Q. FANG et al.: STUDY OF FACTORS INFLUENCING THE WALL SLIP OF A MAGNETORHEOLOGICAL FLUID
689–696
STUDY OF FACTORS INFLUENCING THE WALL SLIP OF A
MAGNETORHEOLOGICAL FLUID
RAZISKAVA FAKTORJEV, KI VPLIVAJO NA DRSENJE POVR[INE
V MAGNETOREOLO[KIH FLUIDIH
Qibo Fang, Yiping Luo
*
, Weicheng Wang, Shicheng Wang, Shichong Song,
Luyun Zhang
School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai, China
Prejem rokopisa – received: 2022-10-07; sprejem za objavo – accepted for publication: 2022-11-04
doi:10.17222/mit.2022.643
The wall slip of magnetorheological (MR) fluids refers to a phenomenon that affects the application of mechanical properties of
magnetorheological fluids due to the relative slippage between the magnetic particles and the transmission wall. In this paper,
we analyze and experimentally verify the factors affecting the wall slip of magnetorheological fluids, which can limit the appli-
cation of magnetorheological-fluid devices. Firstly, from the theoretical point of view, it is considered that the influencing fac-
tors are mainly divided into two parts: magnetorheological fluid’s own parameters and transmission surface roughness, among
which the parameters include viscosity, mass fraction, etc. When studying the influence of the transmission surface roughness, it
is found that different surface morphologies have a great influence on the shear stress. Secondly, a magnetic field simulation
analysis and shear yield stress experiments are conducted on shear blocks with different surface morphologies; the obtained re-
sults are compared and verified, confirming that different surface shapes affect the shear yield stress by changing the magnetic
field distribution of the groove, which in turn changes the wall slip characteristics. These findings provide an effective basis for
further research on the wall slip of magnetorheological fluids to improve the transmission effect.
Keywords: magnetorheological fluid, wall sliding characteristics, magnetic field distribution
Drsenje na stenah magnetoreolo{kih (MR; angl: magnetorheological) fluidov je pojav, ki vpliva na njihovo uporabnost v
povezavi z njihovimi mehanskimi lastnostmi zaradi relativnega drsenja magnetnih delcev in stene. Opisana je analiza in
eksperimentalna verifikacija faktorjev, ki vplivajo na drsenje magnetoreolo{kih fluidov na stenah. V prvem delu ~lanka je
obravnavan problem s teoreti~nega stali{~a s poudarkom, da lahko vplivne faktorje razdelimo na dva dela: notranje oziroma
lastne parametre magnetoreolo{kih fluidov (viskoznost, masni dele` itd.) in parametre sti~ne povr{ine. Med raziskavo vpliva
morfologije povr{ine so avtorji ugotovili, da imajo razli~ne morfologije povr{ine velik vpliv na stri`no napetost. Izvedli so tudi
primerjave in preverili analize simulacij magnetnega polja in poizkusov stri`ne napetosti na meji te~enja s stri`nimi bloki z
razli~no povr{insko morfologijo. Dobljeni rezultati in primerjave so pokazali, da razlike v obliki povr{ine vplivajo na stri`no
mejno napetost te~enja v sozvo~ju s spremembo porazdelitve magnetnega polja povr{ine, ki povratno vplivajo na drsne
karakteristike stene. Ugotovili so, da izvedene raziskave predstavljajo dobro osnovo za nadaljnje raziskovanje obna{anja
magnetoreolo{kih fluidov.
Klju~ne besede: magnetoreolo{ki fluidi, drsenje stene, porazdelitev magnetnega polja
1 INTRODUCTION
With the rapid development of science and technol-
ogy and the advancement of research methods, people
gradually began to pay attention to the wall slip proper-
ties of MR fluids.
1
The wall slip properties of MR fluids
started to receive attention when magnetorheological
products were widely used, and more mature MR prod-
ucts appeared in the 21
st
century. The research on the
wall slip properties of MR fluids is still in its initial stage
and still needs a lot of theoretical knowledge for its sup-
port. The yield stress of MR fluids is an important basis
for their application and an important indicator for deter-
mining the wall slip of MR fluids. However, due to the
complexity of the working environment of MR fluids
and the specificity of their own materials, the yield stress
of MR fluids cannot be characterized more accurately at
present. The accuracy of using the shear yield stress
2
to
determine the occurrence of wall slip characteristics still
needs to be improved.
