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Journal of Engineering Mathematics

, Volume 107, Issue 1, pp 111–132 | Cite as

Motion of a spherical liquid drop in simple shear flow next to an infinite plane wall or fluid interface

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Abstract

The velocity of translation of a spherical liquid drop under the influence of simple shear flow near an infinite plane wall or fluid interface is computed with high accuracy using a boundary-integral method for Stokes flow based on Fourier decomposition in the absence of significant gravitational effects. Accurate results are obtained for very small gaps between the drop surface and the wall or interface, several orders of magnitude smaller than the drop diameter. As the gap decreases, a liquid drop tends to stick to a solid wall but is able to slide over an interface irrespective of the drop and ambient fluid viscosities. In the case of flow near an interface, the dependence of the drop velocity on the drop position and viscosity ratio is not necessarily monotonic. The interfacial deformation is computed to leading order with respect to the capillary number and is shown to exhibit an asymmetry due to the presence of the wall or interface. The predictions of the asymptotic analysis for nearly spherical drops are in agreement with boundary-element simulations of three-dimensional flow.

Keywords

Boundary-element method Liquid drop Shear flow near a wall Shear flow near an interface Simple shear flow 

References

  1. 1.
    Goldman AJ, Cox RG, Brenner H (1967) Slow viscous motion of a sphere parallel to a plane wall. Part II: Couette flow. Chem Eng Sci 22:653–660CrossRefGoogle Scholar
  2. 2.
    Pozrikidis C (2007) Particle motion near and inside an interface. J Fluid Mech 575:333–357ADSCrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Chan PCH, Leal LG (1979) The motion of a deformable drop in a second-order fluid. J Fluid Mech 92:131–170ADSCrossRefMATHGoogle Scholar
  4. 4.
    Magnaudet J, Takagi S, Legendre D (2003) Drag, deformation and lateral migration of a buoyant drop moving near a wall. J Fluid Mech 476:115–157ADSCrossRefMATHGoogle Scholar
  5. 5.
    Kennedy MR, Pozrikidis C, Skalak R (1994) Motion and deformation of liquid drops, and the rheology of dilute emulsions in simple shear flow. Comput. Fluids 23:251–278CrossRefMATHGoogle Scholar
  6. 6.
    Pozrikidis C (2011) Introduction to theoretical and computational fluid dynamics, 2nd edn. Oxford University Press, New YorkMATHGoogle Scholar
  7. 7.
    Taylor GI (1932) The viscosity of a fluid containing small drops of another fluid. Proc R Soc A 138:41–48ADSCrossRefMATHGoogle Scholar
  8. 8.
    Taylor GI (1934) The formation of emulsions in definable fields of flow. Proc R Soc A 146:501–523ADSCrossRefGoogle Scholar
  9. 9.
    Pozrikidis C (1992) Boundary integral and singularity methods for linearized viscous flow. Cambridge University Press, New YorkCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of Chemical EngineeringUniversity of MassachusettsAmherstUSA

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