MAGNETIC FIELD ANALYSIS ON A NOVEL ELECTROMAGNETIC ACTUATOR FOR FLUID HANDLING APPLICATIONS

A.T. Al-Halhouli

Institute for Microtechnology, Technische Universität Braunschweig, Braunschweig, Germany Abstract: This work presents a novel electromagnetic actuation concept that aims at the conversion of electromagnetic force into fluid power to enable gentle handling of biomedical fluids through circular microchannel. This concept is tested successfully on a mesoscale model and showed attractive concept suitable for microfluidic applications. In microtechnology, planar microcoils that offer enough magnetic forces suitable for actuation purposes are required. For this purpose, simple analytical expressions that estimate for the magnetic field intensity at different parameters (current, number of turns and gap between two neighbouring turns) in a planar spiral curved microcoil are developed. Keywords: electromagnetic actuator, microcoils, magnetic field INTRODUCTION

Recently, research and development in the biomedical and lab-on-a-chip fields become highly attractive, where many researchers direct their efforts toward producing efficient chips for online testing and analysis. Many of these devices are concerned with particle-laden fluids and thus require gentle, valve-less handling of the targeted samples. As an example, the function of valves of a pump can be inhibited by carried solid particles by either clogging the valve opening or damaging its seal [1]. In addition, many of the concerned particles are sensitive to shear stresses, and must be handled gently in order to preserve their fragile constituents [2].

The manipulation of fluids carrying particles using magnetic force offers a gentle method since it works at relatively low shear stresses and temperatures and the effect of the magnetic field on particles is not affected by surface charges, pH-level and ionic concentration [2]. Such manipulation can be performed using external magnets or microfabricated planar coils.

Microcoils are key element in the microelectromagnetic devices. They have been used in valves [3] and digital microfluidics [5]. Their magnetic field intensity (

!

H ) can be controlled through adjusting the current passing through the wire. However, the possibility of generating strong magnetic force is also a function of the number of coil turns as well as gap between two neighbouring coil turns, g.

Since the space available for microdevices are limited and the microcoil should be designed within hundreds of micrometers, maximizing the number of coil turns is directly influenced by the geometrical design parameter g.

This investigation introduces the new actuator concept and presents the analytical derivations for the magnetic field intensity for slightly curved microcoils. The effect of geometrical parameters, current and number of turns on the magnetic field intensity will be also described. ACTUATOR CONCEPT

The new electromagnetic actuator is comprised of a fluid housing, two pistons of permanent magnets and coils wrapped around a circular fluidic channel as shown in Fig. 1.

Fig. 1: Electromagnetic actuator components.

The actuation concept depends on controlling the

movement of two permanent magnet pistons. An electronic circuit is used to energize simultaneously a set of coils arranged around a circular fluid (Fig. 2). The pistons are placed in opposing polarities inside the channel to prevent any sticking between them during the actuation cycle [5].

For fluid handling purposes, two of the coils are located between the inlet and outlet ports while the

5 mm

PowerMEMS 2009, Washington DC, USA, December 1-4, 20090-9743611-5-1/PMEMS2009/$20©2009TRF 308

rest are distributed along the channel. According to the required application, pumping or mixing the energization scheme can be controlled through programming a microcontroller.

Fig. 2: Electromagnetic actuator concept.

As an example on fluid handling applications,

pumping action can be described. The two coils located between the inlet and outlet ports are used to hold magnet 1 at position A, so a valving action that prevents the inlet flow from joining the outlet one and direct the pumped fluid into the outlet port is satisfied. The rest of coils distributed around the channel employ a simultaneous magnetic force in steps on the free magnet (piston 2) and move it from one to the other until reaching point C. From this point, the two magnets move together, where piston 2 stops at position A and piston 1 continues the pumping cycle. This process is repeated for the required number of pumping cycles.

For microfluidic applications and by using microfabrication technology, planar microcoils are the source of the magnetic field intensity. However, modifications on the energization schemes are required to ensure enough magnetic force to drag the magnets against the fluid.

