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4a expresses the surface energy in the case of a

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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 surfaces. 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 contact. 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 time. 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 bodies. 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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