The wall effect of MR fluids was first discovered by
Lemaire et al.
3
at the University of Nice, France, who
measured the yield stress of magnetorheological fluids
with a rheometer and found that the yield stress values
were always lower than the predicted values based on
interparticle forces. And through further studies it was
found that the type of material and surface roughness of
a transmission wall had a great influence on the yield
stress values of MR fluids. The MR fluid viscosity con-
sists of magnetic particles and carrier fluid viscosity.
4
It
is known from the Herschel-Bulkley
5
model that with an
increase in the shear rate, a shear thinning
6
phenomenon
occurs, leading to a decrease in the MR fluid viscosity.
Shear thinning also has an impact on the occurrence of
wall slip, so the viscosity of MR fluids must be carefully
selected in order to control the wall slip. The mass frac-
tion of MR fluids undoubtedly changes as a result of the
Materiali in tehnologije / Materials and technology 56 (2022) 6, 689–696 689
UDK 544.272 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 56(6)689(2022)
*Corresponding author's e-mail:
yipingluo@sues.edu.cn (Yiping Luo)

formulation of MR fluids with different viscosities,
which is also one of the main principles affecting the
yield stress of MR fluids.
Gorodkin et al.
7
studied the effect of the radial groove
wall surface and smooth wall surface on the magnitude
of yield stress of MR fluids. They established through
experiments that the effect was most visible under cer-
tain small particle volume fraction and strong magnetic
field conditions, and that the yield stress was increased
by 2.8 times. The radial groove effectively inhibited the
occurrence of a wall defect. Laun et al.
8
studied the ef-
fect of magnetic wall materials, nonmagnetic wall mate-
rials, and the effect of wall roughness on the wall slip
characteristics of MR fluids. The results showed that in-
creasing the roughness and number of grooves of non-
magnetic wall materials could increase the shear stress
transferred by them. While under magnetic wall condi-
tions, the wall roughness had no effect on the magnitude
of the shear stress generated. T. Zuzhi et al.
9
studied the
mechanism of the wall slip generation and the influenc-
ing factors from both theoretical and experimental as-
pects. They investigated the effect of wall slip character-
istics on the transfer capability of MR fluids on different
experimental benches. The results showed that the trans-
fer-wall material type and surface roughness have a sig-
nificant impact on the transfer capability of MR fluids.
C. Fei et al.
10
studied the effect of wall morphology on
the slip phenomenon. The results showed that different
wall morphologies have different effects on the slip. As a
result, the viscosity and mass fraction of MR fluids, as
well as the roughness of the transmission wall surface
can have an impact on the wall slip effect. The role of
different transmission surface topography features on the
prevention of slip is complex.
According to the above, the existing research on wall
slip characteristics is mainly qualitative experimental re-
search. The analysis of the mechanism of occurrence and
quantitative research on the influencing factors are lim-
ited. In the process of measuring the shear yield stress,
the centrifugal and inertia forces have an impact on the
measurement results. As a result, the accuracy with
which the shear yield stress is used to determine the de-
gree of wall slip needs to be improved. The wall slip
phenomenon is unstable, having an impact on the rheo-
logical properties of MR fluids.
11
In this paper, a quanti-
tative experimental study was conducted to verify the ef-
fect of the MR fluid viscosity and mass fraction on the
shear yield stress based on various indicators affecting
the wall slip. A simulation of the magnetic field distribu-
tion of shear blocks with different surface morphology
characteristics was carried out using the COMSOL soft-
ware. The results of the shear stress predicted by the sim-
ulation were compared with the experimental results to
find and verify how the magnetic field distribution of
shear blocks affects the wall slip effect, thus giving a
transmission solution for attenuating the wall slip effect.
2 EXPERIMENTAL PART
2.1 Preparations of experiments
MR fluids with (67, 72 and 77) % mass fraction were
configured using the base fluid replacement method and
placed in beakers with labels.
