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yield stress. With an increased shear rate ferro
uids can show Newtonian and shear
thinning behaviour. The Casson model (Eq. 5.16) considers the yield stress as well
as the shear thinning behaviour. The same is also true for the Herschel
fl
Bulkley
model (Eq. 5.17). Note that the yield stress is associated with the particle size, the
volume fraction and the magnetic
-
eld. The higher these are, the higher will be the
yield stress. This also depends on the potential agglomeration of the particles.
Title
Magnetic nano fl uid properties and some applications (V é k á s[ 33 ])
Materials used for
investigation
Magnetic fluids based on Fe 3 O 4 nanoparticles
Viscosity
Vand ' s equation (Eq. 5.6), and the equation given by Krieger and
Dougherty [ 34 ]
Title
Field-induced rotational viscosity of a ferrofluid: effect of capillary
size and magnetic eld direction (Andhariya et al. [ 35 ])
Materials used for
investigation
Nanomagnetic particles of iron ferrite in water and kerosene-based
ferro
uids. The particles were coated with a bi-layer of surfactant.
For the kerosene-based ferro
fl
uid the magnetite particles were coated
with a single layer of surfactant and dispersed in kerosene. The
volume fraction of particles in the water-based magnetic
fl
fl
uid was
0.64 %, while in the kerosene-based magnetic
uid the particles had
a volume fraction of 2.24 %. The average particle diameter was
10.4 nm. The work is concentrated into eld-induced rotational
viscosity when a ferro
fl
fl
uid
fl
ows through a capillary placed in a
magnetic eld
Viscosity
The authors considered the rotational viscosity by Shliomis
(Eq. 5.23 )
Title
Design method for automatic energy transport devices based on the
thermomagnetic effect of magnetic
fl
uids (Lian et al. [ 36 ])
Materials used for
investigation
A kerosene-based Mn - Zn ferrite magnetic fluid with a saturation
magnetization of 6.5 × 10 4 Am 1 . The average diameter of the
suspended magnetic particles was about 6.8 nm and the volume
fraction of the ferrite magnetic nanoparticles was 0.045
Viscosity
The authors applied Einstein
s equation (Eq. 5.2 ), which they
extended with a linear form to account for the in
'
uence of the
magnetic eld on the viscosity. Using a combination of two
equations they proposed a new equation, which takes into account
the in
fl
fl
uence of the magnetic eld
Title
Influence of large size magnetic particles on the magneto-viscous
properties of a ferrofluid (Shah et al. [ 32 ])
Materials used for
investigation
Three ferro
uid contained
magnetite particles with an average size of 10 nm dispersed in
transformer oil. The second
fl
uids were investigated. The rst ferro
fl
fl
uid, denoted by authors as the
magnetorheological
uid, consisted of large magnetite particles,
having a 30-nm particle size dispersed in transformer oil. The third
fl
fl
uid was labelled as the nano- magnetorheological
fl
uid and
represented a mixture of the rst and the second
uid in different
weight proportions. The particles were coated with oleic acid
surfactant and dispersed in transformer oil. The magnetic eld was
increased from 0 to 1 T
fl
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