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Breakup of concentric double emulsion droplets in linear flows

Published online by Cambridge University Press:  26 April 2006

H. A. Stone  and
L. G. Leal
H. A. Stone
Affiliation:
Division of Applied Sciences, Harvard University. Cambridge, MA 02138, USA
L. G. Leal
Affiliation:
Department of Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
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Abstract

The behaviour of concentric double emulsion droplets in linear flows is examined analytically, for the case when both fluid–fluid interfaces remain nearly spherical, and numerically, for the effect of finite interface deformation. The theoretical analysis is used to calculate the velocity fields interior and exterior to the particle, the first effects of flow-induced deformation, and the effective viscosity of a dilute emulsion of compound droplets. The numerical simulations allow for a complete investigation of the finite deformation of both the outer drop and the encapsulated particle. For concentric multiphase particles, there appear to be two distinct mechanisms of globule breakup: (i) continuous extension of the globule corresponding to non-existence of a steady particle shape or (ii) contact of the two interfaces at the globule centre, owing to incompatibility of the steady inner and outer interface shapes, even though the globule is only modestly deformed. Finally, the effect of different flow-types, i.e. uniaxial or biaxial extensional flows, is shown, in one example, to suggest breakup of the inner droplet even though the outer droplet maintains a steady shape.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 211 , February 1990 , pp. 123 - 156
Copyright
© 1990 Cambridge University Press

