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One-dimensional actuation of a ferrofluid droplet by planar microcoils
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2009 J. Phys. D: Appl. Phys. 42 015004
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IOP P UBLISHING J OURNAL OF P HYSICS D:A PPLIED P HYSICS J.Phys.D:Appl.Phys.42(2009)015004(8pp)doi:10.1088/0022-3727/42/1/015004
One-dimensional actuation of a ferrofluid droplet by planar microcoils
Ali Beyzavi and Nam-Trung Nguyen1
School of Mechanical and Aerospace Engineering,Nanyang Technological University,50Nanyang
Avenue,Singapore639798,Singapore
E-mail:mntnguyen@ntu.edu.sg
Received5September2008,infinal form21October2008
Published12December2008
Online at stacks.iop/JPhysD/42/015004
英语四级 作文Abstract
This paper discuss the simulation of a device for actuation of a ferrofluid droplet using
planar microcoils.The device with two pairs of planar microcoils was designed and fabricated
on a double-sided printed circuit board(PCB).Each pair is placed on each side of the PCB.
The coils on the bottom actuate the droplet along the line connecting their centres.The coils
on the top create a virtual channel to confine the motion of the droplet along a straight line.
The paperfirst formulates the model of the magneticfield of the coils.With the modelled
field,the corresponding forces acting on the droplet were calculated.The equation of
the motion of a ferrofluid droplet immerd in silicone oil is solved numerically.The influence
of different parameters such as driving current,droplet diameter and viscosity of the carrier
fluid is investigated.Theoretical and experimental results agree well quantitatively and
qualitatively.Both theoretical and experimental results show that a higher magneticfield,a
lower oil viscosity and a bigger droplet size will increa the peak velocity of the droplet.
1.Introduction
Thefield of microfluidics was originally established bad on continuousflows,but later also branched towards using droplets[1,2].Droplet-bad microfluidic systems po many benefits such as reducing the time of chemical reactions, using smaller amount of samples,the possibility of using non-mechanical actuation concepts and the resulting incread reliability of the devices[3].
During the past decade,a few actuation concepts have been ud to manipulate droplets.Electrostatic forces[4,5], thermocapillarity[6],acoustics[7]and magnetism[8]are some of the examples.Compared with the concepts, magnetism for manipulation of droplets has certain advantages. Objects can be manipulated by an external magneticfield that is not in contact with thefluid.Furthermore,the effect of magneticfield on particles is generally not affected by surface charges,pH level,ionic concentration or temperature[8].
Ahn et al ud integrated inductive components for paration of magnetic microbeads[9].Ramadan et al discusd the u of current carrying wires for manipulating magnetic particles[10].Lee et al ud a matrix of microcoils and a ring trap to position and control magnetic 1Author to whom any correspondence should be addresd.micro/nanoparticles[11].Rida et al transported magnetic beads in a glass capillary for a long range using planar coils [12].Lehmann et al manipulated magnetic beads suspended in a droplet by planar microcoils[13].Lee et al fabricated a device with integrated
microcoils for manipulating cells tagged by magnetic beads[14].
clothes怎么读
Magnetic beads have diameters ranging from250nm to 6µm,while ferrofluid has particles on the order of a few nanometres[15].The larger size of magnetic beads caus redistribution of the beads in a droplet.In the worst ca, the droplet may be split into two parts,one with and the other without magnetic beads.The one without the beads can no longer be manipulated by the magnetic force.In a ferrofluid droplet,magnetic particles have sizes on the order of nanometres,thus the random motion of the particles overcomes the magnetic force and the homogeneous distribution of the particles in the droplet is not affected by the magneticfield. Therefore,compared with droplets containing magnetic beads ferrofluid droplets are a more suitable candidate for magnetic actuation.Guo et al demonstrated the manipulation of water-bad ferrofluid droplets on a hydrophobic surface using permanent magnets[16].Nguyen et al manipulated ferrofluid droplets immerd in silicone oil using planar microcoils[17]. His rearch group also ud a magnetically driven ferrofluid
(a)
Teflon sheet
Ferrofluid droplet
Electric terminals
Planar
microcoil
Wall of the oil revoir
PCB
(b)
B
B
External permanent
magnetic field
Coils for actuation
Figure 1.The PCB device for manipulation of a ferrofluid droplet:(a )the 3D view of the device;(b )the device components [15].
plug for a polymera chain reaction (PCR)device [18].In this paper,the actuation mechanism of magnetic manipulation using planar coils is modelled in details.Mathematical models for both magnetic field and the droplet motion are formulated and solved.Theoretical results are then compared with the experimental results reported earlier in [17].
