1. Supplementary Materials for Teachers and Workshop Presenters Dr. Rachel Levy Mathematics Department Harvey Mudd College Creative Commons License CC BY-NC-SA 3.0 by Rachel Levy

2. These slides were developed for people to use, modify and share. Please cite this source if you use this material. Thank you! http://creativecommons.org/licenses/by- nc-sa/3.0/

3. Challenge questions: What is a surfactant? What is the difference between Buoyancy Surface tension What is soaps job? How are SOAP and SLOPE related?

4. What is Soap?

5. http://commons.wikimedia.org/wiki/File:Surfactant.jpg Soap is a surfactant The head is hydrophilic (loves water) and the tail is hydrophobic (hates water).

6. Fancy term for soap: surfactant Surface-active-agents lower surface tension With soap the surface tension of water is lower because the bonds between soap and water on the surface are weaker than the bonds on the surface of water with no soap. Surfactants are used in detergents to surround grease in balls called micelles. The hydrophobic tails attach to the bits of dirt and grease. The hydrophilic heads stay on the outer surface of the micelle and help it move into the water and off clothes and dishes.

7. Surfactants can attack dirt Carlota Oliveira Rangel-Yagui1, Adalberto Pessoa Junior, Leoberto Costa Tavares, J Pharm Pharmaceut Sci (www.cspscanada.org) 8(2):147-163, 2005

8. Your First Breath http://hyperphysics.phy-astr.gsu.edu/Hbase/ptens2.html#alv Air inflates the alveoli of lungs Process is like blowing up balloons Natural surfactants make it easier to breathe by lowering surface tension in the alveoli

9. Your lungs need surfactant! http://www.valuemd.com/usmle-step-1-forum/21404-alveoli-surfactant.html

10. Surfactants lower surface tension. (Answer to challenge question: Soaps job is to lower surface tension.) What is surface tension?

11. Wikipedia:WassermoleküleInTröpfchen.svg Surface tension is an attractive force between molecules on the surface of a fluid.

12. Surfactants lower surface tension by weakening the attraction between surface molecules

13. http://www.everythingabout.net/articles/biology/animals/arthropods/i nsects/bugs/water_strider/ Water Strider A water strider is a bug that uses surface tension to walk on water.

14. Agnes Pockels (1862 – 1935) was one of the first people to carefully study surface tension. Lord Rayleigh to Nature magazine (1891): I shall be obliged if you can find space for the accompanying translation of an interesting letter which I have received from a German lady, who with very homely appliances has arrived at valuable results respecting the behaviour of contaminated water surfaces. http://cwp.library.ucla.edu/Phase2 Pockels,_Agnes@871234567.html

15. Agnes Pockels: Nature Magazine I will describe a simple method, which I have employed for several years, for increasing or diminishing the surface of a liquid in any proportion, by which its purity may be altered at pleasure. A rectangular tin trough, 70 cm. long, 5 cm. wide, 2 cm. high, is filled with water to the brim, and a strip of tin about 1 1/2 cm. laid across it perpendicular to its length, so that the underside of the strip is in contact with the surface of the water, and divides it into two halves. By shifting this partition to the right or the left, the surface on either side can be lengthened or shortened in any proportion, and the amount of the displacement may be read off on a scale held along the front of the trough.

16. What is Slope?

17. Definitions of slope Slope = rise run Slope:change in y change in x Slope: y2-y1 x2-x1

18. What is the slope of this line?

22. What is the slope of this curve?

23. Consider tangent lines along the curve -- at each point you can measure a slope using the slope of the tangent line.

24. Where is the slope of this curve… positive? negative? zero?

25. Color gradient graph Let x = position (left to right) y= intensity (darkness) of the blue y x

26. Color gradient graph Let x = position y= intensity of the blue y x

27. Definition of slope Slope: change in one quantity change in another quantity blue intensity position

28. Definition of slope Slope: change in intensity of blue change in position blue intensity position

29. Experiments 1 Divide into teams of three. 2 Give each team member a number: 1, 2, 3. 3 Possible roles: experimenter, recorder, reporter

30. Paperclip Experiment Supplies: Clean hands (no soap, lotion)! One paper plate Cup of water One large paperclip and one small paperclip Piece of paper (optional) Soap

31. Paperclip Experiment Float a paperclip (or two) on the surface of the water. If this is tough, float the paperclip on a scrap of paper, then sink the paper, allowing the paperclip to remain on the surface. Put a drop of detergent near it. What happens? Why?

32. What does it mean for something to float? Sink? Hint: there are two possible answers

33. What does it mean for an object to float? Float could refer to buoyancy… Float could refer to surface tension…

34. Buoyancy Objects less dense than the water will rise to the surface. But metal ships (more dense than water) float! Why? When do metal ships sink?

