Author(s)

Jingying Wei ¹

Affiliation(s)

¹ School of Applied Physics, Chengdu University of Technology, Chengdu, 610059, China

Corresponding Author

Jingying Wei

ABSTRACT

In porous media, when a low-viscosity fluid displaces a high-viscosity fluid, the phenomenon of viscous fingering is formed due to the instability and nonlinear effect at the interface of the two phases, which exhibits a complex branching structure and self-similarity. In numerical simulations, the Hele-Shaw model is often used to simulate the replacement phenomenon in porous media, and the fractal evolution of viscous fingering can also be observed. Based on the two-phase Darcy's law, this paper investigates the influence parameters and fractal differences related to the Hele-Shaw model for the radial injection of miscible two-phase under an annular boundary, in terms of the spreading area and the boundary length. The analytical results show that with the increase in log-viscosity ratio, a tendency of more elongated finger structures and a consequent increase in the number of bifurcations of the main branches are observed. Meanwhile, the decrease in diffusion coefficient led to a more complex fractal structure and further enhanced the splitting effect. In addition, the higher injection rate of the replacement fluid extends the spreading range of the interface, which increases the complexity of the finger structure and the number of "fingers". These results highlight the significant influence of convection and diffusion parameters on the morphology and dynamics of multiphase fluid interfaces and provide important theoretical support for understanding and controlling related engineering and environmental processes.

KEYWORDS

Fractal Finger, Viscous Fingering, Hele-Shaw, Annular Boundary

CITE THIS PAPER

Jingying Wei, Numerical study of viscous fingering patterns under annular boundaries based on the Hele-Shaw model. Modern Physical Chemistry Research (2024) Vol. 4: 81-87. DOI: http://dx.doi.org/10.23977/mpcr.2024.040111.

REFERENCES

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[2] Pramanik S, Mishra M. Comparison of Korteweg stresses effect on the fingering instability of higher or less viscous miscible slices: Linear stability analysis [J]. Chemical Engineering Science, 2014, 110: 144-152.
[3] Deki Y F, Nagatsu Y, Mishra M, et al. Numerical study of the effect of Peclet number on miscible viscous fingering with effective interfacial tension [J]. Journal of Fluid Mechanics, 2023, 965: A22.
[4] Nand S, Sharma V, Das S K, et al. Effect of Hele–Shaw cell gap on radial viscous fingering [J]. Scientific Reports, 2022, 12(1): 18967.
[5] Sharma V, Othman H B, Nagatsu Y, et al. Viscous fingering of miscible annular ring [J]. Journal of Fluid Mechanics, 2021, 916: A14.
[6] Mishra M, Martin M, De Wit A. Differences in miscible viscous fingering of finite width slices with positive or negative log-mobility ratio [J]. Physical Review E, 2008, 78(6): 066306.

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