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

Giovanni P. Galdi, Ashuwin Vaidya, Milan Pokorný, Daniel D. Joseph, Jimmy Feng

Research output: Contribution to journalArticle

17 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)1653-1690
Number of pages38
JournalMathematical Models and Methods in Applied Sciences
Volume12
Issue number11
DOIs
StatePublished - 1 Nov 2002

Fingerprint

Bodies of revolution
Reynolds number
Elasticity
Gravitation
Liquid
First-order
Liquids
Tilt
Perpendicular
Critical value
Gravity
Symmetry
Angle
Coefficient

Keywords

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

Cite this

Galdi, Giovanni P. ; Vaidya, Ashuwin ; Pokorný, Milan ; Joseph, Daniel D. ; Feng, Jimmy. / Orientation of symmetric bodies falling in a second-order liquid at nonzero reynolds number. In: Mathematical Models and Methods in Applied Sciences. 2002 ; Vol. 12, No. 11. pp. 1653-1690.
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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.

In: Mathematical Models and Methods in Applied Sciences, Vol. 12, No. 11, 01.11.2002, p. 1653-1690.

Research output: Contribution to journalArticle

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

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AU - Feng, Jimmy

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