Magnetocaloric Fluids - Magnetocaloric Energy Conversion: From Theory to Applications - page 167

Table 5.1 Some expressions for Newtonian suspension ' s viscosity as a function of a solids volume fraction (see also Darby [ 175 ], Hanks [ 176 ], Steffe [ 177 ],
Bica et al. [ 46 ])
Author Equation Comment Equation

number

Guth and Simha
[ 178 ]

1 / V þ

Interaction between particles (5.4)

g eff ¼ g L 1 þ 2 : 5 / V þ 14 :

Vand (after
Darby) [ 179 ]

No interparticle forces (5.5)

2 : 5 / V
1 0 : 609 / V

g eff ¼ g L exp

/ V
1 0 : 609 / V

Includes doublet collisions, but not triplet (5.6)

2 : 5 / V þ 2 : 7

g eff ¼ g L exp

0

Mooney [ 180 ] K depends upon the system and is de ned experimentally (5.7)

2 : 5 / V
1 K / V

g eff ¼ g L exp : 75 K 1 : 5

\ \

Frankel and Acri-
vos [ 181 ]

Concentrated suspensions only (5.8)

1
3
1 / V =/ max

ð / V =/ max Þ

9
8

g eff ¼ g L 1

3

ð Þ

Jeffrey and Acri-
vos [ 182 ]

g eff ¼ g L 1 ð þ A / V Þ 2 : 5 A 10 Ellipsoid particles (5.9)

\ \

Thomas [ 183 ]

g eff ¼ g L 1 þ 2 : 5 / V þ 10 : 05 / V þ 0 : 00273e 16 : 6 / V

Also includes interaction between the solid particles (5.10)

d p from 0 : 099 to 435 l m

/ V \ 0 : 625

Batchelor [ 184 ]

2 / V

Comprises particle interactions. Brownian motion and
inertia of higher importance

(5.11)

g eff ¼ g L 1 þ 2 : 5 / V þ 6 :

Bicerano [ 185 ]

g eff ¼ g L 1 þ hi/ V þ k H / V

< > is the intrinsic viscosity, k H is the dimensionless

Huggins coefcient

ʷ (5.12)

Extended Einstein ' s equation for higher concentrations Brinkman [ 186 ] g eff ¼ g L

1
1 / V

(5.13) 2 : 5

ð Þ