Slide 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 Slide 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/ Slide 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? Slide 4 What is Soap? Slide 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). Slide 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. Slide 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 Slide 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 Slide 9 Your lungs need surfactant! http://www.valuemd.com/usmle-step-1-forum/21404-alveoli-surfactant.html Slide 10 Surfactants lower surface tension. (Answer to challenge question: Soaps job is to lower surface tension.) What is surface tension? Slide 11 Wikipedia:WassermolekleInTrpfchen.svg Surface tension is an attractive force between molecules on the surface of a fluid. Slide 12 Surfactants lower surface tension by weakening the attraction between surface molecules Slide 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. Slide 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 Slide 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. Slide 16 What is Slope? Slide 17 Definitions of slope Slope = rise run Slope:change in y change in x Slope: y2-y1 x2-x1 Slide 18 What is the slope of this line? Slide 19 Slide 20 Slide 21 Slide 22 What is the slope of this curve? Slide 23 Consider tangent lines along the curve -- at each point you can measure a slope using the slope of the tangent line. Slide 24 Where is the slope of this curve positive? negative? zero? Slide 25 Color gradient graph Let x = position (left to right) y= intensity (darkness) of the blue y x Slide 26 Color gradient graph Let x = position y= intensity of the blue y x Slide 27 Definition of slope Slope: change in one quantity change in another quantity blue intensity position Slide 28 Definition of slope Slope: change in intensity of blue change in position blue intensity position Slide 29 Experiments 1 Divide into teams of three. 2 Give each team member a number: 1, 2, 3. 3 Possible roles: experimenter, recorder, reporter Slide 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 Slide 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? Slide 32 What does it mean for something to float? Sink? Hint: there are two possible answers Slide 33 What does it mean for an object to float? Float could refer to buoyancy Float could refer to surface tension Slide 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? Slide 35 Sinking Gravity pulls the mass of the boat down. The mass of the boat is black. Slide 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. Slide 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 Slide 38 In your experiment, did the paper clip float because of (a) buoyancy or (b) surface tension? Slide 39 Surface Tension! Slide 40 Boat Experiment Supplies: Clean hands (no soap, lotion)! One paper plate Cup of water Paper boat Soap Slide 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? Slide 42 Plotting Surface Tension What is happening to the surface tension of the water in the boat experiment? Slide 43 Plotting Surface Tension Graph x = position y = surface tension (you can also draw your boat!) Slide 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 Slide 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) Slide 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 Slide 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 Slide 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 Slide 49 Time 0 Time 0 before soap is added: zero slope no motion. Slide 50 Slide 51 Time 1 Slide 52 No slope (zero slope) no more motion. Time 2 Slide 53 Time 0 before soap: zero slope no motion. How does the sign of the slope relate to the direction of the boat motion? Slide 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? Slide 55 Time 2 after soap: zero slope no motion How does the sign of the slope relate to the direction of the boat motion? Slide 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. Slide 57 When there is a change in surface tension (time 1) across the bowl, there is surface motion. Slide 58 Slide 59 Slide 60 Slide 61 Slide 62 Pepper Experiment Supplies: Clean hands (no soap, lotion)! One paper plate Pepper or Tea leaves Soap Slide 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 Slide 64 Time 0 Time 2 Time 1 Slide 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! Slide 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? Slide 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 Slide 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? Slide 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 Slide 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. Slide 71 Thank you very much! Dr. Rachel Levy levy@hmc.edu