y.Y Chui, P. de Anna, R. Juanes, Phys. Rev. E, 92, (2015), 041003(R). [3] V. Sharma, S. Nand, S. Pramanik, C.-Y. Chen, M. Mishra J. Fluid Mech., 884, (2020), A16.