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Magnetic drug targeting 201

Magnetic drug transfer thorough larger vessels
The bidimensional study that follows is about the first stage of MDT: the MNPs arrive
with the blood flow in the region where the PM acts. Progressively the vessel
becomes a magnetizable medium, and magnetic body forces come into action. It is
assumed that the magnetic field produced by PM is not perturbed throughout the
dynamic change in the magnetic susceptivity of the vessel content. Eventually after
6 7 periods of the pulsating flow (e.g., at 60 bpm), the entire content becomes a
magnetizable fluid. The magnetostatic field, the flow and the mass transfer model are
1 1
r 3 μ μ r 3 A 2 B rem 5 0;
0 r ð6:21Þ
@u

ρ T ; rUu 5 0;
ð
ð
@t 1 uUrÞu 52 r 2pI 1 η ru 1 ruÞ ð6:22Þ
@c 2
1 uUrÞc 5 Dr c: ð6:23Þ
ð
@t
The initial conditions for the flow and mass transfer are homogeneous. The MAF
is the Carreau-type fluid Eq. (6.20). The boundary conditions for the flow are: zero
velocity for the walls and constant pressure for the exit. Fig. 6.26 depicts the inlet
velocity profile for several periods.
3
The inlet boundary condition for species is C b 5 0.33 mg/cm (Soltani and Chen,
2013), and convection for outlet. The walls are impermeable, assuming that mass

0.1

0.08
u (m/s)

0.06

0.04

0 0.2 0.4 0.6 0.8 1
t (s)
Figure 6.26 Inlet velocity profile for the flow in the MD transfer through vessels of larger size.