Motion of a deformed sphere with slip in creeping flows

    Research output: ResearchConference contribution

    Abstract

    The motion of a rigid particle whose surface is a slightly deformed sphere is studied for creeping flows with the assumption of slip on the particle. Expressions are obtained for the hydrodynamic force and torque exerted by the fluid on a deformed sphere using an asymptotic method introduced by H. Brenner, wherein the normalized amplitude of the deviation from sphericity is assumed to be a small parameter. The Stokes' resistance calculated by this method is validated by comparing with existing solutions the limiting cases of no slip and perfect slip. The equations describing the motion of a deformed sphere with a slip surface in a simple shear flow are also derived and solved. The motion of the deformed sphere is shown to differ significantly from the no-slip case for low values of a dimensionless parameter that incorporates the slip coefficient. The period of rotation of the deformed sphere is longer, and for cases where the slip coefficient is low, the spheroid rotates to a fixed angle and reaches a quasi-steady orientation.

    LanguageEnglish (US)
    Title of host publicationProceedings of the American Society of Mechanical Engineers Fluids Engineering Division Summer Conference
    Pages929-935
    Number of pages7
    Volume1 PART B
    StatePublished - 2005
    Event2005 ASME Fluids Engineering Division Summer Conference - Houston, TX, United States
    Duration: Jun 19 2005Jun 23 2005

    Other

    Other2005 ASME Fluids Engineering Division Summer Conference
    CountryUnited States
    CityHouston, TX
    Period6/19/056/23/05

    Profile

    Shear flow
    Torque
    Hydrodynamics
    Fluids

    Keywords

    • Asymptotic expansion
    • Particles
    • Slip
    • Suspensions

    ASJC Scopus subject areas

    • Engineering(all)

    Cite this

    Jia, L., Bénard, A., & Petty, C. A. (2005). Motion of a deformed sphere with slip in creeping flows. In Proceedings of the American Society of Mechanical Engineers Fluids Engineering Division Summer Conference (Vol. 1 PART B, pp. 929-935). [FEDSM2005-77187]

    Motion of a deformed sphere with slip in creeping flows. / Jia, Liping; Bénard, André; Petty, Charles A.

    Proceedings of the American Society of Mechanical Engineers Fluids Engineering Division Summer Conference. Vol. 1 PART B 2005. p. 929-935 FEDSM2005-77187.

    Research output: ResearchConference contribution

    Jia, L, Bénard, A & Petty, CA 2005, Motion of a deformed sphere with slip in creeping flows. in Proceedings of the American Society of Mechanical Engineers Fluids Engineering Division Summer Conference. vol. 1 PART B, FEDSM2005-77187, pp. 929-935, 2005 ASME Fluids Engineering Division Summer Conference, Houston, TX, United States, 6/19/05.
    Jia L, Bénard A, Petty CA. Motion of a deformed sphere with slip in creeping flows. In Proceedings of the American Society of Mechanical Engineers Fluids Engineering Division Summer Conference. Vol. 1 PART B. 2005. p. 929-935. FEDSM2005-77187.
    Jia, Liping ; Bénard, André ; Petty, Charles A./ Motion of a deformed sphere with slip in creeping flows. Proceedings of the American Society of Mechanical Engineers Fluids Engineering Division Summer Conference. Vol. 1 PART B 2005. pp. 929-935
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    AB - The motion of a rigid particle whose surface is a slightly deformed sphere is studied for creeping flows with the assumption of slip on the particle. Expressions are obtained for the hydrodynamic force and torque exerted by the fluid on a deformed sphere using an asymptotic method introduced by H. Brenner, wherein the normalized amplitude of the deviation from sphericity is assumed to be a small parameter. The Stokes' resistance calculated by this method is validated by comparing with existing solutions the limiting cases of no slip and perfect slip. The equations describing the motion of a deformed sphere with a slip surface in a simple shear flow are also derived and solved. The motion of the deformed sphere is shown to differ significantly from the no-slip case for low values of a dimensionless parameter that incorporates the slip coefficient. The period of rotation of the deformed sphere is longer, and for cases where the slip coefficient is low, the spheroid rotates to a fixed angle and reaches a quasi-steady orientation.

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    KW - Suspensions

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