BME%20551%20Homework%201%20solution - BME551 Homework#1...

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1 BME 551 Homework # 1 1/14/09 Heterogeneous Nano Structures:Multiscale structures with NEMS and MEMS components Surface Tension 1. Define surface tension in terms of force and length. Provide the units Surface tension ( σ ) is defined as the ratio of the magnitude of force ( F ) tangentially applied to the surface of a liquid to the length: ( L ) σ =F/L [n/m] or [dyn/cm] 2. Define Mc (The minimal requirement for static stability on the surface). 1 = = P Mg M c σ , where M denotes mass, g force of gravity, σ surface tension, and P the curvature parameter. 3. What parameters are required to keep the paper clip afloat? To remain stationary on water, a M c ratio will be less than 1. 4. What are the chemical bonds underlying the surface tension? (Hint: Google) a. Hydrogen bonds 5. You were commissioned to design a water robot strider by the Defense Department. This water strider would be able to penetrate into the sewage system underneath the former Soviet Union KGB building. What parameters will influence your design? (Hint: the ratio between the
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body force ( Mg ) and surface tension ( σ P )). Assume that the radius of the sewage system is 1 m, and water is the main component in the sewage. P, the curvature parameter. P=4(L front + L middle + L rear ) M, mass •σ (H 2 O)=67 dyn/cm vs. σ (sea water)=78 dyn/cm at 14 0 C •σ P=curvature force [dyne] Mg=Fg [dyn]=buiyance force + surface tension =L 2 σ sin θ 6. Compare the surface tension between water and soap?(Hint: Google) •σ (H 2 O)=67 dyn/cm. The attraction of water molecules to each other can be disturbed by adding soap. Soap interferes with the attraction between water molecules and breaks the surface tension. Soap has a lower surface tension than water. 7. Can the water strider remain afloat in a high concentration of soap solution? No. Gecko feet/setae 8. A crocodile gecko darts across the unruffled surface of a pond despite a M c > 1. The attractive forces that hold geckos to the surface are van der Waals interactions between the finely divided setae and the surface. Define the van der Waals force. the attractive or repulsive force between molecules (or between parts of the same molecule) other than those due to covalent bonds or to the electrostatic interaction of ions with one another or with neutral molecules. The term includes: permanent dipole–permanent dipole forces permanent dipole–induced dipole forces instantaneous induced dipole-induced dipole ( London dispersion forces ) It is also sometimes used loosely as a synonym for the totality of intermolecular forces. Van der Waals forces are relatively weak compared to normal chemical bonds, but play a fundamental role in fields as diverse as supramolecular chemistry , structural biology , polymer science , nanotechnology , surface science , and condensed matter physics . Electrowetting
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BME%20551%20Homework%201%20solution - BME551 Homework#1...

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