Abstract
The goal of the present study is to investigate analytically, numerically and experimentally the instability of the displacement of viscous fluid by a less viscous one in a two-dimensional channel, and to determine characteristic size of entrapment zones. Experiments on miscible displacement of fluids in Hele-Shaw cells were conducted under microgravity conditions. Extensive direct numerical simulations allowed to investigate the sensitivity of the displacement process to variation of values of the main governing parameters. Validation of the code was performed by comparing the results of model problems simulations with experiments and with the existing solutions published in literature. Taking into account non-linear effects in fluids displacement allowed to explain new experimental results on the pear-shape of fingers and periodical separation of their tip elements from the main body of displacing fluid. Those separated blobs of less viscous fluid move much faster than the mean flow of the displaced viscous fluid. The results of numerical simulations processed based on the dimensions analysis allow to introduce criteria characterizing the quality of displacement. The functional dependence of the dimensionless criteria on the values of governing parameters needs further investigations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barenblatt G.I., Entov V.M., Ryzhik V.M. Theory of fluids flows through natural rocks. Kluwer Academic Publishes — Dordrecht/Boston/London, 1990.
Nield D.A., Bejan A. Convection in porous media. Springer-Verlag — New York/Berlin/Heidelberg/London, 1992.
Bear J., Bachmat Y. Introduction to modelling of transport phenomena in porous media. Kluwer Academic Publishes — Dordrecht/Boston/London, 1990.
Kaviany M. Principles of heat transfer in porous media. Dover Publications Inc. — New York, 1988.
Smirnov N.N., Dushin V.R., Legros J.C., Istasse E., Bosseret N., Mincke J.C., Goodman S. Multiphase flow in porous media — mathematical model and micro-gravity experiments. Microgravity Science and Technology, IX(3), 1996, pp. 222–231.
Smirnov N.N., Legros J.C., Nikitin V.F., Istasse E., Norkin A.V., Shevtsova V.M., Kudryavtseva O.V. Capillary driven filtration in porous media. Microgravity Science and Technology, Hanser Publ., 1999, XII, pp. 23–35.
Smirnov N.N., Nikitin V.F., Norkin A.V., Kiselev A.B., Legros J.C., Istasse E. Microgravity investigation of capillary forces in porous media. Space Forum 2000, 6(1–4), pp. 1–10.
De Wit A., Homsy G.M. Viscous fingering in periodically heterogeneous porous media. Part II. Numerical simulations. J. Chem. Phys. 1997. Vol. 107(22), 9619.
Anderson D.A., Tannenhill J.C., Pletcher R.H. Computational fluid mechanics and heat transfer. New York, McGraw-Hill, 1984.
Yee H.C., Warming R.F., Harten A. Implicit total variation diminishing (TVD) schemes for steady-state calculations. Journal of Computational Physics, 57, pp. 327–360 (1985).
Ilyin V.P. Incomplete factorisation methods for solving algebraic systems. Moscow, Nauka publishes, 1995 (in Russian).
Nikitin V.F., Smirnov N.N., Legros J.C. Effect of fingering in porous media. 52-d IAF Congress. Toulouse, 2001, IAF-01-J.4.10.
Vedernikov A., Scheid B., Istasse E., Legros J.C. Viscous fingering in miscible liquids under microgravity conditions. Physics of Fluids, 2001, Vol. 13, N9, p. S12.
Smirnov N.N., Nikitin V.F., Ivashnyov O.E., Legros J.C., Vedernikov A., Scheid B., Istasse E. Instability in viscous fluids displacement from cracks and porous samples. Proc. 53-d IAF Congress, Houston, 2002, IAC-02-J.2.02., 11p.
Smirnov N.N., J. C. Legros, V. F. Nikitin, E. Istasse, L. Schramm, F. Wassmuth, andD’Arcy Hart. Filtration in Artificial Porous Media and Natural Sands under Microgravity Conditions. Microgravity sci. technol. 2003, XIV/2, pp. 3–28.
Meiburg, E. & Homsy, G.M. Nonlinear unstable viscous fingers in Hele-Show flows. II. Numerical simulation. Phys. Fluids 1988, 31(3).
Tanveer, S. Surprises in viscous fingering. J. Fluid Mech., 2000, vol. 409, p.273.
Zhuravlev, P. Zap Leningrad Com. Inst. 1956, 133, 54 (in Russian).
Saffman, P.G. &Taylor, G.J. The penetration of a fluid into a porous medium of Hele-Show cell containing a more viscous fluid. Proc. R. Foc. Zond. 1958, A 245, 312.
Guan X., Pitchumani R. Viscous fingering in a Hele-Shaw cell with finite viscosity ratio and interfacial tension. ASME Journal of Fluids Engineering, 2003. Vol. 125, No. 2, pp. 354–364.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Smirnov, N.N., Nikitin, V.F., Ivashnyov, O.E. et al. Microgravity investigations of instability and mixing flux in frontal displacement of fluids. Microgravity Sci. Technol 15, 35–51 (2004). https://doi.org/10.1007/BF02870957
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02870957