An experimental table was built. A magnetic field
generation device, shearing device and force measuring
device were used for this experiment. During the experi-
ment, the magnets were placed symmetrically at both
ends of the fixed base in order to produce as uniform a
magnetic field as possible. The drive mechanism, trans-
fer mechanism and reservoir were all part of the shear
device. The model of the stepper motor acting as a power
source was YZ-57BLS120 (Hangzhou Yizhi Technology
Co., Ltd.). In addition, we used a matching driver and
Q. FANG et al.: STUDY OF FACTORS INFLUENCING THE WALL SLIP OF A MAGNETORHEOLOGICAL FLUID
690 Materiali in tehnologije / Materials and technology 56 (2022) 6, 689–696
Figure 1: Experimental bench

controller to control the speed and lifting distance of the
stepper motor. The role of the transfer mechanism is to
convert the motor rotational force into pulling force,
mainly including a pulling rope and fixed pulley. The
reservoir is a device that holds the MR fluid so that the
shear block can be pulled out of the device, fixed by the
fixed base. For the material of the reservoir we selected a
transparent acrylic plate. In addition to allowing us to vi-
sually observe the shear block pulling process, it is also a
non-conductive material. It does not have an impact on
the reservoir magnetic-field distribution uniformity. The
length, width and thickness of the reservoir volume were
(60, 60 and 10) mm, respectively. The force measuring
device included a tension sensor and recorder (Shanghai
Longlv Electronic Technology Co., Ltd.). Finally, the
test stand was built with the above experimental equip-
ment. Its structure and location are shown in Figure 1.
2.2 Viscosity test
An NDJ-5S digital rotational viscometer (Shanghai
Star Optical Instrument Co., Ltd.) was selected. The sur-
face of the measuring rotor of the viscometer was cov-
ered with 60, 120, 240 and 400 grit sandpaper, respec-
tively. The MR fluid with the 72 % mass fraction was
selected and placed in a beaker to measure the viscosity
change under rotational speeds of (6, 12, 30 and
60) min
–1
.
2.3 Mass-fraction experiment and surface-roughness
experiment
Shear-yield-stress experiments were conducted at dif-
ferent magnetic field strengths using MR fluids with dif-
ferent mass fractions, in which a shear block without
sandpaper and the one covered with 60 grit sandpaper
were used.
The shear yield stresses of these two types of shear
blocks were measured at different magnetic field
strengths using the 72 % mass fraction MR fluid and
shear blocks covered with 60 or 400 grit sandpaper.
2.4 Simulation and experimental analysis of surface
morphological features
The magnetic field distribution of each groove on the
transmission surface is changed by different machining
shapes and sizes of the grooves on the surface, resulting
in a change in the force between the magnetic particles
and the transmission surface. The magnetically induced
shear yield stress is affected by the wall slip of MR flu-
ids. In other words, the surface topography has an impact
on the wall slip characteristics of MR fluids. The surface
processing of certain morphological features is a promis-
ing and feasible method for attenuating the wall slip
characteristics. The types of shear block grooves are
shown in Figure 2:
Shear blocks are semicircular, triangular, rectangular
and trapezoidal in shape, with each shear block having
the same number of grooves on one side and a direction
that is perpendicular to the shear direction. The parame-
ters of shear blocks are shown in Table 1.
Table 1: Model parameters of different slot shapes
Shear
blocks
Depth of
grooves (mm)
Width of
grooves (mm)
Number of grooves
Length
(mm)
Width (mm)
Thickness
(mm)
50 50 6 1 2 24
There are three directions of the grooves (horizontal,
45 degrees, vertical). The information of the shear blocks
is shown in Table 2.
Single-sided processing with 3, 6 and 12 vertical
rectangular grooves is applied.
The rectangular groove width of the shear block is
2 mm, and the depths are 1 mm and 2 mm, respectively.