35. Sinking Gravity pulls the mass of the boat down. The mass of the boat is black.

36. Buoyancy Buoyancy pushes the boat up. Archimedes (~250BC): Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. Displaced water is green.

37. Buoyancy If the boat springs a leak and takes on water, how much water can it hold before it sinks? Why do you feel light when you are floating in the water? Can you explain why it is easier to float in salt water than fresh water? Hints: weight = mass* gravitational constant mass = density *volume

38. In your experiment, did the paper clip float because of (a) buoyancy or (b) surface tension?

39. Surface Tension!

40. Boat Experiment Supplies: Clean hands (no soap, lotion)! One paper plate Cup of water Paper boat Soap

41. Boat Experiment Float a paper boat on one side of the bowl. Put a drop of detergent behind it (between the boat and the edge of the bowl). What happens? Why?

42. Plotting Surface Tension What is happening to the surface tension of the water in the boat experiment?

43. Plotting Surface Tension Graph x = position y = surface tension (you can also draw your boat!)

44. Plotting Surface Tension Graph x = position y = surface tension (you can also draw your boat!) Time 0: Before you put the soap in the water

45. Plotting Surface Tension Graph x = position y = surface tension (you can also draw your boat!) Time 0: Before you put the soap in the water Time 1: The second after you put the soap in (before the boat has moved much)

46. Plotting Surface Tension Graph x = position y = surface tension (you can also draw your boat!) Time 0: Before you put the soap in the water Time 1: The second after you put the soap in (before the boat has moved much) Time 2: After the boat has stopped moving

47. Graph x = position y = surface tension and pic of boat Time 0: Before you put the soap in the water Time 1: The second after you put the soap in (before the boat has moved much) Time 2: After the boat has stopped moving Time 0 Surf Tens. Position bowl View of bowl from top Graph surface tension along this line

48. Graph x = position y = surface tension Time 0: Before you put the soap in the water Time 1: The second after you put the soap in (before the boat has moved much) Time 2: After the boat has stopped moving (reminder: soap lowers surface tension) Time 0 Surf Tens. Position across Bowl Time 1 Surf Tens. Position across Bowl Time 2 Surf Tens. Position across Bowl

49. Time 0 Time 0 before soap is added: zero slope no motion.

51. Time 1

52. No slope (zero slope) no more motion. Time 2

53. Time 0 before soap: zero slope no motion. How does the sign of the slope relate to the direction of the boat motion?

54. Time 1 after soap: positive slope motion to right. How does the sign of the slope relate to the direction of the boat motion?

55. Time 2 after soap: zero slope no motion How does the sign of the slope relate to the direction of the boat motion?

56. Surface tension can be high (time 0) or low (time 2), but if there is no change, the surface tension does not cause the fluid on the surface (and the boat) to move.

57. When there is a change in surface tension (time 1) across the bowl, there is surface motion.

62. Pepper Experiment Supplies: Clean hands (no soap, lotion)! One paper plate Pepper or Tea leaves Soap

63. Pepper Experiment Put some water on a plate Sprinkle pepper on the water Put a drop of soap in the middle Graph your results at time 0: before you added the soap time 1: right after you added the time 2: longer after you added the soap

64. Time 0 Time 2 Time 1

65. The big idea: To get the motion you saw in the experiments, there had to be areas with different surface tension. Change in amount of soap change in surface tension motion! Slope: riseorchange in y run change in x Slope: change in surface tensions2-s1 change in positionx2-x1 Agnes Pockels can help you find s2 and s1!

66. Challenge questions revisited: What is a surfactant? What is the difference between Buoyancy Surface tension What is soaps job? How are SOAP and SLOPE related?

67. Dr. Levys research Thin liquid films and surfactants Surfactant moves the fluid Fluid moves the surfactant Changes in space and time Two partial differential equations one equation for height of the film one equation for surfactant concentration

68. Levys research with Harvey Mudd College undergraduate math majors: Students solve these partial differential equations modeling a thin liquid film and surfactant using computer programs How does the film height and surfactant concentration evolve in space and time? How do solutions of this model compare to experiments?

69. The upside down triangle is a fancy sign for slope! The other symbol in yellow is a function that describes how surfactant affects surface tension. Height equation Surfactant concentration equation

70. Collaborator Dr. Karen Daniels, Physics, North Carolina State University In the left picture, you are looking down at an experiment. The red line is from a laser that indicates the glycerine film height. The yellow areas show the variation in the concentration of surfactant on the thin film of glycerine (slope!). The right picture is an enlarged horizontal slice of the image on the left. We compare this experimental data to mathematical solutions of the two equations.

71. Thank you very much! Dr. Rachel Levy levy@hmc.edu