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Control of radial miscible viscous fingering

Published online by Cambridge University Press:  09 December 2019

Vandita Sharma Open the ORCID record for Vandita Sharma [Opens in a new window] ,
Sada Nand ,
Satyajit Pramanik Open the ORCID record for Satyajit Pramanik [Opens in a new window] ,
Ching-Yao Chen Open the ORCID record for Ching-Yao Chen [Opens in a new window]  and
Manoranjan Mishra Open the ORCID record for Manoranjan Mishra [Opens in a new window]
Vandita Sharma
Affiliation:
Department of Mathematics, Indian Institute of Technology Ropar, 140001Rupnagar, India
Sada Nand
Affiliation:
Department of Mathematics, Indian Institute of Technology Ropar, 140001Rupnagar, India
Satyajit Pramanik
Affiliation:
NORDITA, Royal Institute of Technology and Stockholm University, SE 106 91Stockholm, Sweden
Ching-Yao Chen*
Affiliation:
Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan, 30010Republic of China
Manoranjan Mishra*
Affiliation:
Department of Mathematics, Indian Institute of Technology Ropar, 140001Rupnagar, India
*
†Email addresses for correspondence: chingyao@mail.nctu.edu.tw, manoranjan@iitrpr.ac.in
†Email addresses for correspondence: chingyao@mail.nctu.edu.tw, manoranjan@iitrpr.ac.in
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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.

JFM classification

Convection: Convection in porous media Low-Reynolds-number flows: Hele-Shaw flows Interfacial Flows (free surface): Fingering instability

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 884 , 10 February 2020 , A16
Copyright
© 2019 Cambridge University Press

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