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the linear region but lower than the saturation, Ginder et al. [ 63 , 64 ] proposed the
following relation:
p / V l 0 H 2
p
s 0 ¼
M S
ð 5 : 27 Þ
where the term
ʼ 0 M S represents the saturation magnetization. For the saturation
magnetic
eld, Ginder et al. [ 63 , 64 ] proposed another relation for the yield stress:
4
5 2 / V l 0 M S n 3
s 0 H ðÞ ¼
ðÞ
ð 5 : 28 Þ
for which
ʾ
(3) is the Riemann zeta function and was de
ned to be 1.202 as a
constant. The veri
[ 65 ].
Note also that the yield stress of a bidisperse suspension will represent higher
values than that of a more sedimentation-stable monodisperse suspension (see, e.g.
Charles and See [ 66 ], Kittipoomwong et al. [ 67 ], Wereley et al. [ 68 ]).
For more information on the rheology of magnetorheologic
cation of the model was provided by Genc and Phul
é
uids one is also
referred to the chapter by Bossis et al. [ 12 ]. There, the authors present a chain
model for the yield stress in magneto-rheology that was very similar to Eq. ( 5.27 ):
fl
31 / V l 0 H 2
p
s 0 ¼
2
:
M S
ð 5 : 29 Þ
As Bossis et al. [ 12 ] noted, the dependence between the yield stress and the
volume fraction was experimentally con
rmed for not very concentrated suspen-
sions with
0.3 by Ginder et el. [ 69 ], See et al. [ 70 ], and Brady et al. [ 71 ].
Furthermore, with regard to the exponent of the magnetic
ϕ V < 0.2
eld intensity H, different
authors have obtained similar values to 3/2 (e.g. Ginder et al. [ 69 ], Orihara et al.
[ 72 ] and Bonnecaze and Brady [ 73 ]). As denoted by Bossis [ 12 ], this exponent will
decrease with an increase in the magnetic
eld.
Some researchers (see, e.g. Fang et al. [ 74 ], Hato et al. [ 75 ], Hong et al. [ 76 ])
have also applied a correlation basically developed by Cho et al. [ 77 ] and Choi et al.
[ 78 ] for electro-rheological
uid.
The examples in the following pages provide brief information about some
research activities in which the rheology of magnetorheological
fl
uids, but modi
ed for use in MR
fl
fl
uids is investigated.
Title
A new generation of magneto-rheological
fl
uid dampers
(Gordanlnejad et al. [ 79 ])
Materials used for
investigation
Novel magnetorheological-polymer gels (MPRG) were investigated,
with 81 % mass fraction of carbonyl iron particles added to the
synthesized crosslinked polyimide gel with addition of the additives
Constitutive model
Authors applied the Bingham model (Eq. 5.14). Chains of particles
in the form of columnar structures, parallel to the applied eld
hindered the
uid and increased the apparent viscosity of
the suspension. The pressure needed to yield these chain-like
structures increased with applied magnetic eld resulting in a eld-
(continued)
fl
ow of the
fl
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