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# Surface tension

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This presentation has the details about the surface tension of the water

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### Surface tension

1. 1. Surface Tension
2. 2. Water striders are light (like ants) thus don’t “break” surface <ul><li>Ooh! Look at me! I have hydrophobic feet and I weigh less than Fritz does! I’m soooo great! </li></ul>
3. 3. Even a piece of steel can do this trick if it is small (steel  ~ 8x water)
4. 4. 4 H 2 O molecules <ul><li>separated in space from each other </li></ul><ul><li>have partial + and – charges </li></ul><ul><li>what would they do??? </li></ul>but what’s surface tension, really?
5. 5. 4 H 2 O molecules <ul><li>they clump together </li></ul><ul><li>+ and – charges snuggle up close </li></ul><ul><li>potential energy of system has dropped </li></ul>
6. 6. Surface Tension <ul><li>water in bulk has many binding partners </li></ul><ul><li>water at surface has less, has exposed charges left over </li></ul><ul><li>potential energy of water at surface is higher </li></ul><ul><li>deforming droplet to increase surface area takes work </li></ul>
7. 7. Surface Tension <ul><li>E = FX, energy = force * distance </li></ul><ul><li>dE = F dX </li></ul><ul><li>F = dE/dX </li></ul><ul><li>e.g. spring energy = ½ kx 2 , dE/dX = kx = F </li></ul>
8. 8. Surface Tension <ul><li>creating surface area in 20  C water droplet takes </li></ul><ul><li>73 ergs/cm^2 </li></ul><ul><li>droplet thus seems springy </li></ul><ul><li>if mg <<  l it dominates and you can walk on water (Vogel pp 72, 104-109) </li></ul>
9. 9. Surface Tension <ul><li>surface area in 20  C water costs </li></ul><ul><li>73 ergs/cm 2 </li></ul><ul><li>= “  ” </li></ul>
10. 10. Surface Tension <ul><li>surface area in 20  C water costs </li></ul><ul><li>73 ergs/cm 2 </li></ul><ul><li>F = dE/dX </li></ul><ul><li>can get  from F in this apparatus </li></ul><ul><li>if film is w by w cm, how much area has been created? </li></ul>
11. 11. Surface Tension <ul><li>2 W 2 </li></ul>
12. 12. OK so remember this? (steel  ~ 8x water)
13. 13. Floating without floating – The SECRET OF THE STRIDERS REVEALED!!! <ul><li> = 73 ergs/cm 2 = 73 dyne-cm/cm 2 = 73 dynes/cm </li></ul><ul><li>73 dynes/cm is also like a tear strength </li></ul><ul><li>if we stacked poker chips on water it might look like below </li></ul><ul><li>area of chip doesn’t matter so much as the edge (vertical contributions) </li></ul><ul><li>lift = perimeter *  * sin  </li></ul><ul><li>wait, why sin  ? why not pull them all at 90 degrees? </li></ul>
14. 14. Floating without floating - <ul><li> is constant of water / air interface, so can’t just “choose” to pull less </li></ul><ul><li>surface fails when tension along perimeter of chips exceeds 73 dynes/cm </li></ul><ul><li>after that, the water does something else more energetically profitable – </li></ul>
15. 15. Incidentally – Scaling tie-in - Why droplets are droplet-sized - mass increases faster than length or area, so above about 1 cm diameter, water droplet mg >  l, so more likely to get torn apart by its own weight
16. 16. Floating without floating - <ul><li>anyway so if the outlines of your feet are long enough for  L to add up to more than your weight (and your contact angle is high) you too can walk on water </li></ul>
17. 17. Contact Angles <ul><li>here’s a droplet on a surface - </li></ul>
18. 18. Contact Angle <ul><li>here’s a slice of it – </li></ul><ul><li>tangent to droplet edge is “contact angle” </li></ul><ul><li>why is theta theta? </li></ul>
19. 19. Contact Angle <ul><li>balance of forces </li></ul><ul><li>surface tension pulls up </li></ul><ul><li>gravity & adhesion pulls down </li></ul><ul><li>what are the other two? </li></ul>
20. 20. Contact Angle <ul><li>F = dE/dX </li></ul><ul><li>surface/air & surface/water interfaces also have “surface tension”, in ergs/cm 2 </li></ul><ul><li>moving water edge back and forth incurs energy costs/profits </li></ul><ul><li>but units of F are energy/distance, not area?! what’s the deal? </li></ul>
21. 21. Contact Angle <ul><li>problem is 3-D </li></ul><ul><li>surface tension is force per length </li></ul><ul><li>each dL of perimeter contributes  dL force </li></ul><ul><li>F = dE/dX =>  dL </li></ul><ul><li>dE =  dL dX =  dA </li></ul><ul><li>back to ergs/cm 2 </li></ul>
22. 22. Obtuse contact Angles <ul><li>hydrophobic surface </li></ul><ul><li>“ gravity & adhesion” is now “gravity & repulsion” </li></ul><ul><li>if no gravity, drop leaves </li></ul>
23. 23. Contact Angle <ul><li>why doesn’t drop pull or push itself along the surface? </li></ul><ul><li>it did when initially set down, it distorted itself until equilibrium reached </li></ul><ul><li>edge equilibrium is one thing </li></ul><ul><li>equilibrium between  (roundness) & gravity (flatness) & surface coverage (adhesion/repulsion) is another factor... </li></ul>