Geodesic
Control of fingering instability by vibrations
Tatyana Lyubimova1, 2 ; Andrey Ivantsov1, 2 ; Dmitry Lyubimov2
1 Institute of Continuous Media Mechanics, UB RAS, 1 Koroleva Str., 614013, Perm, Russia.
2 Perm State University, 15 Bukireva Str., 614990 Perm, Russia.
Mathematical modelling of natural phenomena, Tome 16 (2021), article no. 40.

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In applications involving the injection of a fluid in a porous medium to displace another fluid, a main objective is the maximization of the displacement efficiency. Displacement fronts moving in porous media are subjected to hydrodynamic instability when a liquid of low viscosity displaces a high-viscosity liquid and consequently finger-like structure forms along the interface. This finger instability is usually undesirable in technical applications and natural filtration processes. We discuss the external periodic forcing as one of the promising ways to control the instability and perform numerical simulation of an initially spherical drop in a porous media under vertical vibrations. The drop is a favorable object to study since in this case one can observe the effect of vibrations on fluid interface domains inclined by different angles with respect to vibration axis. It is shown that under vibrations small-scale perturbations of interface are suppressed and in the case of vibrations of large enough intensity the drop becomes stable. The stability criterion is derived.
DOI : 10.1051/mmnp/2021031

Tatyana Lyubimova 1, 2 ; Andrey Ivantsov 1, 2 ; Dmitry Lyubimov 2

1 Institute of Continuous Media Mechanics, UB RAS, 1 Koroleva Str., 614013, Perm, Russia.
2 Perm State University, 15 Bukireva Str., 614990 Perm, Russia. 
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Tatyana Lyubimova; Andrey Ivantsov; Dmitry Lyubimov. Control of fingering instability by vibrations. Mathematical modelling of natural phenomena, Tome 16 (2021), article  no. 40. doi : 10.1051/mmnp/2021031. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/2021031/

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