Laboratory Setup
In this laboratory it is important to rinse all glassware well before use. Trace amounts of detergent on the glassware will affect the results.
The experiment requires about: 15 minutes of student prep 5 minutes to perform, and 15 - 20 minutes clean up.
The dyes
Sudan IV is a strongly hydrophobic dye and will give good results, but it does have some health hazards, so you may want the students to wear gloves.
Read the stains file entry on Sudan IV here.
http://stainsfile.info/StainsFile/dyes/26105.htm
Methylene blue is pretty safe. It may be an irritant. It is hydrophilic, but if there is detergent in the glass blue dots will also be suspended in the emulsion making results unclear.
The detergent will form an emulsion. Have the students compare the tubes to the control if they have difficulty determining which dyes are hydrophobic.
If methelene blue is unavailable, most store bought food colorings will do. For inexpensive hydrophobic dyes, you might try a deep colored oil. Although I have not had a chance to test it, some brands of hot pepper oil found in the Asian sections of grocery stores are dyed with red dye that may work in this experiment. Test out different substances before hand to see which work best.
relevance
This process of extracting chemicals by seeing which fraction (oil or water) they will dissolve in is a basic technique in organic chemistry.