Biomedical Engineering Reference
In-Depth Information
Replacing
h
by its value from (3.41), we find the capillary force
F
=
2
π γ θ
cos
(3.42)
The capillary force is the product of the length of the contact line 2
πR
times the
line force
f
=
g
cos
q
. This line force is sketched in Figure 3.32.
3.6.4 Capillary Rise Between Two Parallel Vertical Plates
The same reasoning can be done for a meniscus between two parallel plates (Fig-
ure 3.33) separated by a distance
d
= 2
R
. The same reasoning as that of the preced-
ing section leads to
γ θ
ρ
cos
h
(3.43)
=
g R
By substituting in (3.43) the capillary length defined by
γ
-
1
κ
=
(3.44)
ρ
g
one obtains
2
cos
θ
κ
-
h
=
(3.45)
R
Note that the expressions for the two geometries (cylinder and two parallel
plates) are similar. If we use the coefficient
c
, with
c
= 2 for a cylinder and
c
= 1 for
parallel plates [18], we have
2
cos
θ
κ
-
h c
=
(3.46)
R
where
R
is either the radius of the cylinder or the half-distance between the plates.
Figure 3.33
Capillary rise between two parallel vertical plates.