Biomedical Engineering Reference
In-Depth Information
controlled by adjusting the temperature from room temperature to an acceptably low Curie temper-
ature. The temperature dependence of magnetization can be implemented in the first term of (2.189) ;
the magnetic force then has the form [40] :
2 m 0 H vM
1
f magnetic ¼
V
T
þ
m 0 M
V
H
:
(2.190)
vt
It is clear from (2.190) that the high-temperature gradient
VT in microscale can be another advantage
for driving ferrofluid in microchannels. Thus besides microcoils, microheaters can be another tool for
controlling ferrofluid-based micromixers.
2.7.1.1 Electromagnetic effects
Electromagnetic effect or magnetohydrodynamics (MHD) deals with behavior of electrically con-
ducting fluids in a magnetic field. A magnetic field induces currents in a moving conductive fluid. A
current passing through a conductive fluid can create forces on the fluid and affect the magnetic field.
Similar to electrokinetics, MHD effects represent multiphysics problems, which require the coupling
of the different fields. MHD effects can be described by the Navier-Stokes equations of fluid dynamics
and Maxwell's equations of electromagnetism.
The Navier-Stokes equation of an MHD flow has the form:
r D v
2 v
D t ¼
J
B
V
p
þ
m
V
(2.191)
where v is the velocity vector, B is the magnetic field of flux density, and J is the current density. The
term J B represents the Lorentz force. The relation between the current density field, the electric
field, the velocity field, and the magnetic field is:
J
¼
s
ð
E el þ
v
B
Þ¼
s
ðVJ þ
v
B
Þ:
(2.192)
where E el is the electric field and
J
is the electric potential.
2.8 SCALING LAW AND FLUID FLOW IN MICROSCALE
The diffusion coefficient D , kinematic viscosity v , and the thermal diffusivity a ¼ kpc - where k , p , and
c are thermal conductivity, density, and specific heat, respectively - are transport properties and all
have the same unit of m 2 /s. The ratios between these properties represent a group of nondimensional
numbers that are characteristic for the interplay between the competing transport processes. These
nondimensional numbers help to compare molecular diffusion with other transport processes in
microfluidics.
The Schmidt number is the ratio between momentum transport and diffusive mass transport:
momentum transport
diffusive mass transport ¼
v
D ¼
m
rD :
Sc
¼
(2.193)
For most liquids and gases, the Schmidt number is larger than unity Sc
1. This means in most
cases spreading fluid motion is easier than molecules of the species.
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