Tailor-Made and Biodegradable Vascular Scaffolds - Microsurgery: Advances, Simulations, and Applications - page 293

A magnetic force will be obtained when magnetized MSP exposed
to the magnetic ield. Since MSP is generally stable in hexane, the
whole motion control process is conducted in hexane solution.
MSP's gravity force, viscous resistance and dynamic pressure force
between the front part and rear part of the MSP, buoyant force are
the main contributors inluencing the motion of MSP in hexane.
Magnetic force is introduced by the combined coils to balance the
gravity force, overcome the drag force from the hexane and drive the
MSP moving into the desired position toward the scaffold. Figure
8.29 shows the schematic of MSP moving in hexane.

Magnetized
Vasculature
Model

Steered
Particle

Container

MSPs

v
F z +F b +F M2

B r

F

M1

r

Hexane

F g

z

r

B z

Figure 8.29 Dynamic mechanic model for MSP moving in hexane.

8.7.7.2 Fluid dynamics of MSP in hexane
For better control the movement of MSP in hexane, the dynamics
model is established irst.
The movement of MSP in hexane is governed by the Navier-
Stokes equations:

u % % % –% %
u

u

5

S I S

( uu ( ) ) uupF (8.5)

t

where S denotes the luid density (kg/m 3 ), u the velocity vector

(m/s), I the dynamic viscosity (Ns/m 2 ), and the pressure (Pa). The

luid is hexane with a dynamic viscosity of 0.294 × 10 −3

p

Ns/m 2 and a

density of 654.8 kg/m 3 . F is the volume force of MSP.