### 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.

Original language | English (US) |
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Title of host publication | Proceedings of the American Society of Mechanical Engineers Fluids Engineering Division Summer Conference |

Pages | 929-935 |

Number of pages | 7 |

Volume | 1 PART B |

State | Published - 2005 |

Event | 2005 ASME Fluids Engineering Division Summer Conference - Houston, TX, United States |

### Other

Other | 2005 ASME Fluids Engineering Division Summer Conference |
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Country | United States |

City | Houston, TX |

Period | 6/19/05 → 6/23/05 |

### Profile

### Keywords

- Asymptotic expansion
- Particles
- Slip
- Suspensions

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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, 19-23 June.

}

TY - CHAP

T1 - Motion of a deformed sphere with slip in creeping flows

AU - Jia,Liping

AU - Bénard,André

AU - Petty,Charles A.

PY - 2005

Y1 - 2005

N2 - 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.

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.

KW - Asymptotic expansion

KW - Particles

KW - Slip

KW - Suspensions

UR - http://www.scopus.com/inward/record.url?scp=28844440134&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=28844440134&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0791841987

SN - 9780791841983

VL - 1 PART B

SP - 929

EP - 935

BT - Proceedings of the American Society of Mechanical Engineers Fluids Engineering Division Summer Conference

ER -