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The slow motion of slender rod-like particles in a second-order fluid

Leal, L. G. (1975) The slow motion of slender rod-like particles in a second-order fluid. Journal of Fluid Mechanics, 69 (2). pp. 305-337. ISSN 0022-1120.

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The motion of a slender axisymmetric rod-like particle is investigated theoretically for translation through a quiescent second-order fluid and for rotation in a simple shear flow of the same material. The analysis consists of an asymptotic expansion about the limit of rheologically slow flow, coupled with an application of a generalized form of the reciprocal theorem of Lorentz to calculate the force and torque on the particle. It is shown that an arbitrarily oriented particle with fore-aft symmetry translates, to a first approximation, at the same rate as in an equivalent Newtonian fluid, but that the motion of particles with no fore-aft symmetry may be modified at the same level of approximation. In addition, it is found that freely translating particles with fore-aft symmetry exhibit a single stable orientation with the axis of revolution vertical. In simple shear flow at small and moderate shear rates, the non-Newtonian nature of the suspending fluid causes a drift through Jeffery orbits to the equilibrium orbit C = 0 in which the particle rotates about its axis of revolution. At larger shear rates, the particle aligns itself in the direction of flow and ceases to rotate. Comparison with the available experimental data indicates that the measured rate of orbit drift may be used to determine the second normal stress difference parameter of the second-order fluid model. Finally, in an appendix, some preliminary observations are reported of the motion of slender rod-like particles falling through a quiescent viscoelastic fluid.

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Additional Information:© 1975 Cambridge University Press. Received 16 March 1974 and in revised form 10 June 1974. Published online: 29 March 2006. This work was supported by the National Science Foundation under grant GK-35468. The author wishes to acknowledge helpful discussions with Mr Bosco Ho and Dr E. J. Hinch on various aspects of this work. The Separan AP30 was donated by the Dow Chemical Company.
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ID Code:32943
Deposited By: Tony Diaz
Deposited On:06 Aug 2012 21:04
Last Modified:03 Oct 2019 04:05

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