Donovan Filkins, Elizabeth McLean, Robert Wright
I. STATEMENT OF PURPOSE
Use Hele-Shaw method to investigate the relationship between the
viscosity of a substance and its fractal dimension.
II. LIST OF MATERIALS
Hele Shaw apparatus
red food coloring
Palmolive clear dish detergent
Sun Light dish detergent
Suave daily clarifying shampoo
1.0 cc graduated syringe
20 cc graduated syringe
3/4" internal diameter clear plastic tubing, 40 cm (15") in length
5 mm diameter ball bearings
ring stand with two clamps
graph paper with grids of two sizes xeroxed onto transparencies
- Working in teams of three or four, students will develop their
own method to measure viscosity of a range of unknowns.
- Facilitator will introduce the Hele-Shaw apparatus and explain
the procedure. (procedure as outlined in Fractals in Science: An
Introductory Course, June 1996 edition, page 3-18).
- Students will draw their predictions in their lab books.
- All groups will use glycerol and colored water for the first
experiment in order to identify similarities and differences. They can
decide which to inject: water into glycerol or glycerol into water.
- Students will go from group to group to gather data following which a
class discussion will ensue.
- Introduce the concepts of randomness and patterns (with regard to
- Students select two liquids other than glycerol into which to
inject colored water. Have students record their predictions of the
relative viscosities and of the shapes created before carrying out the
tests. Measure the viscosity by timing a ball bearing as it drops
through 20 cm of the fluid in the tubing.
- Students will perform their experiments and record results by
placing Hele-Shaw apparatus on photocopier (or scanner if available)
within five minutes of injecting water. Compare results with original
experiment and note similarities and differences.
- Students will quantify their results by using the box method as
outlined in Fractals in Science: An Introductory Course, June 1996
edition, starting on page 1-11. Record results in a data table in lab
book, and collect class results on chalkboard.
- Students will respond in groups in writing to the following
question: What relationship do you find between the designs you created
and the relative viscosities of the two fluids used?
- Extensions: a. Students bring in viscous transparent fluids from
home to test. b. Use scanner and the fractal dimension program to
analyze the patterns. c. Discuss similar patterns occurring in nature.