Journal Européen des Systèmes Automatisés
Vol. 55, No. 1, February, 2022, pp. 147-153
Journal homepage: http://iieta.org/journals/jesa
Electromagnetic Forces Effects of MHD Micropump on the Blood Movement
Fatima Merdj*, Said Drid
LSP-IE Laboratory, Electrical Engineering Department, University of Batna 2, Batna 05000, Algeria
Corresponding Author Email: merdj.fat@gmail.com
https://doi.org/10.18280/jesa.550116
ABSTRACT
Received: 27 December 2021
Accepted: 17 February 2022
The magnetohydrodynamic pump is an attractive solution, in particular for biomedical
applications. In an MHD pump, an electromagnetic force is created by the applied
magnetic field, which causes the fluid movement. The main advantage of the MHD pump
is there are no mobile (mechanical) parts and it can place directly on veins. The present
paper deals with the blood behaviour in the MHD micropump. A neodymium permanent
magnet is used for applying a magnetic field to the channel in the MHD micropump. The
numerical study examines the influence of the channel dimensions, the flux magnetic
density and the electrode potentials on the blood velocity. This micropump can be easily
controlled by a low voltage source. The numerical simulation analysis for the adopted
model was implemented in order to verify the micropump operation. The magnetic and
electrical fields have a strong influence on blood velocity in the MHD micropump. Finite
element modelling software was used for this process. The second objective of this work
is the possibility to exploit the properties of this pump in hemodialysis to pump blood and
cleaning fluid.
Keywords:
biomedical
microsystems,
micropumps,
magnetohydrodynamic (MHD), DC MHD,
Lorentz force
produces the actuation mechanism to transfer with potential
for impact over a wide field of research [6].
With the potential to impact a broad field of research, the
main criteria for classifying them are their principle of
operation, design, size, precise flow control, low energy
consumption and compatibility with other microfluidic
systems. The applications of these microfluidic devices are
mainly in the biomedical field. In general, mechanical and
non-mechanical micropumps are the two types of micropumps
available. Micropumps that have mechanical parts in motion
are designated as mechanical micropumps whereas those
which do not have moving parts are called non-mechanical
micropumps. MHD domain access to biomedical applications
was noticed, especially in the blood flow study. When the
human body is subjected to an MRI scanner, blood flow is
considered as a conductor that is submitted into the magnetic
field creating “Lorentz force” and inducing electrical voltages
across vessel walls [7]. This attracts more attention in the most
recent studies [8, 9].
The magnetic properties of blood allow being treated with
an electromagnetic field. In comparison to conventional
medical pumps, electromagnetic blood flow pumps have a
more elegant and long-lasting technology [10].
The MHD pump with high output pressure, rapid response
time and low power consumption are one of the actuation
technologies that is often discussed due to its simplicity [11].
the fundamental working concept of such pumps is the study
of the interaction between an electrical current and a
perpendicular magnetic field passes through moving,
conducting fluids [12], where the magnetic field has many
effects on natural and artificial flows. As a result, the fluid ions
are subjected to a Lorentz force [13]. This force causes a
pressure difference in the flow cell that pumps the fluid flow.
The MHD pumps advantages are the absence of moving
1. INTRODUCTION
The human body in its natural state, kidneys, these 2 small
biological organs in the renal system represent a vital function.
By assisting the body in excreting waste as urine and
filtering blood before returning it to the heart, they serve a
variety of vital activities [1]. Kidneys that have been damaged
lose their capacity to execute these functions, and there are a
variety of treatments for chronic renal failure but dialysis is
currently the only treatment available for this kind of patient
in the absence of a transplant [2].
Hemodialysis is a method of cleansing blood outside the
body that involves drawing blood from a vein and putting it
through a synthetic filter called a dialyzer. The dialyzer is also
known as an "artificial kidney" since it filters waste products,
chemical substances, and fluids from the blood before
returning it to the body. A dialysis machine governs the
process by pumping blood across the circuit, adding dialysis,
and regulating the cleansing process. Hemodialysis, which
takes three to six hours on average and is done at least three
times a week, is normally done in a medical centre [3]. New
innovations are required in this field in order to develop an
intelligent dialysis system that can analyse and understand
changes in patient homeostasis and respond properly in realtime.
Technological advances are needed in machine size,
efficiency, and robustness to ensure continuous patient
monitoring and treatment optimization [4]. It is concerned
with the creation of miniature devices capable of detecting,
pumping, mixing, and controlling small quantities of fluids.
