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TECHNICAL PAPERS

The Instability of Shear Thinning and Shear Thickening Spiralling Liquid Jets: Linear Theory

[+] Author and Article Information
J. Uddin

School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdomuddinj@maths.bham.ac.uk

S. P. Decent

School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdomdecentsp@for.mat.bham.ac.uk

M. J. Simmons

School of Chemical Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdomm.j.simmons@bham.ac.uk

J. Fluids Eng 128(5), 968-975 (Mar 09, 2006) (8 pages) doi:10.1115/1.2238876 History: Received November 27, 2005; Revised March 09, 2006

The linear instability of a power law liquid emerging as a jet from an orifice on the surface of a rotating container is investigated, with applications to industrial prilling. Asymptotic methods are used to examine the growth rate and wavenumber of the most unstable traveling wave mode for different flow index numbers. Comparison with Newtonian liquids show that for small rotation rates shear thinning liquids are most stable to disturbances. In contrast for higher rotation rates we find shear thickening liquids are more stable than shear thinning liquids. The influence of viscosity, surface tension, and rotation rate on the growth rates and most unstable wavenumbers associated with both types of liquids are also examined.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

The trajectory and radius of an inviscid jet when We=20

Grahic Jump Location
Figure 3

The growth rate ωr against arc length when Reα˜=3 and We=20 for a high (Rb=0.75, top) and a low (Rb=4, bottom) rotation rate. The dashed curve represents α=1.

Grahic Jump Location
Figure 4

The growth rate (top) and most unstable wavenumber (bottom) against s for different Rb numbers. α=0.6, Reα˜=3, and We=20.

Grahic Jump Location
Figure 6

The effects of changing the Weber number on ωr (top) and k* (bottom) for shear thickening liquids (α=1.4, -dashed line) and shear thinning liquids (α=0.6, solid line) where Rb=1.25 and Reα˜=3

Grahic Jump Location
Figure 8

The growth rate of the most unstable mode for various Weber numbers (Rb=2 and Reα˜=300)

Grahic Jump Location
Figure 2

The most unstable wavenumber against arc length when Reα˜=3 and We=20 for a high (Rb=0.75, top) and a low (Rb=4, bottom) rotation rate. The dashed curve represents α=1.

Grahic Jump Location
Figure 5

The growth rate (top) and most unstable wavenumber (bottom) against s for different Rb numbers. α=1.4, Reα˜=3, and We=20.

Grahic Jump Location
Figure 7

The effects of changing the Reynolds number on ωr (top) and k* (bottom) for shear thickening liquids (α=1.4, -dashed line) and shear thinning liquids (α=0.6, solid line) where Rb=1.25 and We=20

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