Effect of nonlinear drag on the onset and the growth of the miscible viscous fingering in a porous medium

Kim, Min Chan

doi:10.1007/s11814-021-0954-6

Cited by 2 publications

(1 citation statement)

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“…The problem has been modelled by coupling the convection–diffusion equation for the solvent with the Darcy–Korteweg equation (Pramanik & Mishra 2013) for fluid flow velocity. Although the VF dynamics involving inertia effects by using Forchheimer's model (Joseph, Nield & Papanicolaou 1982) has recently been paid attention (Kim 2022), we, here, investigate the effect of on the VF dynamics by employing the Darcy–Korteweg equation, which has been used in several studies of VF with EIT. The model described by the Darcy–Korteweg equation can be governed by the following equations (Joseph & Renardy 1992; Pramanik & Mishra 2013, 2014, 2015 b ; Swernath et al.…”

Section: Problem Description and Governing Equationsmentioning

confidence: 99%

Numerical study of the effect of Péclet number on miscible viscous fingering with effective interfacial tension

Deki,

Nagatsu,

Mishra

et al. 2023

J. Fluid Mech.

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Viscous fingering or Saffman–Taylor instability shows fingering interfacial patterns when a more mobile fluid displaces a less mobile one in porous media. The effective interfacial tension (EIT) is like capillary force, acting at the miscible interface on time scales shorter than interface relaxation. It has been numerically reported so far that the fingers are wider with EIT compared with those without EIT. A recent experiment observed finger widening with increasing flow rate in a miscible system with EIT, which is not observed in classical immiscible and miscible systems. In this study, we have numerically investigated the effect of $Pe$ (which corresponds to the injection flow rates in the experiment) on miscible viscous fingering with/without EIT. We have shown that the fingers are monotonically thinner with an increase in $Pe$ in the system without EIT, while finger widening with increasing $Pe$ is observed in the system with EIT. Furthermore, we have also examined a one-dimensional underlying concentration profile and EIT profile by using a one-dimensional diffusion–convection model because EIT is proportional to the squared concentration gradient. We have then shown that the concentration gradient is steeper and, thus, the EIT is larger as $Pe$ is larger. Therefore, this is the first numerical study that can theoretically verify finger widening with increasing flow rate, which occurs only in a miscible system with EIT to the extent of our targeting EIT values, and explain the mechanism by one-dimensional analysis.

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