Among the microfluidic systems are micro-pumps, which are
an interesting device that provides the means to control and
distribute small volumes of flow rates [5]. As a result, the
micropump is an important part of drug delivery systems that
147
parts, simple fabrication processes, no risk of mechanical
fatigue and continuous fluid flow [14]. A prototype of an
MHD pump was realized in the LSPIE Lab at the University
of Batna 2, Figure 1.
J = 0
(3)
E = 0
(4)
where, B is the magnetic induction, E is the electric field, 0 is
the volume density and 0 is the permittivity of space, D is
Electrical induction. By combining with Ohm's Law:
J = [E + u B]
(5)
J = [− + u B]
(6)
Ohm's Low:
The electromagnetic part of the problem is presented by
Maxwell-Ampere’s law in Eq. (1), Ohm’s law in Eq. (5) and
the conservation of the electrical current in Eq. (6), u is the
velocity of the fluid, J is the total current density, is the
electrical conductivity, is the permeability. Here the
electrical potential scalar is determined by solving the
Poisson equation:
2 = (u ( Α))
where, A is the magnetic potential vector. In such a situation
where a current is allowed to flow across the medium, an
additional force is present. this force is generated by the
interaction between the external magnetic field and that of the
conductor.
Lorentz force which is written:
Figure 1. Laboratory setup
In the Figure 1 we can identify the channel which is made
of PVC material with two electrodes, a magnetic circuit, a coil
to vary the magnetic field and a flexible pipe to channel the
liquid, as well as measuring devices (running and voltage) and
two DC sources.
The main contribution of this work is the design and the
optimization of the DC-MHD parameters to improve the
efficiency the pumping of blood movement.
2. THEORETICAL ANALYSIS
(1)
D =
(2)
F = JB
L
(8)
1
F = ( B ) B
L
0
(9)
where, FL is the Lorentz force, J is the total current density, B
is the magnetic induction and through the derivation of the
behaviour of interacting magnetic fields, Maxwell’s equations
can then be applied to fluid flow and MHDs.
Inducing current in a moving conductive fluid in the
presence of a magnetic field generates a force on the
conductive fluid's electrons and also modifies the magnetic
field itself, according to MHD theory [14].
The laminar flow models must be applied. The steady-state
magnetohydrodynamic model's formulation has been defined
by
the
Navier-Stokes
equations,
coupled
with
Electromagnetism, defined by Maxwell's equations.
In both flow models, a Newtonian incompressible fluid was
considered [15].
(No magnetic monopoles )
B = 0
B
(Faraday law )
E = −
t
E = o
(Gauss law )
o
B = J + E
(Ampere law )
o
o o t
(7)
2.1 Application of Lorentz force to fluid flow
In this study of MHD micropump, a steady-state is
considered, an incompressible laminar flow and the velocity
of the fluid along the y and z axes also estimated to be nulls
are chosen. Based upon the above assumption, the axial flow
velocity (u) is invariant along the x-direction such that. On the
other hand, the influence of surface tension is ignored because
the microchannel is assumed to be filled with fluids.
For the simplified flow field, the governing equations can
be written as follows:
Equations systems (10) and (11) represent respectively the
continuity equation and Navier-Stokes equations which define
the physics of the fluid flow [16].
Steady Maxwell Equations:
148
.u = 0
(10)
( u. ) = −P + 2u + F
(11)
In Eq. (18), the static temperature is T, ρ is density, Cp is
specific heat and thermal conductivity is k. The source term (S)
in Eq. (18) is shown by [18, 19]:
Particulate interactions must be considered when blood
flow in the human body is exposed to a magnetic field. The
total electromagnetic force can also be represented as the sum
of the Lorentz, magnetophoretic, and electrostatic forces, and
these solutions are generally considered homogeneous and
electrically neutral flow.
F =F +F
+F
L
B
E
S =
(12)
u
t
1
( B ) B
0
+ u.u = −P + 2u +
2T
2T
+
0=k
2 z 2
y
(
(13)
)
= (1 + 0.02T
0
2
2
u
+
z
)
(21)
The geometry of the MHD pump is a rectangular crosssection, and domain requirements are dependent on blood's
physical properties as indicated in Table 1. The Figure 2
represents the structure and dimensions of the studied MHD
pump.
