Biomedical Engineering Reference
In-Depth Information
To approximate the area of interaction, we need to make some assumptions about the cells' con-
tact area. Assume that the endothelial cell can be represented as a stiff plane and the red blood cell
as a sphere. This would suggest that the contact area would only be one point on the red blood cell
membrane. However, we know that the red blood cell can deform when it comes into contact with
the endothelial cell. If we make the assumption that the deformation will encompass a 60
arc length
(in three-dimensional space) of the original red blood cell, we get that the potential contact area is
2
πð
μ
Þ
4
4
m
m
2
A
60
5
5
33
:
51
μ
6
For interest, we will show other area calculations as well:
2
4
πð
4
μ
m
Þ
m
2
A
30
5
:
μ
5
16
75
12
2
4
πð
4
μ
m
Þ
m
2
A
120
5
67
:
02
μ
5
3
The effective force of interaction for these three contact areas are
2
12
m
m
2
3
m
m
2
2
2
ð
m
2
Þe
2
3
μ
m
=
8
:
012
μ
m
F
ef
ðdÞ
5
33
:
51
μ
2
:
50
μ
N
5
12
C
2
Nm
2
75 8
:
85
E
2
2
2
12
m
m
2
3
m
m
2
2
ð
m
2
Þe
2
3
μ
m
=
8
:
012
μ
m
F
ef
ðdÞ
5
16
:
75
μ
1
:
25
μ
N
5
12
C
2
Nm
2
75 8
:
85
E
2
2
12
m
m
2
3
m
m
2
2
2
m
2
Þe
2
3
μ
m
=
8
:
012
μ
m
F
ef
ðdÞ
5
ð
67
:
02
μ
5
μ
N
5
12
C
2
Nm
2
75 8
:
85
E
2
As we can see, with an increasing contact area, the effective force increases as well.
The third type of force that comprise adhesive forces is capillary forces, which are sub-
divided into adhesion, cohesion, and surface tension. Surface tension is a fluid property
that causes a surface of liquid to be attracted to another surface (such as a container for
wetting). Surface tension arises due to the intermolecular forces within the fluid. For a
fluid element within the bulk fluid phase, the intermolecular forces acting on that element
are balanced in all directions. However, at the surface of the fluid, there is an interface
between the fluid elements and the surrounding medium (e.g., for a glass of water, the
fluid at the surface will tend to be pulled into the water because the intermolecular forces
for water-water are stronger than water-air). This inward force is balanced by the tendency
of the fluid to resist compression until the energy (and hence the fluid surfaces) reaches
equilibrium at a low energy state. The surface tension is defined as the force that is
required to maintain the fluid in this low energy state per unit length. Surface tension (
)
is quantified by the pressure difference across the surface and the curvature that the sur-
face takes in the low energy state, using the Young-Laplace equation:
γ
1
r
1
1
1
r
2
Δp
5
γ
ð
7
:
18
Þ
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