Figure 2 shows how the shear block models were im-
ported into the COMSOL software for a magnetic field
analysis. The set uniform boundary conditions included
room temperature, 101.3 kPa (1 atm), spherical air do-
main outside the shear block and an air boundary radius
of 50 mm. The magnetization direction was perpendicu-
lar to the surface of the shear block, and the intensity
was 200 kA/m. A steady-state solution was used to ob-
Q. FANG et al.: STUDY OF FACTORS INFLUENCING THE WALL SLIP OF A MAGNETORHEOLOGICAL FLUID
Materiali in tehnologije / Materials and technology 56 (2022) 6, 689–696 691
Table 2: Parameters of different slotting directions
Size of shear blocks
(mm×mm×mm)
Material Shape of grooves Number of grooves
Size of grooves width
(mm) × depth (mm))
50 × 50 × 6 Aluminum Rectangle 24 2 × 1
Figure 2: Different slotting types of shear blocks: a) different shapes,
b) different directions, c) different densities, d) different depths

serve the magnetic field distribution around the shear
block grooves by dividing the tetrahedral mesh freely.
Then, on the constructed experimental table, a MR
fluid sample with 72 % mass fraction was measured un-
der the conditions of different surface characteristics of
the shear block, and a lifting experiment was performed
to obtain the variation in the shear yield stress with the
magnetic field.
3 SIMULATION RESULTS
3.1 Different slotting shapes
Magnetic field concentration is generated at the re-
cesses, as shown in Figure 3, in the magnetic field simu-
lation of the above four slotted shapes. A concentrated
magnetic field is located on both sides of a groove. The
concentrated areas of the magnetic fields in the semicir-
cular groove and rectangular groove are larger than those
in the trapezoidal groove and triangular groove. The
magnetic field distributions of the trapezoidal and rectan-
gular recesses fluctuate greatly and the maximum values
of the magnetic field are also large, so wall slips occur
easily. The magnetic field distribution of the semicircle
is small, as is the maximum value, and a wall slip is easy
to occur. According to the above analysis, the magnetic
particles produce greater magnetic adsorption on both
sides of a groove than at its bottom. It means that it is
easier for them to anchor at the sides (i.e., there is stron-
ger adsorption between the particles at the end of the
particle chain and the drive surface). It can be predicted
that the shear blocks with trapezoidal grooves and rect-
Q. FANG et al.: STUDY OF FACTORS INFLUENCING THE WALL SLIP OF A MAGNETORHEOLOGICAL FLUID
692 Materiali in tehnologije / Materials and technology 56 (2022) 6, 689–696
Figure 4: Magnetic field simulation of shear blocks in different grooving directions: a) horizontal, b) vertical, c) 45° direction
Figure 3: Magnetic field distribution at the grooves with different shapes: a) semicircular, b) triangular, c) rectangular, d) trapezoidal

angular grooves have more difficulties with the wall slip
than those with semicircular and triangular grooves.
3.2 Different slotting directions
As can be seen from Figure 4, the magnetic field in
the groove position is the smallest for all three grooving
directions. Magnetic field concentration is generated at
the ends of both faces of a groove. It demonstrates that
irrespective of the grooving conditions used, the end of
the magnetorheological fluid particle chain is under the
action of an anchor bolt.
In an actual working process, both vertical slotting
and 45° slotting have a certain blocking effect on the
movement of the particle chain. According to a compre-
hensive analysis and comparison, the order of the wall
slip characteristics of an MR fluid from difficult to easy
should be: vertical direction > 45° direction > horizontal
direction.
3.3 Different slotting densities
According to the previous analysis, processing rect-
angular recesses on the surface of a shear block produces
a magnetic field concentration effect at the rectangular
recesses. From the specific analysis from Figure 5,itcan
be seen that machining different numbers of rectangular
recesses on a surface can effectively produce the above
phenomenon at each recess. The larger the number of
rectangular recesses, the larger is the number of the posi-
tions where the magnetic particles can be anchored. The
greater the shear yield stress, the more obvious is the ef-
fect on suppressing the MR-fluid wall-slip phenomenon.
3.4 Different slotting depths
The magnetic field distribution for the two grooves in
the shear block transverse center is shown in Figure 6.
