Unformatted text preview: larliquid-air0interface liquid will be noncontact angle the ger than ◦ and the
r = radius spreading (ﬁgurethe meniscus of liquid
of curvature of 3).
If the solid–air surface tension is larger than the sum
of the liquid–air and solid–liquid surface tensions, then it
will be energetically favorable for the liquid to spread. The
contact angle will be equal to 0◦ . A drop bridging two
surfaces will form thin liquid ﬁlms outside the bridged area
(ﬁgure 4). assumed that the liquid is conﬁned to a bridged area Ab ,
which is smaller than or equal to the total facing areas At .
(4a ) expresses the surface energy in the case of a spreading
liquid, (4b) that for a non-spreading liquid:
Es = 2 At γs l + γl a − Ab γl a = 2 At γs l
+γl a − Ab γl a cos θC Es = At γs a − Ab γs a − γs l
−Ab γl a cos θC . 386 © N. Dechev, University of Victoria (4a)
(4b) In (4a , b) the energy of the liquid–air meniscus area is
neglected, which is a fair assumption if the gap g between
the plates is small, so that the meniscus area is small
compared to the bridged area. The total area At and the
surface tensions are constant. Therefore, the total surface
energy as a function of the bridged area can be written in Based on the above expression, the force between the two plates
can be expressed as: where: = 2 At γs a A = Area between the two plates
#c = contact angle between liquid and solid
d = separation distance between plates 30 Stiction due to Hydrogen Bridging
Some materials absorb water to a small depth just below their
surface layer, and are said to have ‘hydrated surfaces’.
For example, hydrophilic (favorable to water) silicon surfaces,
under atmospheric conditions and temperatures well below 200˚C,
contain adsorbed water layers.
When two of these hydrated surfaces are brought into close
contact, hydrogen bonds may form between oxygen and the
hydrogen atoms of the adsorbed water layers in each of the
This is a chemical bond that will remain, as long as the surfaces
remain hydrated. © N. Dechev, University of Victoria 31 Stiction due to Electrostatic Attraction
Electrostatic force can serve two functions in stiction:
Firstly, it can act over a distance to bring two micro-objects into
Secondly, if there is a dielectric layer of material present between
the two bodies in contact, such as silicon dioxide, or other
material, the charge between the two bodies may remain for some
After the contact occurs, the electrostatic charges will dissipate or
equalize over time, based on the material dielectric properties,
resulting in no net force. © N. Dechev, University of Victoria 32 Stiction due to van der Waals Force
The Van der Waals forces between two bodies are caused by
mutual electric interaction of the induced dipoles in the two
These bodies can be considered as molecules or for the case of
MEMS, grains within a polycrystalline material.
The effect of van der Waals force depends on a material’s
properties, and it is usually n...
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