Biomedical Engineering Reference
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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.
 
 
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