MATHEMATICAL MODELIGN OF H IN SPIRAL PLANAR CURVED MICROCOILS

The concept of the new electromagnetic actuator depends on controlling the rotation of two pistons in a circular microchannel to satisfy a fluid handling action. For this purpose and since magnetic force plays a dominant role in the actuator design, curved spiral microcoils are electroplated between SU 8 protrusions as shown in Fig. 3. The magnetic force in such microcoils is a function of the number of coil turns and coil geometrical design parameters: gap between coil turns, g and the distance of the first turn from coil center, ao.

By considering slightly curved microcoils (Fig. 4a), the mathematical model can be simplified by approximating the curved microcoils into a rectangular coils with a mean dimensions (Fig. 4b).

Fig. 3: microfabricated spiral coils.

This approximation can be used to investigate the effect of gap between coil turns, g on

!

H in a coil of n-turns carrying current I (Fig. 5a).

Fig. 4: Curved microchannel approximate model.

Further simplification can be implemented by considering that the coil is a set of closed square turns (Fig. 5b). The solution then begins by estimating for !

H in a segment until reaching a complete model in n-turn, multilayer coil.

Fig. 5: representations of the coil in the x-y plane. Magnetic fields of a single square planar turn

The Biot-Savart law gives a relation for !

H at a point in space due to a current I [6]. Generally,

!

H at a point in space P(x, y, z) due to a current I located at P′(x′, y′, z′) (Fig. 6) can be predicted from:

!

""" #=

b

a R

RldIH

2

4

1

$

(1)

Cu

SU 8

(a) (b)

(a) (b)

100 µm

309

Fig. 6: Magnetic field intensity in a wire segment.

To estimate for the magnetic field intensity!

H at a point P(x, y, z) in a single square turn, four segments (1 – 4) are considered (Fig. 7).

Fig. 7: representations of the magnetic field in a square turn.

The total magnetic field !

H can be estimated as !!!!!

+++=4321

HHHHH (2) Solve for segment 1 between y2 and y1, Eq. 1 can be

written as

!

""" #=

1

2

21

4

1y

y R

RlIdH

$

(3)

or

!"#

$%&

'()*+

,- .+(

)*+

,- .+(

)*+

,- .

((((

)

*

++++

,

-

..

.

=/ 1

2

3/22

'2

'2

'

'

1

.

)(

0

4

1y

yzzyyax

dy

ax

zz

H

0

(4)

where a represents the distance between the centre of the coil and the targeted segment. (x, y, z) and (x′,

y′, z′) are the coordinates of the vectors !

r and !'

r respectively. So the magnetic field components can be presented for each component as:

!"#

$%&

'()*+

,- .+(

)*+

,- .+(

)*+

,- .

.=

/ 1

2

3/22

'2

'2

''

1

. )(

4

1y

y

x

zzyyax

dyzzH

0

(5)

0.01=

!

yH (6)

!"#

$%&

'()*+

,- .+(

)*+

,- .+(

)*+

,- .

..=

/ 1

2

3/22

'2

'2

'

1

. )(

4

1y

y

z

zzyyax

dyaxH

0

(7)

The same can be done with the rest of segments and results are summarized as below:

!"#

$%&

'()*+

,- .+(

)*+

,- ..+(

)*+

,- .

((((

)

*

++++

,

-

...

=/ 1

2

3/22

'22

'

''

2

)(

.

))((

0

4

1x

xzzayxx

dx

ay

zz

H

0

(8)

!"#

$%&

'()*+

,- .+(

)*+

,- .+(

)*+

,- ..

((((

)

*

++++

,

-

...

.

=/ 2

3/22

'2

'2

'

'

3

1 )(

.

))((

0

4

1y

yzzyyax

dy

ax

zz

H

0

(9)

!"#

$%&

'()*+

,- .+(

)*+

,- .+(

)*+

,- .

((((

)

*

++++

,

-

.

.

=/ 2

1

3/22

'22

'

''

4

)

.