The magnetic field concentration in the 2-mm-deep
groove is more uniform, and the concentration area is
more evenly distributed on both sides of the groove. On
the other hand, the magnetic field concentration in the
1-mm-deep groove is mainly concentrated near the outer
Q. FANG et al.: STUDY OF FACTORS INFLUENCING THE WALL SLIP OF A MAGNETORHEOLOGICAL FLUID
Materiali in tehnologije / Materials and technology 56 (2022) 6, 689–696 693
Figure 5: Magnetic field simulation of shear blocks with different grooving densities: a) 3 grooves, b) 6 grooves, c) 12 grooves
Figure 6: Magnetic field simulation of shear blocks with different grooving depths: a) 1 mm, b) 2 mm

surface of the groove. The magnetic field concentration
becomes more visible as you get closer to the sharp cor-
ner of the outer surface. The maximum magnetic field
generated by the 1-mm groove is larger than that gener-
ated by the 2-mm groove on the whole groove surface of
the shear block. The magnetic field concentration loca-
tion of the 1-mm groove is close to the outer surface of
the shear block, which is more likely to produce the an-
chor bolt phenomenon. So it can be predicted that the
1-mm-deep recess should theoretically be more difficult
to generate a wall slip than the 2-mm-deep recess.
4 EXPERIMENTAL RESULTS
4.1 Viscosity experimental analysis
The viscosity of the MR fluid as a function of shear
rate is depicted in Figure 7a. The viscosity value of the
MR fluid varies with different-surface roughness values.
The rougher the surface, the higher is the viscosity value
at the same speed. At the same roughness of the rotor,
the zero-field viscosity value of the MR fluid decreases
as the shear rate increases, which is due to the shear thin-
ning phenomenon when the MR fluid is shearing. There-
fore, the viscous resistance can be increased by increas-
ing the roughness of the transmission surface, which in
turn weakens the wall-slip phenomenon.
4.2 Experimental analysis of the mass fraction and
roughness
Figure 7a represents the variation in the shear yield
stress at different mass fractions. The shear yield stress
increases as the mass fraction of the MR fluid increases,
as can be seen in the figure. This is due to the increase in
the mass fraction, which increases the number of mag-
netic particle chains. The measured yield stress increases
with the increase in the surface roughness of the shear
block. This indicates that the surface roughness has a
certain inhibitory effect on the wall slip of the MR fluid.
The degree of increase in the shear yield stress varies be-
tween the two types of mass fractions, indicating that the
influence on the MR fluid wall slip varies between the
two types of mass fractions.
At low mass fractions, the wall slip of the MR fluid
can be better suppressed by changing the external rough-
ness. This phenomenon is caused by a small number of
magnetic particles, poor chain aggregation under the
magnetic field, and a simple chain structure, which is
more likely to cause a wall slip. In this case, increasing
the surface roughness can have a better inhibition effect.
However, as the mass fraction of the MR fluid decreases,
the shear yield stress decreases, which has an impact on
practical applications. Although the average improve-
ment rate decreases as the mass fraction of the MR fluid
increases, the decrease is small and can still reduce the
wall slip within a certain range. In summary, a MR fluid
with a medium to high mass fraction should be used as
the working fluid. As can be seen from Figure 7b, when
the surface of the shear block is coated with sandpaper,
the shear yield stress of the MR fluid is greater under the
same magnetic-field working conditions, indicating that
an increase in the surface roughness effectively sup-
Q. FANG et al.: STUDY OF FACTORS INFLUENCING THE WALL SLIP OF A MAGNETORHEOLOGICAL FLUID
694 Materiali in tehnologije / Materials and technology 56 (2022) 6, 689–696
Figure 7: Variation of: a) zero-field viscosity under different rough-
ness surfaces, b) shear yield stress under different mass fractions,
c) shear yield stress under different surface roughness values

presses the occurrence of a wall slip of a magneto-
rheological fluid. The shear yield stress gradually in-
creases with an increase in the magnetic field strength.
But the increasing trend is gradually slowed down, indi-
cating that the effect of roughness on the wall-slip phe-
nomenon starts to weaken under the working conditions
of a high magnetic field strength.
4.3 Experimental analysis of surface morphological
characteristics
4.3.1 Different slotting shapes
As can be seen from Figure 8a, all four grooving
shapes have an effect on the wall slip of the MR fluid.
