Control of radial miscible viscous fingering. (9th December 2019)

• Record Type: Journal Article
• Authors: Sharma, Vandita; Nand, Sada; Pramanik, Satyajit; Chen, Ching-Yao; Mishra, Manoranjan
• Is Part Of: Journal of fluid mechanics. Volume 884(2020)
• Publication Date: 2019-12-09
• Subjects: convection in porous media, -- Hele-Shaw flows, -- fingering instability; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2019.932
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : Abstract : We investigate the stability of radial viscous fingering (VF) in miscible fluids. We show that the instability is determined by an interplay between advection and diffusion during the initial stages of flow. Using linear stability analysis and nonlinear simulations, we demonstrate that this competition is a function of the radius $r_{0}$ of the circular region initially occupied by the less-viscous fluid in the porous medium. For each $r_{0}$, we further determine the stability in terms of Péclet number ( $Pe$ ) and log-mobility ratio ( $M$ ). The $Pe{-}M$ parameter space is divided into stable and unstable zones: the boundary between the two zones is well approximated by $M_{c}=\unicode[STIX]{x1D6FC}(r_{0})Pe_{c}^{-0.55}$ . In the unstable zone, the instability is reduced with an increase in $r_{0}$ . Thus, a natural control measure for miscible radial VF in terms of $r_{0}$ is established. Finally, the results are validated by performing experiments that provide good qualitative agreement with our numerical study. Implications for observations in oil recovery and other fingering instabilities are discussed.