Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-30T16:26:34.531Z Has data issue: false hasContentIssue false
  • English
  • Français

Experiments on gravitational phase separation of binary immiscible fluids

Published online by Cambridge University Press:  30 October 2007

MISUZU SATO  and
IKURO SUMITA
MISUZU SATO
Affiliation:
Division of Earth & Environmental Sciences, Graduate School of Natural Sciences and Technology, Kanazawa University, Kanazawa 920-1192, Japan
IKURO SUMITA
Affiliation:
Division of Earth & Environmental Sciences, Graduate School of Natural Sciences and Technology, Kanazawa University, Kanazawa 920-1192, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

We conduct experiments on gravitational phase separation of binary immiscible fluids using an oil–water mixture and study how the volumetric and viscosity ratios of the two phases control the separation process. First, we change the volumetric fraction of the two phases. We find that the initial phase separation rate depends strongly on the volumetric ratio of the two phases, and can be modelled by a buoyancy-driven permeable flow using the Blake–Kozeny–Carman permeability formula. Next, we change the viscosity ratios of the two fluids, and we find that there are two distinct regimes with different styles of phase separation. Small viscosity ratio (<100) cases are characterized by a sharp lower boundary and a vertically homogeneous mixture layer. On the other hand, high viscosity ratio (>100) cases are characterized by a diffuse lower boundary and a large vertical gradient of porosity. A polyhedral foam structure develops at the top of the mixture layer which is slow to rupture and to transform into a uniform oil layer. These differences can be interpreted to arise from a faster coalescence rate relative to the separation rate at high viscosity ratios. We simultaneously measured electrical resistivity in order to monitor the temporal change of the mean porosity in the mixture layer. The measurements were found to be consistent with the visual observation.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 591 , 25 November 2007 , pp. 289 - 319
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bazhlekov, I. B., Chesters, A. K. & van de Vosse, F. N. 2000 The effect of the dispersed to continuous-phase viscosity ratio on film drainage between interacting drops. Intl J. Multiphase Flow 26, 445–466.CrossRefGoogle Scholar
Bear, J. 1972 Dynamics of Fluids in Porous Media. Elsevier.Google Scholar
Bottinga, Y. & Weill, D. F. 1972 The viscosity of magmatic silicate liquids: a model for calculation. Am. J. Sci. 272, 438–475.CrossRefGoogle Scholar
Brady, J. F. & Bossis, G. 1988 Stokesian dynamics. Annu. Rev. Fluid Mech. 20, 111–157.CrossRefGoogle Scholar
Bray, A. J. 2003 Coarsening dynamics of phase-separating systems. Phil. Trans. R. Soc. Lond., A 361, 781–792.CrossRefGoogle ScholarPubMed
Cau, F. & Lacelle, S. 1993 Late-stage phase separation and sedimentation in a binary liquid mixture. Phys. Rev. E 47, 1429–1432.Google Scholar
Chesters, A. K. 1991 The modelling of coalescence processes in fluid-liquid dispersions: A review of current understanding. Trans. Inst. Chem Engrs 69, 259–270.Google Scholar
Colombani, J. & Bert, J. 2004 Early sedimentation and crossover kinetics in an off-critical phase-separating liquid mixture. Phys. Rev. E 69, 011402.Google Scholar
Davis, R. H. & Acrivos, A. 1985 Sedimentation of noncolloidal particles at low Reynolds numbers. Annu. Rev. Fluid Mech. 17, 91–118.CrossRefGoogle Scholar
Davis, R. H., Schonberg, J. A. & Rallison, J. M. 1989 The lubrication force between two viscous drops. Phys. Fluids A 1, 77–81.CrossRefGoogle Scholar
Dullien, F. A. L. 1979 Porous Media Fluid Transport and Pore Structure. Academic.Google Scholar
Faber, T. E. 1995 Fluid Dynamics for Physicists. Cambridge University.CrossRefGoogle Scholar
Friedman, S. P. 2005 Soil properties influencing apparent electrical conductivity: a review. Computers Electronics in Agriculture 46, 45–70.CrossRefGoogle Scholar
Hanai, T. 1968 Electrical properties of emulsions. In Emulsion Science (ed. Sherman, P.). Academic.Google Scholar
Keene, B. J. 1995 Interfacial tension between ferrous melts and molten slags. In Slag Atlas, 2nd Edn, pp. 463–511. Verein Deutscher EisenHüttenleute.Google Scholar
Kjarsgaard, B. A. & Hamilton, D. L. 1989 The genesis of carbonatites by immiscibility. In Carbonatites: Genesis and Evolution (ed. Bell, K.), pp. 70–86. London: Unwin Hyman.Google Scholar
