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 Cet article a éte moissonné depuis la source EDP Sciences

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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

[1] M. Alava, M. Dubé, M. Rost Imbibition in disordered media Adv. Phys 2004 83 175

[2] G.I. Barenblatt, V.M. Entov and V.M. Ryzhik, Theory of Fluid Flows Through Natural Rocks. Springer, Netherlands (1990).

[3] S. Berg, H. Ott Stability of CO2–brine immiscible displacement Int. J. Greenhouse Gas Control 2012 188 203

[4] J.U. Brackbill, D.B. Kothe, C. Zemach A continuum method for modeling surface tension J. Comput. Phys 1992 335 354

[5] D. Coumou, T. Driesner, S. Geiger, C.A. Heinrich, S. Matthäi The dynamics of mid-ocean ridge hydrothermal systems: splitting plumes and fluctuating vent temperatures Earth Planet. Sci. Lett 2006 218 231

[6] L. Cueto-Felgueroso, R. Juanes Nonlocal interface dynamics and pattern formation in gravity-driven unsaturated flow through porous media Phys. Rev. Lett 2008

[7] M. Hekmatzadeh, M. Dadvar, M. Sahimi Pore-network simulation of unstable miscible displacements in porous media Transp. Porous Media 2016 511 529

[8] A.O. Ivantsov, T.P. Lyubimova Dynamics of a liquid drop in porous medium saturated by another liquid under gravity J. Phys.: Conf. Ser 2016 012040

[9] V. Joekar-Niasar, S.M. Hassanizadeh Analysis of fundamentals of two-phase flow in porous media using dynamic pore-network models: a review Crit. Rev. Environ. Sci. Technol 2012 1895 1976

[10] L.W. Lake Enhanced oil recovery 1989

[11] D.V. Lyubimov, S.V. Shklyaev Instability of the motion of a drop in filtration flows Fluid Dyn 2005 777 784

[12] D.V. Lyubimov, S. Shklyaev, T.P. Lyubimova, O. Zikanov Instability of a drop moving in a brinkman porous medium Phys. Fluids 2009 014105

[13] D.V. Lyubimov, T.P. Lyubimova On a straight-through method of calculation for problems with deformable interface Model. Mech 1990 136 140

[14] D.V. Lyubimov, G.A. Sedel’Nikov Effect of vibration on the stability of a plane displacement front in a porous medium Fluid Dyn 2006 3 11

[15] P. Macneice, K.M. Olson, C. Mobarry, R. De Fainchtein, C. Packer PARAMESH: a parallel adaptive mesh refinement community toolkit Comput. Phys. Commun 2000 330 354

[16] D.A. Nield, A. Bejan Convection in Porous Media Convection in Porous Media 2017

[17] S. Osher, J.A. Sethian Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations J. Comput. Phys 1988 12 49

[18] H.S. Rabbani, D. Or, Y. Liu, C.-Y. Lai, N.B. Lu, S.S. Datta, H.A. Stone, N. Shokri Suppressing viscous fingering in structured porous media Proc. Natl. Acad. Sci 2018 4833 4838

[19] Y. Saad, M.H. Schultz, Gmres a generalized minimal residual algorithm for solving nonsymmetric linear systems SIAM J. Sci. Stat. Comput. 1986 856 869

[20] M. Sahimi, Flow and Transport in Porous Media and Fractured Rock. Wiley-VCH Verlag GmbH Co. KGaA (2011).

[21] V. Sharma, S. Nand, S. Pramanik, C.-Y. Chen, M. Mishra Control of radial miscible viscous fingering J. Fluid Mech 2020 A16

[22] M. Sussman, P. Smereka, S. Osher A level set approach for computing solutions to incompressible two-phase flow J. Comput. Phys 1994 146 159

[23] M. Trojer, M.L. Szulczewski, R. Juanes Stabilizing fluid-fluid displacements in porous media through wettability alteration Phys. Rev. Appl 2015

[24] C.-Y. Wang Fundamental models for fuel cell engineering ChemInform 2004

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