as compared to that in [89].
4.4 Results and Discussions 59
(a)
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
44.8 45.0 45.2 45.4 45.6 45.8 46.0 46.2 46.4 46.6 46.8
H(kA/m)
x-axis (mm) Mode 1
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
0.630 0.632 0.634 0.636 0.638 0.640 0.642 0.644 0.646 0.648 0.650
H(kA/m)
x-axis (mm) Mode 2
(b)
Figure 4.5: (a) Magnetic field intensity with respect to position and time along the space available in between the symmetrical coils, and (b) magnetic field intensity along the channel diameter for Mode 1 and Mode 2 respectively.
Fig.4.5shows the variation of magnetic field intensity (H) operating alternately throughout the navigation process in the following two modes: (i) Mode 1 for steering the MNPs to Outlet 1 and (ii) Mode 2 for releasing the stuck MNPs from the sidewalls of the channel. Fig.4.5a represents the variation of H with respect to both time and position. The plot depicts the overall behaviour ofH along the space available in between the coils (−40 mm to 40 mm). Note that the region of interest lies along the channel diameter (−0.5 mm to 0.5 mm). Fig 4.5b shows the 2D behaviour of H with respect to position for both the modes of operation, specific to the region of interest i.e, (−0.5 mm to 0.5 mm). Without any loss of brevity, we present an analysis of TVMF at the center of the Y-shaped channel (x= 0), as shown in Fig.4.6. Here,TON andTOF F are the ON and OFF time of the switch operated in Mode 1 and Mode 2 respectively. From extensive simulation analysis, the optimal duration of ON time and OFF time required for effective
0.0 0.1 0.2 0.3 0.4 0.5 0
10 20 30 40 50
Mode2TOFF
MagneticFieldIntensity(kA/m)
t (sec) T
ON
Mode1
Figure 4.6: Magnetic field intensity with respect to time.
navigation as well as minimization of stiction and aggregation of MNPs is found to beTON = 3TOF F. During the ON time (Mode 1) of the switching operation, the MNPs are steered to Outlet 1, which results in aggregation and stiction of MNPs at the sidewalls. During OFF time (Mode 2) of the switching operation, the stuck MNPs are released from the sidewalls and disaggregated under the influence of dominant fluidic force. The switching operation of the H takes place in this
-40 -20 0 20 40
0 20 40 60 80 100 120 140
-20 -10 0 10 20 0.0
0.5 1.0
MagneticFieldIntensity(kA/m)
x-axis (mm) Mode 1
Mode 2
(a)
-40 -20 0 20 40
0 500 1000 1500 2000 2500 3000 3500 4000
-20 -10 0 10 20
-40 -30 -20
MagneticFieldGradient(kA/m
2)
x-axis (mm) Mode 1
Mode 2
(b)
Figure 4.7: (a) Magnetic field intensity, (b) Magnetic field gradient along thex-axis for both Mode 1 and Mode 2.
4.4 Results and Discussions 61
-40 -30 -20 -10 0 10 20 30 40 -0.2
-0.1 0.0 0.1 0.2
-40 -30 -20 -10 0 10 20 30 40 -20
-15 -10 -5 0
FMAP
(fN)
Position, x (mm) Mode 1 (Proposed)
Mode 2 (Proposed)
Mode 1 [84]
Mode 2 [84]
FMAP
(fN)
Position, x (mm) x 10
-5
Figure 4.8: Magnetophoretic force for both Mode 1 and Mode 2.
fashion at all positions throughout the region of interest (along x-axis), as shown in Fig. 4.5a.
In Fig. 4.7, the variation ofH and field gradient (∇H) are plotted. It may be observed from Fig.4.7a & 4.7b that H and ∇H are positive in Mode 1. Clearly, a positive FM AP is produced in Mode 1 to steer the MNPs to Outlet 1, following (3.9). However, Mode 2 produces a monotonically decreasing positive magnetic field intensity along the positive x-axis, as shown in Fig. 4.7a, which implies a negative magnetic field gradient as shown in4.7b. Consequently,FM AP is negative following (3.9) and the magnitude is small enough to ensure that the MNPs get demagnetized and detached from the sidewalls and move forward with drag force.
The dominance ofFD overFM AP facilitates the disaggregation of MNPs in Mode 2.
In Fig. 4.8, the variation of magnetophoretic forces (FM AP) for both Mode 1 and Mode 2 are simulated and plotted. It may be noted thatFM AP experienced by the MNPs in a fluidic channel is proportional to the particle volume [93]. It may be observed from Fig. 4.7 that H and ∇H is positive in Mode 1. Consequently, a positive FM AP is produced (3.9) in Mode 1, which steers the MNPs to Outlet 1.
However, Mode 2 produces a monotonically decreasing positive magnetic field along the positivex-axis, as shown in Fig. 4.7, which implies a negative magnetic field gradient. Consequently,FM AP is negative following (3.9) and the magnitude is small enough to ensure that the MNPs get demagnetized and detached from the sidewalls. Fig.4.8 shows the simulation based performance comparison of our proposed system with that in [87]. In [87], two coils are configured such that a positive magnetic field is produced for steering (labeled as Mode 1) and an equal and oppositely directed magnetic field is produced to detach (labeled as Mode 2)
0.0 0.1 0.2 0.3 0.4 0.5 0.5
0.6 0.7 0.8 0.9 1.0
ParticlePosition(mm)
t (sec)
Figure 4.9: MNP trajectory inside the channel.
the MNPs from the vessel wall. Consequently, the magnitude of FM AP remains same for both Mode 1 and Mode 2, while acting in opposite direction. It can be clearly seen that the FM AP for steering the MNPs in both the systems using Mode 1 follows the same profile with comparable magnitude. The justification lies in the fact that both the systems show a similar magnetic field strength profile during Mode 1. However, in Mode 2,FM AP produced in our system is much lower than that in [87]. Comparing the values of FM AP at three different points in the region of interest, i.e.,x=−20mm,x= 0mm andx= 20mm, we observe that the force exerted to release the MNPs are respectively 99.48%, 99.8% and 99.9% lower in our system than that in [87]. This highlights that the force used to mitigate the stiction issue in our system does not have adverse affect of guiding the MNPs to the undesired outlet.
Fig. 4.9 represents the analysis of trajectory of MNPs with the switching op- eration. The movement of MNPs are tracked inside the Y-shaped channel having radius 0.5 mm. In Mode 1, the MNPs are steered along the positive x direction, which results in a net displacement along the sidewalls of the channel. Subse- quently, in Mode 2, the MNPs are pulled back from the sidewalls in the opposite direction, to avoid stiction and aggregation of MNPs at the sidewalls. From sim- ulation analysis, we find that the optimal time duration required to pull back the MNPs at the center of the channel is given by TOF F = 20 ms. If the switching time in Mode 2 exceeds the optimal value, the resultant magnetic field intensity
4.5 Chapter Summary 63