NON-NEWTONIAN FLUID MECHANICS

Well-defined outcome: The student will be able to use measurement, measurement tools, and the scientific process to determine the effect of the percentage of water on the viscosity of a non-Newtonian fluid. Students will represent their findings using the general form of functions (including comparison of linear and quadratic) to describe the effect of % water on viscosity of silly putty and apply the general form of the quadratic parent function to explain non-linear flow of a non-Newtonian fluid (silly putty).

Objectives Mathematics (Algebra 1) The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. a) The student describes independent and dependent quantities in functional relationships. b) The student gathers and records data, or used data sets, to determine functional (systematic) relationships between quantities. c) The student represents relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities. d) The student interprets and makes inferences from functional relationships. 2. The student uses the properties and attributes of functions. a) The student identifies and sketches the general forms of linear (y=x) and quadratic (y=x2) parent functions. b) For a variety of situations, the student identifies the mathematical domains and ranges and determines reasonable domain and range values for given situations. c) In solving problems, the student collects and organizes data, makes and interprets scatterplots, and models, predicts, and makes decisions and critical judgments.

Science (Integrated Physics and Chemistry) 1. IPC 7A) investigate and identify properties of fluids including density, viscosity, and buoyancy; 2. IPC 8A) distinguish between physical and chemical changes in matter such as oxidation, digestion, changes in states, and stages in the rock cycle.

Materials 4% Borax solution (premixed for students but not for inservice). If students are expected to make the solution provide balances and suitable measures to prepare the quantity of putty expected. Smaller quantities are preferred at the high school level and larger quantities at the elementary and middle levels because the preciseness of the measures is less important with larger quantities.

Elmer’s Glue (Not the washable kind, it does not work as well – hmmm?) 2 Quarts of glue (one container) available at a craft store. This is VERY important. If you provide glue bottles students will USE ALL THE GLUE and you will not get multiple attempts. By providing a specific amount of glue students will have to make decisions about partitioning and usage.

(100) Plastic/Paper wax coated cups Timers Baggies – 1 per group Meter Sticks or rulers – 1 per group Markers Funnels – 1 per group Stirrers Graph paper/acetates/Overhead marking pens (8) Permanent sharpies (four color) ultra fine point (4) Large water containers with pouring spout (8) Graduated cylinders (8) 200 ml or similar size beakers (not too large) 50 ml will also work (100) Popsicle sticks (2) Food coloring (ALL FOUR COLORS) (8) 1/8 teaspoon measures

139 Background: The task is group based with each group having a different project. Students cannot rely on the results they see from other groups. You will need to have done some preparation with students to understand the context as described on the briefing sheets. The teacher will also have to talk about corporate espionage and the need for students to develop their own recipe and to keep track of those recipes. It also helps if students already know or have been told directly that they should only change one variable at a time in the recipe. They should all know what this means so you might want to be explicit about the borax, water, and glue, each being a variable. Conditionally, how they combine the three components is also a variable. So if they choose to dilute the glue by adding water or to dissolve the borax in water and decanting the solution from the undissolved solute would each be separate conditions so quantities of each of the three variables should be help constant so they can observe the what happens as a result of these choices. If they vary the quantity of one component, they should hold the quantity of the other two variables constant. For example, if they start with 1/8 teaspoon each of borax, glue, and water and they want to alter the water in the next mixture they should keep the borax and glue at 1/8 teaspoon of each and only change the water. Groups should observe the result, write notes about the product and make a decision about what to do next. A common misconception held by students is that they change each variable in turn keeping the previously doubled variable. For example, 1/8 teaspoon of each borax, glue, and water, they double one component leaving the other two constant, note, the results, double the next component adding the previously doubled component and one component constant, note results and then double the last component to the other two doubled components and note the result. The misconception is that they believe 1/4 teaspoon of each ingredient will result in a different product than did the 1/8-teaspoon of each ingredient even though the proportions are exactly the same. All they did was make twice as much but not a different product. Be sure that they have learned about proportions and ratios.

School based silly putty is typically created my mixing equal amounts of a 4% Borax solutions and Elmer’s GlueTM, although some web-based resources recommend diluting the glue or altering the 1:1 mixing ratio.

Preparation: Decide if you are preparing the Borax solution or expecting students to do it. Preparation of the solution can take a bit of time because you may find you did not make enough. For a class of 25 consider making about 2000ml of solution and giving each group 400ml. Expect spillage and waste so you may want to distribute 200ml and allow one refill or make careful use of the solution a criteria on the grading rubric. IF you are having students create the solution provide only small amounts of the Borax, consider standard supplies of about ¼ teaspoon and you can also prevent waste by including its careful use valued on the rubric.

Question: What role do different mixing conditions and proportions of ingredients have on the product each group is charged with making?

Explanation: You are going to be put into groups and each group will be an engineering team with a separate project (see Corporate Briefing). Assign each group a different Corporate Briefing. While the tasks may appear different they all require the set of skills. Each project will be related to silly putty. You must keep your task a secret and you will have to prepare a PowerPoint or a video for the purpose of showing how well your product meets the expectations of the firm that hired you. This is a sales pitch. Remember address ALL the requirements in the briefing. (Refer to the Appendix for the storyboarding guide, and rubrics on presentations, and team work or design your own guidelines.) The additional explanation is for the teacher and may or may not be read in part or whole to the class.

The glue contains a polymer called polyvinyl acetate resin. We changed the polymers behaviors twice in this activity; once when we added water to the Elmer’s glue and the second time when we added borax. What did the borax actually do? The borax is called a cross-linker. It chemically ‘ties together’ the long strands of the polyvinyl acetate. This tying together changed the viscosity of the glue. It increased the viscosity because the new cross-linked chains interfere with the ability of the solution to flow. As a result the silly putty is ‘stiffer.’ It is not a solid though. How do we know this? If we leave the silly putty alone on a table it will flatten out. It is also not a liquid because we can form it into a shape. So what is it?

Many fluids exhibit a non-linear response to stress, and are called non-Newtonian fluids. Such fluids fall halfway between being a solid (where the stress depends on the instantaneous deformation). For such ‘soft

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