Unformatted text preview: of stiction. These
Van der Waals forces © N. Dechev, University of Victoria 28 Stiction due to Capillary Forces
Capillary forces occur when there is a liquid-solid interface.
N Tas et al
Consider the following example of two parallel plates with a
liquid between them: d Figure 2. Liquid drop (L) on a solid (S), in air (A). θC is the
contact angle between liquid and solid in air. Surface Tension Between Plates
[Image from N. Tas, et al.]
Figure 1. A thin layer of liquid working as an adhesive between two plates. θ is the
If the angle of the contact angleair, g isis lesscontact angle between is the force F
than 90˚, then a
and solid in #c the liquid layer thickness, and A
wetted area. A force F is applied to maintain equilibrium.
will exist between the two plates.
C © N. Dechev, University of Victoria where γl a is the surface tension of the liquid–air interface,
and r is the radius of curvature of the meniscus (negative
if concave). In ﬁgure 1, the liquid is between the plates
and the liquid contacts the solid at the ﬁxed contact angle.
From simple geometry it follows that r = −g /2 cos θC . In
equilibrium, an external force F separating the plates must
be applied to counterbalance the capillary pressure forces:
F = − pl a A = 2Aγl a cos θC
g Figure 3. Liquid bridging two solids. The liquid is
non-spreading. The solid is only covered in the bridged
area Ab . At is the total facing area. 29 (2) where A is the wetted area. Note that a positive force F
corresponds to a negative Laplace pressure. The pressure
inside the liquid is lower than outside and the plates are
pushed together by pressure forces. For stiction calculations
it is convenient to calculate the surface energy stored at the
interface that is bridged by a drop of liquid . Consider
a drop of liquid placed on a solid, surrounded by air
(ﬁgure 2). In equilibrium, the contact angle between liquid
and solid is determined by the balance between the surface
tensions of the three interfaces. This balance is expressed
by Young’s equation : Stiction due to Capillary Forces Figure 4. Liquid bridging two solids. The liquid is
spreading. Outside the bridged area Ab , a thin liquid ﬁlm
covers the solid. The total surface
the area between the plates
The pressure difference between the liquid-air interface is given calculated byenergy ofthe surface tensions of the
by the equation:
γ = γ + γ cos θ
solid–air, solid–liquid and liquid–air interfaces . It is
sa where: sl la C C where γs a is the surface tension of the solid–air interface
and γs l is the surface tension of the solid–liquid interface.
Young’s equation is also valid for conﬁgurations other than
that of ﬁgure 2. The contact angle is the same on a curved
or irregular shaped surface, inside a capillary etc.
If the solid–air surface tension is smaller than the sum
$pla = pressure differenceandliquid-air interface tensions, then the
of the liquid–air at solid–liquid surface
%la = surface tension ofis...
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