Permanent magnets are installed at the top and bottom of
the tube holding electrodes, as shown in Figure 2. Separate
voltages (+V) and (-V) are applied to the two electrodes. The
fluid can be moved by applying a voltage to the electrodes.
(15)
The pressure gradient created by applied DC electric and
magnetic fields in the flowing fluid. After substituting the
pressure gradient in Eq. (14). the momentum equation is
written as Eq. (16) [17].
=0
(16)
The volumetric flow rate Q in the microchannel area is
given by Eq. (17).
Q = u ( y , z )dydz
Figure 2. Structure of the studied MHD pump
Table 1. Parameters for numerical solution
(17)
Parameter
Channel length
Channel width
Channel high
Electrode width
Electrode length Le
Magnetic flux density Br
Density ρ
Electric Conductivity σ
Maximum input voltage
Specific heat
Thermal conductivity
Inducing current in a flowing conductive fluid in the
presence of a magnetic field produces a force on the
conductive fluid's electrons, as well as modifying the magnetic
field and causing a temperature change, according to MHD
theory [10]. As a result, we need to look into how it affects the
blood.
Equation of energy:
2
T
2
= k T + ( u ) + S
t
C p
(20)
3. THE MHD PROBLEM AND THE NUMERICAL
MODELING
In the MHD micropump, the Lorentz force acts on the whole
body of the fluid and generates a body force which is
considered as pressure drop uniformly distributed over the
channel region, This ∆P acts on the cross-sectional area of the
channel by the Lorentz force. where Δp is the pressure along
of the channel is given by the cross products of the length of
electrode Le and the vector product of the current density and
magnetic field, the equation is represented bellow:
2
BEL
2
2
e − B Le u + u + u
L
y 2 z 2
L
(19)
The relationship between electrical conductivity and fluid
temperature is as follows [20]:
(14)
P = ( J B ) .Le
+ u
y
+ E 2 + u 2B − 2uB
under electromagnetic interactions, the Lorentz forces
affecting the fluid particles are assumed to be a hydrostatic
pressure uniformly distributed over the entire channel region,
it is written as follow:
P = P
L
x
)
Combining Eqns. (18) and (19) gives:
In most clinical uses of the MHD effect, applied magnetic
field is homogeneous and static, the magnetophoretic and
electrostatic forces are also assumed to be zero in Eq. (12),
then the only remaining force is the Lorentz force Eq. (9) to be
replaced in the Navier-Stokes equation Eq. (13). This
represents the flow of a conductive fluid when exposed to an
external magnetic field.
(
J2
= E 2 + u 2B − 2uB
(18)
149
Value
0.04 m
0.008m
0.004m
0.004 m
0.008 m
0.4 T-1.2T
1060 (kg/m3)
0.667 (S/m)
2-10V
3750 (J/kg-K)
0.6(W/m-K)
the distribution of heat in the channel for different voltage
values. The Figures 12-16 illustrate velocity of the liquid in
the channel according the voltage, induction variations and
electrodes dimensions.
Figure 3. Coupling and resolution method
The boundary conditions can be specified as follows:
Inlet velocity for blood is considered 0.05m/s. No slip
condition for all walls, 𝑢(𝑥, 0, 𝑧) = 0, 𝑢(𝑥, 𝑊, 𝑧) =
0, 𝑢(𝑥, 𝑦, 0) = 0, 𝑢(𝑥, 𝑦, 𝐻) = 0 Pressure in outlet was Outlet
P= 0 Pa. walls: body force: FL (Lorentz force).
An initial temperature of 310 Kelvin is applied to the blood
channel.
The Figure 3 represents the hydrodynamic-electromagneticthermal coupling method used in this study. The finite element
method is applied to solve the magnetohydrodynamic and
thermic problem to determine the velocity, the pressure and
the temperature of the fluid in the channel. The weak coupling
is used because it is easy for implementation and gives good
results.
In the steady-state operation, the 3D MHD equations given
here are conveniently solved using a finite element
discretization approach. Due to the coupling between these
sets of equations, an iterative solution approach is used. the
electromagnetic components as given by the Gauss law and
the magnetic induction are solved to determine the magnetic
flux density (B). The electric potential (Φ), the electric field
(E) and current densities (J) are then determined by solving the
Poisson equation and Ohm's law. After that, the Lorentz force
is calculated as a vector cross product of the current density
and magnetic flux density vectors. Different results are
represented in the next section.
