Tailor-Made and Biodegradable Vascular Scaffolds - Microsurgery: Advances, Simulations, and Applications - page 294

At the direction of gravity force, when no external force is applied,
the ordinary differential equation that describes the force balance
is
mz = F g + F z + F b (8.6)
where m denotes the mass of the particle, z(m) the position of the
particle, F g the gravitational force, F b the buoyancy force and F z
the z -component of the force that hexane exerts on the MSP. The
difference of gravitational force and buoyancy force is given by
F g - F b = ( S M - S ) V m g (8.7)
where V M is the volume of the MSP and S M is the density. is g = 9.81 m/
s 2 the acceleration due to gravity. The force that hexane exerts on the
MSP is calculated by integrating the normal component of the stress
tensor over the surface of the particle. The force's z -component is
given by

±

T

F z = 2 Q (-

I %%

rn pI ( u ( u ) )) ds (8.8)

S

where r is the radial coordinate and n is the normal vector on the
surface of the MSP, and I is the identity 3 × 3 tensor (or matrix). The
initial values for the position and velocities are zero. Similar result of
r -component F r also can be obtained by Eq. 8.8.

8.7.7.3 Electromagnetic analysis for magnetic steering
When placing a magnetized particle in magnetic ield, surface
magnetization current and volume magnetization current inside the
ferromagnetic material will be generated after its magnetization in
the magnetic ield, the magnetic force is interpreted as the magnetic
force on molecular current. For isotropic medium it can be calculated
as:

±±±

s s

F M = ( M ) V (8.9)

V

And for the transient analysis of gradient magnetic ield and
uniform magnetic ield, electromagnetic conversion problem is
governed by Biot-Savart law:

N
Q

Idl

s

r

0

s

dB = (8.10)

3

4

r

where N 0 is the permeability of the vacuum, magnetic constant, r is
the displacement unit vector in the direction pointing from the wire