Biomedical Engineering Reference
In-Depth Information
through micro-channels. The current chapter will present the most relevant theoret-
ical and technical issues related to both methods and also a comparison between
them. Additionally, our most recent confocal micro-PIV/PTV results of blood flow
behaviour in both glass and polydimethylsiloxane (PDMS) micro-channels are
reviewed.
9.2 PIV/PTV Principles
9.2.1 Calculation Methodology
The principle of calculating several physical parameters (displacement, velocity,
shear stress, etc.) related to fluid mechanics is common to both PIV and micro-PIV.
The traditional way consists of measuring the displacement of fluorescent tracer
particles flowing within the working fluid. However, to measure physiological
fluids, such as blood, it is also common to use labelled blood cells as natural tracer
particles. By applying a powerful light source, the tracer particles or cells of interest
are illuminated and as a result objects with a known time interval (
D
t
) can be
recorded by a high speed camera. By using a short
t
, it can be assumed that the
magnitude and direction of the object velocities are constant. As a result, the
location of a particle on two consecutive images can be used to estimate its
instantaneous velocity as:
D
x
t
þD
t
~
x
t
¼
~
u
~
(9.1)
D
t
y
t
þD
t
~
y
t
¼
~
v
~
(9.2)
D
t
where
u
and
v
are respectively the velocity components of the particle in the
x
and
y
direction. Figure
9.1
shows an overview of the PIV/PTV principle.
The approach used to calculate the velocity of one particle can be extended to the
entire flow field of interest. In microfluidics it is common practice to average the
instantaneous velocities over a large number of recorded image pairs (
N
usually
greater than 20). Hence, the time-average mean velocity vector of the flow can be
defined as
N
X
N
1
U
¼
1
~
u
t
(9.3)
t
¼
N
X
N
1
V
¼
1
~
v
t
(9.4)
t
¼
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