Koh, A., Gillies, G., Gore, J. & Saunders, B. R. 2000 Flocculation and coalescence of oil-in-water polydimethylsiloxane emulsions. J. Colloid Interface Sci. 227, 390–397.CrossRefGoogle ScholarPubMed
Kushner IV, J., Rother, M. A. & Davis, R. H. 2001 Buoyancy-driven interactions of viscous drops with deforming interfaces. J. Fluid Mech. 446, 253–269.CrossRefGoogle Scholar
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics. Pergamon.Google Scholar
Larson, R. G. 1999 The Structure and Rheology of Complex Fluids. Oxford University Press.Google Scholar
Lowenberg, M. 1998 Numerical simulation of a concentrated emulsion flows. Trans ASME: J. Fluids Engng 120, 824–832.Google Scholar
Lowenberg, M. & Hinch, E. J. 1996 Numerical simulation of a concentrated emulsion in shear flow. J. Fluid Mech. 321, 395–419.CrossRefGoogle Scholar
Lowenberg, M. & Hinch, E. J. 1997 Collision of two deformable droplets in shear flow. J. Fluid Mech. 338, 299–315.CrossRefGoogle Scholar
Martin, D. & Nokes, R. 1988 Crystal settling in a vigorously convecting magma chamber. Nature 332, 534–536.CrossRefGoogle Scholar
Mavko, G., Mukerji, T. & Dvorkin, J. 1998 The Rock Physics Handbook. Cambridge University Press.Google Scholar
McKenzie, D. 1984 The generation and compaction of partially molten rock. J. Petrol. 25, 713–765.CrossRefGoogle Scholar
Ohtani, E., Ringwood, A. E. & Hibberson, W. 1984 Composition of the core ii. effect of high pressure on solubility of FeO in molten iron. Earth Planet. Sci. Lett. 71, 94–103.CrossRefGoogle Scholar
Onuki, A. 1994 Domain growth and rheology in phase-separating binary mixtures with viscosity difference. Europhys. Lett. 28, 175–179.CrossRefGoogle Scholar
Philpotts, A. R. 1982 Compositions of immiscible liquids in volcanic rocks. Contrib. Mineral. Petrol. 80, 201–218.CrossRefGoogle Scholar
Rother, M. A., Zinchenko, A. Z. & Davis, R. H. 1997 Buoyancy-driven coalescence of slightly deformable drops. J. Fluid Mech. 346, 117–148.CrossRefGoogle Scholar
Safronov, V. S. 1978 The heating of the earth during its formation. Icarus 33, 3–12.CrossRefGoogle Scholar
Scott, D. & Stevenson, D. 1984 Magma solitons. Geophys. Res. Lett. 11, 1161–1164.CrossRefGoogle Scholar
Segré, P. N., Liu, F., Umbanhowar, P. & Weitz, D. A. 2001 An effective gravitational temperature for sedimentation. Nature 409, 594–597.CrossRefGoogle ScholarPubMed
Solomatov, V. S. 2000 Fluid dynamics of a terrestrial magma ocean. In Origin of the Earth and Moon (ed. Canup, R. & Righter, K.), pp. 323–338. University of Arizona Press, Tucson, Arizona.CrossRefGoogle Scholar
Spiegelman, M. 1993 Flow in deformable porous media. part 2 numerical analysis - the relationship between shock waves and solitary waves. J. Fluid Mech. 247, 39–63.CrossRefGoogle Scholar
Stevenson, D. J. 1980 Saturn's luminosity and magnetism. Science 208, 746–748.CrossRefGoogle ScholarPubMed
Stevenson, D. J. 1982 Interiors of the giant planets. Annu. Rev. Earth Planet. Sci. 10, 257–295.CrossRefGoogle Scholar
Stevenson, D. J. 1990 Fluid dynamics of core formation. In Origin of the Earth (ed. Newsom, H. E. & Jones, J. H.), pp. 231–249. Oxford University Press.CrossRefGoogle Scholar
Stevenson, D. J. & Salpeter, E. E. 1977 The phase diagram and transport properties for hydrogen-helium fluid planets. Astrophys. J. Suppl. 35, 221–237.CrossRefGoogle Scholar
To, K.-W. & Chan, C.-K. 1992 Scaling behaviour in the demixing of a binary-liquid mixture under gravity. Europhys. Lett. 19, 311–316.CrossRefGoogle Scholar
To, K.-W. & Chan, C.-K. 1994 Morphology and dynamics of a separating immiscible binary liquid mixture under gravity. Physica A 205, 320–329.CrossRefGoogle Scholar
Urakawa, S., Kato, M. & Kumazawa, M. 1987 Experimental study on the phase relations in the system Fe-Ni-O-S upto 15 GPa. In High-Pressure Research in Mineral Physics (ed. Manghnani, M. H. & Syono, Y.), pp. 95–111. TERRAPUB.CrossRefGoogle Scholar
Wang, H. & Davis, R. H. 1995 Simultaneous sedimentation and coalescence of a dilute dispersion of small drops. J. Fluid Mech. 295, 247–261.CrossRefGoogle Scholar
Wang, H., Zinchenko, A. & Davis, R. H. 1994 The collision rate of small drops in linear flow fields. J. Fluid Mech. 265, 161–188.CrossRefGoogle Scholar
Yiantsios, S. G. & Davis, R. H. 1990 On the buoyancy-driven motion of a drop towards a rigid surface or a deformable interface. J. Fluid Mech. 217, 547–573.CrossRefGoogle Scholar
Yoon, Y., Borrell, M., Park, C. C. & Leal, L. G. 2005 Viscosity ratio effects on the coalescence of two equal-sized drops in a two-dimensional linear flow. J. Fluid Mech. 525, 355–379.CrossRefGoogle Scholar