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The creeping motion of immiscible drops through a converging/diverging tube

Published online by Cambridge University Press:  20 April 2006

W. L. Olbricht  and
L. G. Leal
W. L. Olbricht
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125 Present address: School of Chemical Engineering, Cornell University, Ithaca, New York 14853.
L. G. Leal
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125
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Abstract

Results of experiments on the low-Reynolds-number flow of liquid drops through a horizontal circular tube with a diameter that varies sinusoidally with axial position are reported. Measurements of the contribution of the drop to the local pressure gradient and the relative velocity of the drop are correlated with the time-dependent drop shape. Both Newtonian and viscoelastic suspending fluids are considered. The viscosity ratio, volumetric flow rate and drop size are varied in the experiment, and both neutrally buoyant and non-neutrally buoyant drops are studied. Comparison with previous results for a straight-wall tube shows that the influence of the tube boundary geometry on the drop shape is substantial, but the qualitative effect of the tube shape depends strongly on the relative importance of viscous forces compared to interfacial tension for the particular experiment. For Newtonian fluids, two modes of drop breakup, which are distinguished by the magnitude of the viscosity ratio, are observed. When the suspending fluid is viscoelastic, both shear-thinning and time-dependent rheological effects are present.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 134 , September 1983 , pp. 329 - 355
Copyright
© 1983 Cambridge University Press

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References

Acrivos, A. & Lo, T. S. 1978 Deformation and breakup of a single drop in an extensional flow J. Fluid Mech. 86, 461.Google Scholar
Chin, H. B. & Han, C. D. 1979 Studies on droplet deformation and breakup. I. Droplet deformation in extensional flow J. Rheol. 23, 557.Google Scholar
Chin, H. B. & Han, C. D. 1980 Studies on droplet deformation and breakup. II. Breakup of a droplet in non-uniform shear flow J. Rheol. 24, 39.Google Scholar
Deiber, J. A. & Schowalter, W. R. 1979 Flow through tubes with sinusoidal axial variations in diameter AIChE J. 25, 638.Google Scholar
Deiber, J. A. & Schowalter, W. R. 1981 Modeling the flow of viscoelastic fluids through porous media AIChE J. 27, 912.Google Scholar
Elata, C., Burger, J., Michlin, J. & Takserman, U. 1977 Dilute polymer solutions in elongational flow Phys. Fluids Suppl. 20, S49.Google Scholar
Fedkiw, P. & Newman, J. 1977 Mass transfer at high Peclet numbers for creeping flow in a packed-bed reactor AIChE J. 23, 255.Google Scholar
Franzen, P. 1979 Zum Einfluss der Porengeometrie auf den Druckverlast bei der Durchströmung von Porensystemen. I. Versuche an Modellkanälen mit variablem Querschnitt Rheol. Acta 18, 392.Google Scholar
Grace, H. P. 1971 Dispersion phenomena in high viscosity immiscible fluid systems and application of static mixers as dispersion devices in such systems. Engng Foundation 3rd Res. Conf. on Mixing, Andover, New Hampshire, and Chem. Engng Communs 14, (1982), 225.Google Scholar
Han, C. D. & Funatsu, K. 1978 An experimental study of droplet deformation and breakup in pressure-driven flow through convergent and uniform channels J. Rheol. 22, 113.Google Scholar
Hinch, E. J. & Acrivos, A. 1980 Long slender drops in simple shear flow J. Fluid Mech. 98, 305.Google Scholar
Ho, B. P. & Leal, L. G. 1975 The creeping motion of liquid drops through a circular tube of comparable diameter J. Fluid Mech. 71, 361.Google Scholar
James, D. F. & Mclaren, D. R. 1975 The laminar flow of dilute polymer solutions through porous media J. Fluid Mech. 70, 733.Google Scholar
Leal, L. G., Skoog, J. & Acrivos, A. 1971 On the motion of gas bubbles in a viscoelastic fluid Can. J. Chem. Engng 29, 569.Google Scholar
Marshall, R. J. & Metzner, A. B. 1967 Flow of viscoelastic fluids through porous media Ind. Engng Chem. Fund. 8, 393.Google Scholar
Michele, H. 1977 Zur Durchflusscharakteristik von Schüttungen bei der Durchströmung mit verdünnten Lösungen aus langkettigen Hochpolymeren Rheol. Acta 16, 413.Google Scholar
Neira, M. A. & Payatakes, A. C. 1979 Collocation solution of creeping Newtonian flow through sinusoidal tubes AIChE J. 25, 725.Google Scholar
Olbricht, W. L. 1980 Ph.D. thesis, California Institute of Technology.
Olbricht, W. L. & Leal, L. G. 1982 The creeping motion of liquid drops through a circular tube of comparable diameter: the effect of density differences between the fluids. J. Fluid Mech. 115, 187.
Olbricht, W. L., Rallison, J. M. & Leal, L. G. 1982 Strong flow criteria based on microstructure deformation J. Non-Newt. Fluid Mech. 10, 291.Google Scholar
Payatakes, A. C. 1982 Dynamics of oil ganglia during immiscible disporous media. Ann. Rev. Fluid Mech. 14, 365.
Payatakes, A. C. & Neira, M. 1977 Model of the constricted unit cell typorous media. AIChE J. 23, 922.
Payatakes, A. C., Tien, C. & Turian, R. M. 1973 A new model for granu J. 18, 58.
Payatakes, A. C. & Tilton, J. N. 1983 Collocation solution of creeping Newtonian flow through sinusoidal tubes: a correction. AIChE J. (to appear).Google Scholar
Rallison, J. M. 1980 Note on the time-dependent deformation of a drop which is almost spherical J. Fluid Mech. 98, 625.Google Scholar
Rallison, J. M. 1981 A numerical study of the deformation and burst of a viscous drop in general shear flows J. Fluid Mech. 109, 465.Google Scholar
Rallison, J. M. & Acrivos, A. 1978 A numerical study of the deformation and burst of a viscous drop in an extensional flow J. Fluid Mech. 89, 191.Google Scholar
Savins, J. G. 1969 Non-Newtonian flow through porous media Ind. Engng Chem. 81, 18.Google Scholar
Schowalter, W. R. 1978 Mechanics of Non-Newtonian Fluids. Pergamon.
Sheffield, R. E. & Metzner, A. B. 1976 Flows of non-linear fluids through porous media AIChE J. 22, 736.Google Scholar
Taylor, G. I. 1934 The formation of emulsions in definable fields of flow Proc. R. Soc. Lond. A146, 501.Google Scholar
Wasan, D. T., Mcnamara, J. J., Shah, S. M., Sampath, K. & Aderansi, N. 1979 The role of coalescence phenomena and interfacial rheological properties in enhanced oil recovery: an overview. J. Rheol. 23, 181.Google Scholar