Among them, the shear yield stress of the shear block
with semi-circular grooves is slightly lower than that of
the shear block without grooves, indicating that the
semi-circular grooves have limited effect on suppressing
the occurrence of a wall slip. On the other hand, the tri-
angular grooves, rectangular grooves and trapezoidal
grooves all increase the shear yield stress to a certain ex-
tent. Rectangular and trapezoidal grooves have a better
effect, which is consistent with the simulation results. As
a result, rectangular or trapezoidal grooves on a wall sur-
face can be used to effectively reduce the wall-slip effect.
4.3.2 Different slotting directions
Figure 8b shows that under the same magnetic-field
operating conditions, the rectangular groove in the verti-
cal direction produces the highest shear yield stress and
the lowest stress in the horizontal direction, which is the
same as predicted by the simulation. The rectangular
groove in the horizontal direction does not improve the
shear yield stress of the MR fluid because the horizontal
groove direction is the same as the shear direction. The
magnetic particle chain of the MR fluid contributes to
the occurrence of a wall slip during the shear process. As
a result, grooves in the drive wall can be made in the ver-
tical direction or at an angle of 45° to the shear direction
to suppress the wall-slip effect.
4.3.3 Different slotting densities
According to Figure 8c, the shear yield stress of the
MR fluid does not increase significantly when the shear
block has 3 grooves on one side. The stress increases sig-
nificantly when the groove density reaches 6 and 12 on
one side. The simulation results are consistent with the
experimental results. The suppression effect, on the other
hand, decreases as the magnetic field strength increases,
indicating that the magnetic field strength has begun to
dominate. In summary, in order to effectively suppress
Q. FANG et al.: STUDY OF FACTORS INFLUENCING THE WALL SLIP OF A MAGNETORHEOLOGICAL FLUID
Materiali in tehnologije / Materials and technology 56 (2022) 6, 689–696 695
Figure 8: Variation in the shear yield stress under different surface morphologies: a) different shapes, b) different directions, c) different densi-
ties, d) different depths, e) different widths

the slip, more grooves should be machined on the trans-
mission surface.
4.3.4 Different slotting depths
Figure 8 shows that all the shear blocks increase the
shear yield stress after machining the grooves. However,
the shear block with 2-mm grooves produced less yield
stress than the shear block with 1-mm grooves, indicat-
ing that the grooving depth should not be too large. The
magnetic field concentration phenomenon is more obvi-
ous in the shear block simulation for the 1-mm notch
shear block. It means that the magnetic field concentra-
tion can make the magnetic particle chain anchor tighter
and generate a greater yield stress. This is due to the
fixed position of the magnetic field generating device
and the fixed working gap on the outer surface of the
shear block. When the depth of the groove increases, the
working gap on the inner surface of the groove becomes
larger, resulting in a loss of the magnetic field inside the
groove and a reduction in the stress. As a result, in order
to effectively suppress the phenomenon of the MR-fluid
wall slip, the depth of groove wall should not be too
large, and good results can be achieved at 1 mm.
5 CONCLUSIONS
The article experimentally confirms that the MR fluid
parameters and transmission surface roughness can influ-
ence the wall slip characteristics. Both the viscosity and
mass fraction of a MR fluid can effectively improve the
yield stress during shear by increasing the viscosity and
mass fraction of the MR fluid. The research demon-
strates that changing the viscosity and mass fraction can
be beneficial. The roughness of the transmission surface
has an impact on the wall slip. The viscous resistance of
the MR fluid increases with an increase in the surface
roughness. In addition, the shear yield stress is greatly
influenced by surface morphological characteristics. As
different groove shapes lead to different magnetic field
distributions, the structure of the magnetic particle chain
varies. The thicker and tighter the magnetic particle
chain, the greater is the anchor bolt force, and the more
likely it is to prevent the occurrence of a wall slip.
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Q. FANG et al.: STUDY OF FACTORS INFLUENCING THE WALL SLIP OF A MAGNETORHEOLOGICAL FLUID
696 Materiali in tehnologije / Materials and technology 56 (2022) 6, 689–696