A spherical drop of viscosity and radius is surrounded by a spherical shell of viscosity , internal radius , and external radius , beyond which there is an unbounded matrix fluid of viscosity . An arbitrary axisymmetric singularity acts inside or outside the viscous spherical shell. It is established that the Stokes’ stream function induced in this heterogeneous medium is explicitly expressible solely in terms of the corresponding stream function for the unperturbed homogeneous unbounded medium. As an application of the general solution, it is shown that there exists a homogeneous spherical drop of viscosity and radius , which is equivalent to the spherical drop of viscosity and radius , surrounded by the spherical shell of viscosity and outer radius . A new formula is also established for the effective viscosity of a multiphase medium comprising an incompressible fluid of viscosity in which are embedded small identical spherical drops of viscosity , surrounded by spherical shells of viscosity , assuming that the interference effects of these coated spherical drops are negligible, and that their arrangement is axisymmetrical. The corresponding two-dimensional results are also presented, by slightly modifying the three-dimensional results.
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November 2009
Research Papers
Theory of Images in Spherical-Layered Axisymmetric Viscous Hydrodynamics
K. Aderogba
K. Aderogba
Department of Mathematics,
e-mail: kanmiaderogba@yahoo.com
University of Lagos
, Lagos 23401, Nigeria
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K. Aderogba
Department of Mathematics,
University of Lagos
, Lagos 23401, Nigeriae-mail: kanmiaderogba@yahoo.com
J. Appl. Mech. Nov 2009, 76(6): 061007 (9 pages)
Published Online: July 23, 2009
Article history
Received:
November 19, 2007
Revised:
February 9, 2009
Published:
July 23, 2009
Citation
Aderogba, K. (July 23, 2009). "Theory of Images in Spherical-Layered Axisymmetric Viscous Hydrodynamics." ASME. J. Appl. Mech. November 2009; 76(6): 061007. https://doi.org/10.1115/1.3130450
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