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References

Acrivos, A. 1983 The breakup of small drops and bubbles in shear flows. 4th Intl Conf. on Physicochemical Hydrodynamics. Ann. NY Acad. Sci 404, 1–11.Google Scholar
Barthès-Biesel, D. & Acrivos, A. 1973a Deformation and burst of a liquid droplet freely suspended in a linear shear field. J. Fluid Mech. 61, 1–21.Google Scholar
Barthès-Biesel, D. & Acrivos, A. 1973b The rheology of suspensions and its relation to phenomenological theories for non-Newtonian fluids. Intl J. Multiphase Flow 1, 1–24.Google Scholar
Batchelor, G. K. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545–570.Google Scholar
Bentley, B. J. & Leal, L. G. 1986 An experimental investigation of drop deformation and breakup in steady two-dimensional linear flows. J. Fluid Mech. 167, 241–283.Google Scholar
Brunn, P. O. & Roden, T. 1985 On the deformation and drag of a type-A multiple drop at low Reynolds number. J. Fluid Mech. 160, 211–234.Google Scholar
Chervenivanova & Zapryanov. 1988 On the deformation of compound multiphase drops at low Reynolds number. Submitted to Intl J. Multiphase Flow.Google Scholar
Cox, R. G. 1969 The deformation of a drop in a general time-dependent fluid flow. J. Fluid Mech. 37, 601–623.Google Scholar
Davis, A. M. J. & Brenner, H. 1981 Emulsions containing a third solid internal phase. J. Engng. Mech. Div. ASCE 107, 609–621.Google Scholar
Florence, A. T. & Whitehill, D. 1981 Some features of breakdown in water-in-oil-in-water multiple emulsions. J. Colloid Interface Sci. 79, 243–256.Google Scholar
Frankel, N. A. & Acrivos, A. 1970 The constitutive equation for a dilute emulsion. J. Fluid Mech. 44, 65–78.Google Scholar
Johnson, R. E. 1981 Stokes flow past a sphere coated with a thin fluid film. J. Fluid Mech. 110, 217–238.Google Scholar
Johnson, R. E. & Sadhal, S. S. 1983 Stokes flow past bubbles and drops partially coated with thin films. Part 2. Thin films with internal circulation - a perturbation solution. J. Fluid Mech. 132, 295–318.Google Scholar
Johnson, R. E. & Sadhal, S. S. 1985 Fluid mechanics of compound multiphase drops and bubbles. Ann. Rev. Fluid Mech. 17, 289–320.Google Scholar
Ladyzhenskaya, O. 1969 The Mathematical Theory of Viscous Incompressible Flow, 2nd edn. Gordon & Breach.
Lamb, H. 1932 Hydrodynamics, 6th edn. Dover.
Lee, S. H. & Leal, L. G. 1982 The motion of a sphere in the presence of a deformable interface. II. A numerical study of the translation of a sphere normal to an interface. J. Colloid Interface Sci. 87, 81–106.Google Scholar
Li, N. N. 1971a Separation of hydrocarbons by liquid membrane permeation. Ind. Engng. Chem. Process Des. Dev. 10, 215–221.Google Scholar
Li, N. N. 1971b Permeation through liquid surfactant membranes. AIChE J. 17, 459–463.Google Scholar
Maugh, T. H. 1976 Liquid membranes: New techniques for separation, purification. Science 193, 134–137.Google Scholar
Rallison, J. M. 1980 Note on the time-dependent deformation of a viscous drop which is almost spherical. J. Fluid Mech. 98, 625–633.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, 465–482.Google Scholar
Rallison, J. M. 1984 The deformation of small viscous drops and bubbles in shear flows. Ann. Rev. Fluid Mech. 16, 45–66.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, 191–200.Google Scholar
Rushton, E. & Davies, G. A. 1983 Settling of encapsulated droplets at low Reynolds numbers. Intl J. Multiphase Flow 9, 337–342.Google Scholar
Sadhal, S. S. & Oguz, H. N. 1985 Stokes flow past compound multiphase drops: the case of completely engulfed drops/bubbles. J. Fluid Mech. 160, 511–529.Google Scholar
Schowalter, W. R., Chaffey, C. E. & Brenner, H. 1968 Rheological behaviour of a dilute emulsion. J. Colloid Interface Sci. 26, 152–160.Google Scholar
Sherwood, J. D. 1988 Breakup of fluid droplets in electric and magnetic fields. J. Fluid Mech. 188, 133–146.Google Scholar
Stone, H. A. & Leal, L. G. 1989a Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid. J. Fluid Mech. 198, 399–427.Google Scholar
Stone, H. A. & Leal, L. G. 1989b A note concerning drop deformation and breakup in biaxial extensional flows at low Reynolds numbers. J. Colloid Interface Sci. (to appear).Google Scholar
Stoos, J. A. & Leal, L. G. 1989 Particle motion in axisymmetric stagnation flow toward an interface AIChE J. 35, 196–212.Google Scholar
Stroeve, P. & Varanasi, P. P. 1984 An experimental study on double emulsion drop breakup in uniform shear flow. J. Colloid Interface Sci. 99, 360–373.Google Scholar
Taylor, G. I. 1932 The viscosity of a fluid containing small drops of another fluid. Proc. R. Soc. Lond. A 138, 41–48.Google Scholar
Taylor, T. D. & Acrivos, A. 1964 On the deformation and drag of a falling viscous drop at low Reynolds number. J. Fluid Mech. 18, 466–476.Google Scholar
Torza, S. & Mason, S. G. 1969 Coalescence of two immiscible liquid drops. Science 163, 813–814.Google Scholar
Torza, S. & Mason, S. G. 1970 Three-phase interactions in shear and electrical fields. J. Colloid Interface Sci. 33, 67–83.Google Scholar
Tsamopoulos, J. A. & Brown, R. A. 1987 Dynamic centering of liquid shells. Phys. Fluids 30, 27–35.Google Scholar
Ulbrecht, J. J., Stroeve, P. & Prabodh, P. 1982 Behaviour of double emulsions in shear flows. Rheol. Acta 21, 593–597.Google Scholar
Youngren, G. K. & Acrivos, A. 1975 Stokes flow past a particle of arbitrary shape; a numerical method of solution. J. Fluid Mech. 69, 377–403 (corrigendum 69, 813).Google Scholar