### Abstract

We study the steady translational fall of a homogeneous body of revolution around an axis a, with fore-and-aft symmetry, in a second-order liquid at nonzero Reynolds (Re) and Weissenberg (We) numbers. We show that, at first order in these parameters, only two orientations are allowed, namely, those with a either parallel or perpendicular to the direction of the gravity g. In both cases the translational velocity is parallel to g. The stability of the orientations can be described in terms of a critical value E_{c} for the elasticity number E = We/Re, where E_{c} depends only on the geometric properties of the body, such as size or shape, and on the quantity (ψ_{1} + ψ_{2})/ψ_{1}, where ψ_{1} and ψ_{2} are the first and second normal stress coefficients. These results are then applied to the case when the body is a prolate spheroid. Our analysis shows, in particular, that there is no tilt-angle phenomenon at first order in Re and We.

Original language | English |
---|---|

Pages (from-to) | 1653-1690 |

Number of pages | 38 |

Journal | Mathematical Models and Methods in Applied Sciences |

Volume | 12 |

Issue number | 11 |

DOIs | |

State | Published - 1 Nov 2002 |

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### Keywords

- Orientation
- Second-order fluid
- Sedimentation
- Tilt angle
- Torque

### Cite this

*Mathematical Models and Methods in Applied Sciences*,

*12*(11), 1653-1690. https://doi.org/10.1142/S0218202502002276

}

*Mathematical Models and Methods in Applied Sciences*, vol. 12, no. 11, pp. 1653-1690. https://doi.org/10.1142/S0218202502002276

**Orientation of symmetric bodies falling in a second-order liquid at nonzero reynolds number.** / Galdi, Giovanni P.; Vaidya, Ashuwin; Pokorný, Milan; Joseph, Daniel D.; Feng, Jimmy.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Orientation of symmetric bodies falling in a second-order liquid at nonzero reynolds number

AU - Galdi, Giovanni P.

AU - Vaidya, Ashuwin

AU - Pokorný, Milan

AU - Joseph, Daniel D.

AU - Feng, Jimmy

PY - 2002/11/1

Y1 - 2002/11/1

N2 - We study the steady translational fall of a homogeneous body of revolution around an axis a, with fore-and-aft symmetry, in a second-order liquid at nonzero Reynolds (Re) and Weissenberg (We) numbers. We show that, at first order in these parameters, only two orientations are allowed, namely, those with a either parallel or perpendicular to the direction of the gravity g. In both cases the translational velocity is parallel to g. The stability of the orientations can be described in terms of a critical value Ec for the elasticity number E = We/Re, where Ec depends only on the geometric properties of the body, such as size or shape, and on the quantity (ψ1 + ψ2)/ψ1, where ψ1 and ψ2 are the first and second normal stress coefficients. These results are then applied to the case when the body is a prolate spheroid. Our analysis shows, in particular, that there is no tilt-angle phenomenon at first order in Re and We.

AB - We study the steady translational fall of a homogeneous body of revolution around an axis a, with fore-and-aft symmetry, in a second-order liquid at nonzero Reynolds (Re) and Weissenberg (We) numbers. We show that, at first order in these parameters, only two orientations are allowed, namely, those with a either parallel or perpendicular to the direction of the gravity g. In both cases the translational velocity is parallel to g. The stability of the orientations can be described in terms of a critical value Ec for the elasticity number E = We/Re, where Ec depends only on the geometric properties of the body, such as size or shape, and on the quantity (ψ1 + ψ2)/ψ1, where ψ1 and ψ2 are the first and second normal stress coefficients. These results are then applied to the case when the body is a prolate spheroid. Our analysis shows, in particular, that there is no tilt-angle phenomenon at first order in Re and We.

KW - Orientation

KW - Second-order fluid

KW - Sedimentation

KW - Tilt angle

KW - Torque

UR - http://www.scopus.com/inward/record.url?scp=0036858788&partnerID=8YFLogxK

U2 - 10.1142/S0218202502002276

DO - 10.1142/S0218202502002276

M3 - Article

AN - SCOPUS:0036858788

VL - 12

SP - 1653

EP - 1690

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

SN - 0218-2025

IS - 11

ER -