Biomedical Engineering Reference
In-Depth Information
Figure 1. (A) Sessile drop in equilibrium on a solid surface, with contact angle and surface tensions
γ L S ,and γ SL . (B) Action of liquid surface tension γ L and Laplace pressure P .
We can neglect gravity, and thus the effect of the hydrostatic pressure which would
flatten the drop, when the drop is smaller than the capillary length
γ L
ρg ,
=
K
(2)
where ρ is the density of the liquid and g the gravitational acceleration. For water,
γ L =
9 . 8m/s 2 . The shape of the drop is thus not
influenced by gravity if the radius of curvature is well below
1g/cm 3
0 . 072 N/m, ρ
=
and g
=
2 mm.
In addition to the surface tensions acting at the TPCL, another force plays a major
role. Due to its curvature, the pressure inside the drop is higher than outside. The
difference between in and out is called Laplace or capillary pressure [41]
2 γ L
2 γ L sin
a
P
=
R =
,
(3)
where R is the radius of curvature of the drop, which is related to the contact radius
a and to the contact angle (Fig. 1).
As an example, for a drop of water forming a contact angle of 60 with a surface,
the pressure difference is P
=
1 . 2 mbar when a
=
1 mm, and P
=
1200 mbar
when a
1µm.
Thus, when a small, non evaporating microdrop is sitting on a surface and forms
a finite contact angle with it, the macroscopic picture is:
=
(i) the drop has a spherical shape,
(ii) Young's equation accounts for the in plane (horizontal) balance of forces at the
TPCL,
(iii) the vertical component of the surface tension γ L sin is pulling upwards at the
TPCL and is counterbalanced by the Laplace Pressure P , which is pushing
uniformly downwards over the whole contact area
a 2 .
π
2. Evaporating Drop
Until now we discussed drops in thermodynamic equilibrium. What changes when
a drop evaporates, and why does a drop evaporate at all? A liquid with a planar
surface evaporates only when its vapour pressure P 0 is higher than the pressure of
its vapour in its surroundings. Thus, if the surroundings are saturated with its vapour
the liquid does not evaporate. It is in equilibrium, because at any time the number
of molecules evaporating from and condensing to the surface is similar. However,
 
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