Slow steady fall of rigid bodies in a second-order fluid

• Published in: Journal of non-Newtonian fluid mechanics Vol. 90; no. 1; pp. 81 - 89
• Main Author: Galdi, Giovanni P.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-04-2000; Elsevier
• Subjects: Cross-disciplinary physics: materials science; rheology; Exact sciences and technology; Fluid dynamics; Force; Fundamental areas of phenomenology (including applications); Heterogeneous liquids: suspensions, dispersions, emulsions, pastes, slurries, foams, block copolymers, etc; Material form; Non-newtonian fluid flows; Physics; Rheology; Second-order fluid; Stability; Steady fall; Torque; Steady fall; Torque; Stability; Second-order fluid; Force; Rigid bodies; Constitutive equation; Oblate spheroid; Second order fluid; Fall; Slow flow; Non-Newtonian fluids; Forces; Analytical solution; Sedimentation
• ISSN: 0377-0257; 1873-2631
• DOI: 10.1016/S0377-0257(99)00045-2

We consider the steady, slow translational fall of a rigid body
B
in a second-order fluid, under the action of the force of gravity
g. We find a general expression for the total force and torque acting on
B
. In particular, the force per unit area is always compressive, if the first normal stress coefficient
Ψ
1 is positive. We then specialize these formulas to the case when
B
is a prolate spheroid of eccentricity
e, and show that, when 0
<
e
<
1, there are only two orientations of fall allowed, namely, when the major axis of
B
is either perpendicular or parallel to
g. However, we show that if
Ψ
1 >0, only this latter orientation is stable to small disorientations, in agreement with the recent experimental results of Joseph and coworkers.