Motion of a deformed sphere with slip in creeping flows

Research output: Chapter in Book/Report/Conference proceedingConference 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: Chapter in Book/Report/Conference proceedingConference 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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