2.Modelling of the magnetic field
In a magnetic field,magnetic particles are attracted to the field maximum [19].The manipulation of the droplet in our device is bad on changing the location of magnetic field maximum.Switching the peak of the magnetic field can move the droplet back and forth.Figure 1shows the device ud in our analysis and experiments.The device has two pairs of planar microcoils.Each pair is located on each
side of a double-sided printed circuit board (PCB).A rervoir is made around the coils on the top side to contain silicone oil as carrier fluid.A ferrofluid droplet is placed on a Teflon sheet inside the rervoir.The ferrofluid droplet is immerd in silicone oil and actuated by the magnetic field of the planar microcoils.The magnetic field of the top coils creates a virtual channel to limit the droplet motion along the x -axis,while the bottom coils provide the actuation force.The following ction reports the model of the magnetic field induced by two planar coils.2.1.Modelling the magnetic field of a pair of planar microcoils
The planar microcoils depicted in figure 1consist of a ries of wire gments with a finite length (figure 2(a )).The magnetic
field of a wire gment with finite length can be obtained by solving the Biot and Savart’s integral [20].Superimposing the magnetic field of the wire gments results in all components of the magnetic field of a single planar microcoil [21]:H x,coil =
n i =1justmatch
H x,i ,
H y,coil =
n i =1
H y,i ,
H z,coil =n i =1
H z,i ,
(1)
where n is the total number of gments in a coil and H x,i ,H y,i ,H z,i are the x ,y and z magnetic fields of wires in a single planar microcoil,respectively.Superimposing the magnetic field of two coils results in the combined magnetic field:圣诞节活动主题
myhobbyH x =H x,coil1+H x,coil2,H y =H y,coil1+H y,coil2,
H z =H z,coil1+H z,coil2.
(2)
The total magnitude of the field strength is then:
H total =
H 2x +H 2y +H 2z
.(3)
The magnetic flux B can subquently be obtained by
B =µ0H (1+χm ),
(4)
where χm is the magnetic susceptibility of the medium in which the magnetic field is to be calculated and µ0=4π×10−7is the permeability of free space.
The magnetic field on the line connecting the centres of two coils was measured using a Gauss meter (GM05,Hirst Magnetic Instruments,UK),in order to validate the model for the two coils.The theoretical model was implemented and calculated in Matlab (MathWorks Inc,USA).distribution of the field strength was determined for a line running along the x -axis and through the centre of the two coils.Figure 3shows that the experimental and theoretical results of the magnetic field agree relatively well.2.2.Actuation mechanism
The above model of the magnetic field can be ud to describe the actuation mechanism for the device depicted in figure 1.As mentioned above,the two coils on the back side of the PCB are ud to move the droplet.Without a permanent magnetic field,there are two field maxima at the two coil centres where the ferrofluid will be trapped,figure 2.Thus,actuation will not be possible without the superposition of an external permanent magnetic field.If the currents in the two coils are running in opposite directions,the superposition with the external permanent magnetic field creates a single peak of the total magnetic field strength H total as shown in figure 4.A pair of permanent magnets create a homogeneous magnetic field in the area between the two coils,figure 1(b ).The ferrofluid droplet is attracted by this single field maximum.The field of the permanent magnets also helps to increa
艨艟0H x (A /m )
0H z (A /m )
-12
H y (A /m )
(a)
(b)
Coil 1
x (m)
H t o t a l (A /m )
Coil 1Coil 2
Figure 2.The magnetic field of the driving coils at y =0mm,z =0.75mm (without superposition with external permanent field,coils have opposite polarities,number of gments n =47,current I =0.8A,gap between gments g =200µm),centre-to-centre distance L =6mm):(a )arrangement of the coils and the coordinate;(b )three components of the magnetic field strength.
the magnetic force acting on the ferrofluid droplet.If the currents in the two coils rever their direction,the location of the field maximum also shifts from the centre of one coil to the centre of the other coil.Using an electronic control circuit and the experimental tup reported previously [17],the location of the field maximum can be switched periodically causing the ferrofluid droplet to move back and forth along the x -axis.