Figure 5. Current density in the length of the channel
Figure 6. Distribution of Lorentz volumic force along the
channel
4. RESULTS
Figure 7. Lorentz volumic force along the channel
Figure 4. Current density in the length of channel
The current density is presented in Figures 4 and 5. The
Lorentz volumic force is presented in Figures 6-9. They
present the Lorentz force in the MHD channel for different
values of voltage and induction. The Figures 10 and 11 present
Figure 8. Volume force for different values of Br
150
Figure 9. Volume force for different values of Voltage
Figure 13. Blood velocity field for different values of voltage
Figure 10. Distribution of temperature a long of the channel
Figure 14. Blood velocity for different electrode length
Figure 11. Temperature for different values of electric
voltage
Figure 15. Distribution of blood velocity for Le=8mm
and V=4V
Figure 16. Distribution of blood velocity for Le=8mm
and V=10V
Figure 12. Blood velocity x component along the channel
151
the pump corresponds to a notable increase in the exit of the
channel. The effect of the electric field on the speed of the
blood is noticeable and cannot be overlooked. It is observed
that the increase in tension slows the movement of blood in the
channel. This can be explained by the effects of the appearance
of turbulence.
The speed and the temperature of the flow blood in MHD
pump are strongly reliant on both the magnetic and electrical
fields. The performance of the DC-MHD pump is optimal for
4V and 0.4T.
Another optimized prototype of DC-MHD pump will be
designed according this study and included in the
haemodialysis system.
5. DISCUSSIONS
The Lorentz volumic force is presented in Figures 6 and 7.
Where the force is created in the active length of the MHD
micropump. The value of the force is high in the active part of
the magnetic times Br=1.2T) in the middle of the channel,
while the value of the magnetic flux near the electrodes is
about 0.01T. The intensity of the magnetic field is stronger at
the centre of the electromagnetic domain.
The volumic force is represented in Figures 8 and 9. The
increasing of Br needed the increasing of Lorentz force; it
attaints maximum value (200N/m3) for Br=0.4T and
maximum value (600N/m3) for Br=1.2T.
Figures 8 and 9 illustrate Lorentz force contribution for
different y positions for V=2V and Br=0.4T, the maximum
value of the Lorentz force was located in the middle of the
channel and 0N in the Iron for the applied volume. The
volumic force is represented for different values of the electric
voltage of 2V to 10V for a Br=0.8T. The maximum volumic
force is 400N/m for V=2V and 2000N/m3 for 10V.
It considered that the electric current passing in any carrier
solution is accompanied by a variation in temperature, figure
10 present the distribution of heat in the channel, we note that
the temperature takes maximum values in the field near the
electrodes.
Figure 11 illustrate the temperature profile along the
channel for different values of tension, the increase in the
value of electrical tension increases the blood temperature. In
Figures 12-15 the effect of electromagnetic field on blood
velocity for 0.8T and 2V, 4V and10V.
Figure 12 presents the effect of electromagnetic field on
velocity profile in V=2 volt of electrical voltage and remanent
magnetic density of 0.4 to 1.2 T is provided. we have a velocity
profile while the maximum velocity of 0.078 m/ s in Y = 0 mm
is reached. By variation of the magnetic flux density, there is
a Small significant change of the velocity profile
approximately 17mm from the channel inlet. We notice that
the velocity is almost laminar and it was 0.05m/s in the inlet
and maximal in the outlet of the channel, it attains value
0.08m/s.
We notice that for low voltages the speed of the blood varies
almost linearly along the channel. But from some voltage
values, we observe a drop in blood speed. This phenomenon is
comparable to the armature magnetic reaction of the DC motor,
Figure 12-14.
Also, we notice that the increase of the electrode length
improves blood velocity profile, Figure 14.
In Figures 15 and 16 the velocity profile is represented, with
an electrode length of 8mm under two voltage values V=4V
and V=10V.
In Figure 15 we can see the presence of turbulence in the
active part of the electrode.
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This work presents a study of a DC-MHD pump which was
realized in the laboratory. The goal of the study is to improve
the efficiency of the pump by optimizing the electrical,
magnetic and dimension parameters. The obtained results are
matched expected based on theoretical considerations, as well
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The speed of blood flow presents a maximum at the middle
of the MHD channel. However, the pressure of the fluid inside
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