ISSN: 0304-128X ISSN: 2233-9558
Copyright © 2024 KICHE. All rights reserved


Conflict of Interest
In relation to this article, we declare that there is no conflict of interest.
Publication history
Received December 3, 2023
Revised December 26, 2023
Accepted December 27, 2023
articles This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright © KIChE. All rights reserved.

Most Cited

Numerical Simulation on the Onset of Radial Fingering in a Hele-Shaw Cell or a Porous Medium

Jeju National University
Korean Chemical Engineering Research, February 2024, 62(1), 112-117(6), 10.9713/kcer.2024.62.1.112 Epub 1 February 2024
downloadDownload PDF


Numerical simulations on the onset and the growth of viscous fingering during the miscible displacement due to the radial source flow were conducted. With introduction of a new stability criterion, the critical log-viscosity ratio, Rc, was found as a function of the Peclet number, Pe. Similar to the previous linear stability analyses, Pe made the system unstable, i.e., accelerated the onset of instability. For a large Pe system, the present numerical simulation yielded much stable results than the previous theoretical predictions This discrepancy was commonly encountered in the comparison between the theoretical prediction and the experimental finding. Additionally, the difference between the rectilinear system and the present one was also discussed. The present system was found more insensitive to the Peclet number than the rectilinear one.


1. Homsy, G. M., “Viscous Fingering in Porous Medium,” Ann. Rev.
Fluid Mech. 19, 271(1987).
2. Tan, C. T. and Homsy, G. M., “Stability of Miscible Displacements
in Porous Media: Radial Source Flow,” Phys. Fluids 30,
3. Pritchard, D., “The instability of Thermal and fluid Fronts During
Radial Injection in a Porous Medium,” J. Fluid Mech. 508, 133
4. Kim, M. C., “Onset of the Radial Viscous Fingering in a Hele-
Shaw Cell,” Korean J. Chem. Eng. 29, 1688(2012).
5. Kim, M. C., “Some Analytical Aspects of the Radial Fingering
in Porous Medium,” Z. Angew. Math. Phys. 63, 713(2012).
6. Sharma, V., Nand, S., Pramanik, S., Chen, C.-Y. and Mishra, M.,
“Control of Radial Viscous Fingering,” J. Fluid Mech. 862, 624
7. Nand, S., Sharma, V., Das, S. K., Padhee, S. S. and Mishra, M.,
“Effect of Hele-Shaw Cell Gap on Radial Viscous Fingering,”
Scientific Reports 12, 18967(2022).
8. Kim, M. C., “Effect of Nonlinear Drag on the Onset and the
Growth of the Miscible Viscous Fingering in a Porous Medium,”
Korean J. Chem. Eng. 39, 548(2022).
9. COMSOL AB, Comsol multiphysics v. 5.4 reference manual
10. Kim, M. C., Pramanik, S., Sharma, V. and Mishra, M., “Unstable
Miscible Displacements in Radial flow with Chemical Reactions,”
J. Fluid Mech. 917, A25(2021).
11. Sharma, V., Othman, H. B., Nagatsu, Y. and Mishra, M. “Viscous
Fingering of Miscible Annular Ring,” J. Fluid Mech. 916, A14
12. Kim, M. C., “Theoretical and Numerical Studies on the Interface
Movement and the Onset of Gravitational Instability During
the Carbon Dioxide Dissolution Into Oil,” Phys. Fluids 34, 024102
13. Kim, M. C. and Pramanik, S., “Miscible Viscous Fingering in a
Packed Cylindrical Column: Theory and Numerics,” Phys. Rev.
Fluids 8, 013901(2023).
14. Hong, J. S. and Kim, M. C., “Theoretical and Numerical Studies
on Dissolution of Horizontal Salt Body and Pattern Formation
Incorporated with a Dynamic Moving Interface,” J. Fluid
Mech. 960, A6(2023).
15. Hong, J. S. and Kim, M. C., “Gravitational Fingering and Droplet
Formation During the Phase Separation of a Partially Miscible
Binary Mixture in a Vertical Hele-Shaw Cell,” Int. J. Heat Mass
Transfer 201, 123665(2023).
16. Kim, M. C., “Numerical Simulations on Thermocapillary Flow on
Heated Sinusoidal Topography,” Korean J. Chem. Eng. (2024).
17. Jha, B., Cueto-Felgueroso, L. and Juanes, R., “Fluid Mixing from
Viscous Fingering,” Phys. Rev. Lett. 106, 194502(2011).
18. Verma, P., Sharma, V. and Mishra, M., “Radial Viscous Fingering
Induced by An Infinitely Fast Chemical Reaction,” J. Fluid Mech.
945, A19(2022).
19. Ryoo, W. S. and Kim, M. C., “Linear and Non-linear Analyses
on the Onset of Miscible Viscous Fingering in a Porous Medium,”
Korean J. Chem. Eng. 35, 1423(2018).
20. Perkins, T. E., Johnston, O. E. and Hoffman, R. N., “Mechanics
of Viscous Fingering in Miscible Systems,” Soc. Pet. Eng. J., 5,

The Korean Institute of Chemical Engineers. F5, 119, Anam-ro, Seongbuk-gu, 233 Spring Street Seoul 02856, South Korea.
Phone No. +82-2-458-3078FAX No. +82-507-804-0669E-mail :

Copyright (C) KICHE.all rights reserved.

- Korean Chemical Engineering Research 상단으로