Magnetocaloric Fluids - Magnetocaloric Energy Conversion: From Theory to Applications - page 173

The magneto-viscous effect (MVE) can be de ned according to Odenbach [ 18 ]as

g H g eff
g eff

MVE ¼ ð 5 : 25 Þ

where ʷ H represents the viscosity of the ferro fl uid under an applied magnetic eld

H and ʷ eff represents the viscosity of the ferro fl uid in the absence of the magnetic

eld.

5.2.1.1 Rheologic Models Applied for Ferro fl uids

The following examples provide brief information about the different research
activities in which the rheology of ferro fl uids have been investigated.

Title Synthesis, rheological properties and magneto-viscous effect of

Fe 2 O 3/ paraf n ferrofluids (Hezaveh et al. [ 27 ])

Materials used for
investigation

Fe 2 O 3 magnetic nanoparticle powder with average size of <50 nm,
pure liquid parafn as base fl uid, oleic acid (OA) used as surfactant

of nanoparticles
Fe 2 O 3 nanoparticles in different weight fractions (5, 10, 15, 20, 25,
and 30 %) were mixed with oleic acid by 15 % weight relative to the
solid powder

Constitutive model Bingham model (Eq. 5.14): better predictions in lower concentra-

tions (Bingham plastic region) rather than higher concentrations
Casson model (Eq. 5.16): in comparison to the Bingham model, the
Casson model shows poor predictability for the system

Viscosity The authors compared the measured viscosity of Einstein ' s equation

(Eq. 5.2 ), Brinkman ' s equation (Eq. 5.13) and Roscoe ' s model [ 28 ].
It was shown that these models do not offer a good prediction of the
viscosity of the suspension. The viscosity of ferrofluids has been
investigated for different weight fractions at a constant shear rate of
5s − 1 and under different magnetic elds. The results show that at a
constant shear rate the viscosity increases with increased magnetic
eld. However, the authors have noted that this increment was
followed by a decrease in viscosity after a certain peak value and
pointed out that at high mass concentrations (30 %) this phenomenon
was more sensible. The authors have explained this as the result of
the phase separation in the ferro fl uid, e.g. due to particle aggregation

As can be seen from these examples, different constitutive models have been
applied for characterization of the rheology of different ferro fl uids. Most of these

models regard Bingham (see for instance L ó pez et al. [ 16 ], Hezaveh et al. [ 27 ],

Hong et al. [ 29 ], Hosseini et al. [ 30 ], Rodr guez-Arco et al. [ 31 ], Shah et al. [ 32 ]).

The Casson model has been applied by Hezaveh et al. [ 27 ] and Hong et al. [ 29 ],
however, it did not provide the best

í

Bulkley model was
applied by Hong et al. [ 29 ]. In the Bingham model (Eq. 5.14), when the shear stress

tting. The Herschel

-

˄

is smaller than the yield stress uid motion. The shear rate in the

Bingham model is directly proportional to the difference between the shear stress and

˄ B , there will be no fl