Abstract
Viscous fingering experiments were performed by injecting a liquid to radially displace a much more viscous liquid in a Hele-Shaw cell consisting of two parallel closely-spaced glass plates. Both smooth and etched plates were used to study the influence of plate roughness on the fingering mechanism. Effect of flow rate and interfacial tension was also demonstrated. The results show that symmetric dendritic finger patterns can form in the presence of anisotropy provided by an etched square network, for both miscible and immiscible fingers. Chaotic finger patterns can form both in a cell with smooth surfaces and in one having a network of randomly oriented channels etched on one plate. Due to interfacial tension, the immiscible finger patterns are less ramified than their miscible counterparts, are more sensitive to the flow rate and become compact as the flow rate decreases. Possible applications of two-phase displacement studies in Hele-Shaw cells are discussed, which include two-phase flow in porous media and acid fracturing of oil reservoirs.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ben-Jacob, E.; Goldenfeld, N.; Langer, J. S.; Schon, G. 1983: Dynamics of interfacial pattern formation. Phys. Rev. Lett. 51, 1930–1932
Ben-Jacob, E.; Godbey, R.; Goldenfeld, N. D.; Koplik, J.; Levine, H.; Mueller T.; Sander, L. M. 1985: Experimental demonstration of the role of anisotropy in interfacial pattern formation. Phys. Rev. Lett 55, 1315–1318
Chen, J. D.; Wilkinson, D. 1985: Pore scale viscous fingering in porous media. Phys. Rev. Lett. 55, 1892–1895
Chen, J. D. 1987a: Pore scale difference between miscible and immiscible viscous fingering in porous media. AIChE J. 33, 307–311
Chen, J. D. 1987b: Experiments on radial viscous fingers in a Hele-Shaw cell. (In preparation)
Chuoke, R. L.; van Meurs, P.; van der Poel, C. 1959: The instability of slow, immiscible, viscous liquid-liquid displacements in permeable media. Pet. Trans. AIME 216, 188–194
Daccord, G.; Nittmann, J.; Stanley, H. 1986: Radial viscous fingers and diffusion-limited aggregation. Phys. Rev. Lett. 56, 336–339
DeGregoria, A. J.; Schwartz, L. W. 1985: Finger breakup in Hele-Shaw cells. Phys. Fluids 28, 2313–2314
Gupta, S. P.; Varnon, J. E.; Greenkorn, R. A. 1973: Viscous finger wavelength degeneration in Hele-Shaw models. Water Resour. Res. 9, 1039–1046
Hele-Shaw, H. S. 1898: Investigation of the nature of surface resistance of water and of stream-line motion under certain experimental conditions. Trans. Inst. Nav. Archit. London 40, 21–46
Kessler, D. A.; Koplik, J.; Levine, H. 1984: Numerical simulation of two-dimensional snowflake growth. Phys. Rev. A 30, 2820–2823
Kessler, D. A.; Koplik, J.; Levine, H. 1985: Local modeling of dendritic growth. Physicochem. Hydrodyn. 6, 507–520
Langer, J. S. 1980: Instability and pattern formation in crystal growth. Rev. Mod. Phys. 52, 1–28
Nittmann, J.; Daccord, G.; Stanley, H. E. 1985: Fractal growth of viscous fingers. Nature 314, 141–144
Nittmann, J.; Stanley, H. E. 1986: Tip splitting without interfacial tension and dendritic growth patterns arising from molecular anisotropy. Nature 321, 663–668
Park, C. W.; Homsy, G. M. 1985: The instability of long fingers in Hele-Shaw flows. Phys. Fluids 28, 1583–1585
Paterson, L. 1981: Radial fingering in a Hele-Shaw cell. J. Fluid Mech. 113, 513–529
Paterson, L. 1985: Fingering with miscible fluids in a Hele-Shaw cell. Phys. Fluids 28, 26–30
Saffman, P. G.; Taylor, G. I. 1958: The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. Roy. Soc. London, Ser. A 245, 312–329
Stalkup, F. I. 1984: Miscible Displacement. Dallas: Soc. Pet. Eng. AIME
Van Meurs, P. 1957: The use of transparent three-dimensional models for studying the mechanism of flow process in oil reservoirs. Trans. AIME 210, 295–301
Williams, B. B.; Gidley, J. L.; Schechter, R. S. 1979: Acidizing Fundamentals, Chap. 5. Dallas: Soc. Pet. Eng. AIME
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chen, J.D. Radial viscous fingering patterns in Hele-Shaw cells. Experiments in Fluids 5, 363–371 (1987). https://doi.org/10.1007/BF00264399
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00264399