)(

0

4

1x

xzzayxx

dx

ay

zz

H

0

(10)

The resultant magnetic field intensity on the point P is the summation of each component in the (x, y, z) coordinates for the four segments (I = 1, 2, 3 and 4):

!= "

""

#

$

%%%

&

'

="""

#

$

%%%

&

'4

1i

iz

iy

ix

z

y

x

H

H

H

H

H

H

(11)

Magnetic field of Multi-layer square planar coil

To estimate for !

H in one layer with n-turns, the initial distance from the centre to the n-turn segment (aj) can be written as

gjaaoj

)1( !+= (12) where j is the turn number, j = 1, 2, ..n and g is the

gap between two neighbouring turns (Fig. 5b). Further, if multilayer coils are considered, then the z-coordinate will vary according to

dkzzk

)1(''

!!= (13) where k = 1, 2,..k is the number of coil layers, and d

is the distance between two simultaneous layers. The resultant

!

H of multilayer coil can be estimated according to:

!!!= = =

"

###

$

%

&&&

'

(

=###

$

%

&&&

'

(

=k

k

n

j i

iz

iy

ix

z

y

x

H

H

H

H

H

H

H1 1

4

1

(14)

310

RESULTS AND DISCUSSION The strength of the magnetic field plays an

important role in electromagnetic microactuators design and performance. Optimizing the microcoil design parameters will improve the attracting/repelling magnetic force exerted on the moving or holding magnets and minimizing the power consumption in the final devices within available space. Matlab (MathWorks Inc, 2008) program is developed to predict

!

H at different parameters. !

zH

along the centreline of a one layer coil (y = 0) are shown in Fig. 8.

Fig. 8: z–magnetic field intensities (n=12, g=200 µm, z=1 mm, I=0.5 A).

Results showed typical curve of

!

H in a rectangular coil and offer indicator for the maximum displacements that can be considered under targeted magnetic field strength.

Figure 9 shows the direct proportionality between !

H and the number of turns. This means that our design should contain the maximum number of turns within available compact place and encourage optimizing the gap between two neighbouring turns, g.

Fig. 9: z–magnetic field intensities at different coil turns (ao=75 µm, g=26 µm, z=1 mm, I=0.5 A).

As given in Fig. 10, an interesting results is deduced for the effect of g on

!

H . It increases by increasing g until certain limit ( g = 50 µm) and then decreases again. This introduces a critical g value that should be considered for each design. The critical

value is related to the optimal point of intersection of the magnetic field lines to obtain maximum strength.

Fig. 10: z–magnetic field intensity at different g’s (n=37, ao=75 µm, z=1 mm, I=0.5 A). CONCLUSION

A novel electromagnetic actuation concept that depends on the rotation of two permanent magnets in a circular channel is introduced. For microfluidic applications, the magnetic field intensity in a planar spiral curved microcoil at different parameters is studied toward optimum strengths analytically. Results showed that the microcoil design parameters have critical values that can be calculated for each design using developed model. Further experimental work is recommended to validate the results. ACKNOWLEDGEMENTS

This work is supported by the Deutsche Forschungsgemeinschaft (DFG). REFERENCES [1] Hatch A, Kamholz A E, Holman G, Yager P,

Bohringer K F 2001 A ferrofluidic magnetic micropump. J. Microelectromech. Syst. 10 215-21.

[2] Nguyen N, Chai M 2009 A stepper micropump for ferrofluid driven microfluidic systems. Micro and Nanosystems 1 17-21.

[3] Krishnan M, Victor M U, Burns M A 2002 PCR in a Rayleigh-Bénard Convection cell. Science, 298 793

[4] Oda R P, Strausbauch M A, Huhmer A F R, Borson N, Jurrens S R, Craighead J, Wettstein P F, Eckloff B, Kline B, Landers J P 1998 Infrared-mediated thermocycling for ultra-fast polymerase chain reaction amplication of DNA. Anal. Chem., 70 918–922.

[5] Al-Halhouli A T, Kilani M I, Büttgenbach S 2009 Development of a novel meso-scale electromagnetic pump for biomedical applications. Procedia chemistry, 1 349-352.

[6] Ida N 2000 Engineering Electromagnetics (Springer-Verlag New York, Inc).

n = 48

n = 23

n = 5 n = 12

n = 60

311