The two coils on the top of the PCB as depicted in figure 1(a )are ud to make a virtual channel to confine the droplet along the x -axis.In this ca,the field maximum should be located between the two coils.Figure 5shows the simulation results of two coils with the same field polarity and the same magnitude.After adding the homogeneous field of the permanent magnets,only a single peak of the field strength is located between them.This field maximum acts as a trap and keeps the ferrofluid droplet on the line
connecting the centres of the actuating coils on the other side of the PCB.
0x (mm)
H z (A /m )
Figure 3.The z -component of the magnetic field strength
宿迁中考查分(I =0.3A,n =47,centre-to-centre distance L =6mm,measured position y =0mm and z =0.8mm).
01000
2000H z (A /m )
1000
2000x (m)
H t o t a l (A /m )
Coil 1
Coil 2
Figure 4.The magnetic field of the driving coils at y =0mm,z =0.75mm (with superposition with external permanent field in z -axis,coils have opposite polarities,number of gments n =47,current I =0.8A,gap between gments g =50µm,centre-to-centre distance L =6mm,permanent field strength H 0=1000A m −1):(a )z component of the resultant magnetic field;(b )the total magnetic field.
-0.015
-0.01
-0.005
00.005
0.01
0.015
x (m)
H t o t a l (A /m )Figure 5.The magnetic field of the coils for virtual channel at y =0mm,z =1mm (with superposition with external permanent field in z -axis H 0=500A m −1,coils have the same polarity,number of gments n =47,current I =0.8A,gap between gments g =200µm,centre-to-centre distance L =6mm).
3.Modelling of magnetic actuation of a ferrofluid droplet
3.1.Forces acting on the droplet moving in silicone oil With the device depicted in figure 1,the ferrofluid droplet is immerd in oil and actuated by the magnetic force.The kinematic behaviour of the droplet is determined by the forces acting on it.The ferrofluid droplet is assumed to have a spherical shape.This assumption is justified bad on the measurement of the contact angle between the ferrofluid and the Teflon sheet.The contact angle of a ferrofluid droplet and the Teflon surface immerd in silicone oil was measured as 127◦using a tensiometer (FTA200,First Ten Angstrom)[17].
The inertial force,the drag force and the driving magnetic force are three forces acting on the ferrofluid droplet when it moves in silicone oil.Considering the assumption of spherical droplet,the drag force is calculated as [22]
F drag
=3πDηU 1−2η/3ηff
1+η/ηff
,
(5)
where D is the diameter of the droplet,ηis the dynamic viscosity of the carrier fluid (silicone oil),ηff is the dynamic viscosity of the ferrofluid and U is the velocity of the droplet in oil.If the viscosity of the ferrofluid is much larger than that of the silicone oil ηff η,the drag force can be simplified as
F drag =3πDηU.
(6)
In a system with two coils,the magnetic force can be calculated by superposition of the magnetic forces of both
coils.The magnetic force acting on the ferrofluid droplet with a volume V is
F =
V χ
µ0(B ·∇)B (7)and can be formulated in the three spacial components as
F x =V χ
µ0 B x ∂B x ∂x +B y ∂B x ∂y +B z ∂B x ∂z
sir,
F y =V χ
µ0 B x ∂B y ∂x +B y ∂B y ∂y +B z ∂B y ∂z
,F z =V χ
µ0 B x ∂B z ∂x +B y ∂B z ∂y +B z ∂B z ∂z
.
(8)
The resultant magnetic force of two coils is determined by
superposition:
F x,total =F x,coil1+F x,coil2,F y,total =F y,coil1+F y,coil2,F z,total =F z,coil1+F z,coil2.
(9)proportionate
Since the droplet is actuated one dimensionally along the x -axis and its motion in other directions is confined by the virtual channel,only the force component F x is considered in our subquent model.The magnetic field of the permanent magnets is also considered.Measurements showed that the magnetic field strength H 0of the permanent magnets ud in our experiments ranges from 500to 8000A m −1in the actuation domain,depending on their positions.Figure 6shows the modelled magnetic force distribution for a ferrofluid droplet with a diameter of 1mm.The results show that the
