Biomedical Engineering Reference
In-Depth Information
Consider a material particle, that at time
t
=
0 enters the domain at the
position with coordinates
x
=
1[m],
y
=
1[m].
y
3
2
1
0
1
2
x
Calculate the time at which the considered particle leaves the shaded
domain.
9.4
In a Cartesian
xyz
-coordinate system a rigid body is rotating around the
z
-
axis with constant angular velocity
ω
. For the velocity field, in an Eulerian
description, the following expression holds:
v
(
x
)
=
·
x
with
=
ω
(
−
e
x
e
y
+
e
y
e
x
).
˙
Consider, the associated acceleration field
a
(
x
)
=
v
(
x
) and show that the
result can be written as:
x
, with
H
a constant tensor.
Give an expression for
H
formulated as
a
(
x
)
=
H
·
H
=
H
xx
e
x
e
x
+
H
xy
e
x
e
y
+···+
H
zz
e
z
e
z
.
9.5
A method that is sometimes used to study the mechanical behaviour of
cells is based on the so-called cross flow experiment. An example of such
an experiment is given in the right figure below (image courtesy of Mr
Patrick Anderson). In this case a fluorescent fibroblast is positioned almost
in the centre of the cross flow. There are several ways to create such a flow.
The set-up, that is shown in the left figure, consists of a reservoir with four
cylinders which rotate with the same angular velocity. The figure gives a
top view of the set-up. A cell can be trapped in the centre of the cross flow
and thus be stretched by the flow.
.
y
Flow
x
z
Flow
Flow
100
m
m
Flow
(a)
(b)
