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PixiePlots - Bubbles


Bubbles can be great fun. They also behave according to mathematical rules. Here we look at some of the rules and why they occur. We also look at how bubbles behave as a result.
A word of warning: bubbles can be very messy. Do not do bubble activities on carpet. Either use them outside or on some easily cleaned indoor surface.

Last, but not least, please remember slippery surfaces can be a safety hazard.

Mathematical idea

A sphere has the smallest area for its volume of any solid shape.
Bubbles always try to make the smallest possible surface.

Materials needed

For these activities you will need some bubble mix, several bubble frames and some wool or thread. For the demonstrations mentioned below, the frames needed are a simple round ring (at lease 10 cm wide) and a cubical frame. You may also want some models of various simple geometric shapes.

"The Golden Rule of Bubbles"

Whether it is a lone bubble or a group of bubbles joined together, bubbles get their shape by following one simple rule:
Bubble film will always try to make the smallest possible surface
Bubbles are a real-world example of what mathematicians call a minimal surface. A minimal surface is one that has the smallest area possible, while meeting certain conditions. For example, the smallest surface that contains a certain amount of air. There is a whole field of mathematics called Minimal Surface Theory that deals with the sort of shapes that bubbles form. It also produces lots of fascinating and bizarre images that can be found by searching for "Minimal Surfaces" on the internet.

Demonstration 1: The Bubble Trampoline
Take the ring and dip it into the bubble mix, so a film forms. Now hold the ring horizontally and move it up and down, without forming bubbles. The film will bounce up and down, like a trampoline (if you are doing this for an audience you may want to use a bit of mime and introduce a "performing flea").
Bubble film is elastic. When you form a film on the ring, it has to stretch out over the gap in the ring. When you bounce the ring you stretch the bubble film even more. This elasticity is important, it lets the film stretch to make a bubble.

Demonstration 2: Woolly Jumper
Use the ring again, but this time tie a piece of thread or wool across the middle of the ring. Don't make it taunt, it should be reasonably loose. Make another bubble film. Use a finger to burst the film on one side of the thread. The thread will jump over towards the other side, until it is held taunt. It should be possible to hold it vertically, with the bubble film up the top so it is supporting the weight of the thread.
Just like a stretched rubber band, a stretched bubble film is under tension. When you burst one side of the bubble, the tension in the other side pulls on the thread.
This sort of thing happens with bubbles in general. The tension in the bubble film will always try to shrink the film to make the smallest surface possible. Sometimes there may be restrictions, like having to contain air (a bubble) or being stretched over a bubble frame.

Demonstration 3: Shapes
Show various different shapes, such as a cube, pyramid and other geometric shapes. Explain that they have more surface area than sphere with the same volume. Blow several bubbles. Bubbles form spheres because spheres have the smallest possible surface area for their volume.
The table below compares several different shapes and their surface areas to a sphere.
Surface areas of shapes with the same volume
Shape Number of sides Volume (units3) Surface Area (units2) Area/(Area of sphere) (Area of sphere)/ Area
Tetrahedron 7.21  1.49  0.67 
Cube 1.24  0.81 
Octahedron 5.72  1.18  0.85 
Dodecahedron 12  5.32  1.10  0.91 
Icosahedron 20  5.15  1.06  0.94 
Sphere infinite 4.84 

Demonstration 4: Cubical Bubble
Use a cube shaped bubble frame. Dip the frame completely into the bubble mix. This makes several bubble films forming a square in the middle. Dip again, but only immerse one side of the frame. A near-cubical bubble will form in the centre of the frame, surrounded by films (it may be necessary to burst a few bubbles near the center to get just one bubble).
Burst the films around the bubble one at a time. The 'cube' will be revealed to be a sphere stretched out by the films around it.
Although a single bubble will always try to form a sphere, other shapes can be made by having several bubbles and films touching. When bubbles and bubble films meet, they always obey certain rules:
Films and edges always meet each other at equal angles, so three films meeting at an edge will be 120° and four films will be 90° apart.
There are never more than two films at an edge.
There can never be more than four edges or six films meeting at a point.
These rules are all consequences of the "Golden Rule of Bubbles". From these rules, it can be shown that the bubble was not a true cube, as the edges and faces did not meet in right angles. It bulged slightly.

Bubble Mix

There are lots of different bubble mixture recipes available on the internet, but most of them are written by Americans and use American detergents. This recipe is used by the Questacon Maths Squad using ingredients available in Australia.
3 parts dishwashing liquid (Morning Fresh works well)
7 parts hot water
1 part glycerol (or sugar)
The glycerol helps the bubbls to last longer, by preventing them from drying out. Glycerol is available from chemists. If you cannot get any glycerol, use sugar instead.
Mix the ingredients very thoroughly. The Maths Squad's batch was mixed for around half an hour. If you are making a large amount, try an electric drill with a paint-stirrer attachment, or even a bent piece of coathanger wire. Otherwise a flat stick works fine.
There are a few things that may affect how well your bubble mix works.
Bubble mix gets better with age. With time, some water may evaporate from the bubble mix and it may need more water added.
Humidity can seriously affect your bubbles. Bubbles burst when they dry out, so the more humid it is the longer they last. Bubbles work best at night, in the shade and while it is raining. Air conditioners can dry the air which bursts bubbles faster.
The quality of the tap water in your area may also affect your bubble mixture. Hard water doesn't work as well as soft water. You may need to try distilled water instead of tap water.
You may need to "fine-tune" your bubble mix, either by adding more detergent or more water. Experiment a little. Remember to stir thoroughly.
Froth on the top can interfere with making bubbles.


Vinegar can be very effective for cleaning up bubble mixture. If you are using metal bubble frames, they will need to be wiped down with water, then with vinegar, then with water again. Otherwise they will corrode. The bubble mix can be kept in an airtight container.
Further activities
Try other shapes.
Try a pyramid-shaped frame.
Try a helix.
Two circles held near each other can produce a shape called a hypercycloid, like a cylinder that gets narrow near the middle.

Bubble Recipes

All of these bubble recipes make great bubbles for children.  The Magic Bubble recipe is the favorite with my kids.  That recipe makes bigger bubbles that last a bit longer.  See hints for ideas on where to buy Glycerine.
Basic Bubbles
2 tblsp dish soap
1 cup water   
Sweet Bubbles
1 tblsp corn syrup
2 tblsp dish soap
1 cup water   
Magic Bubbles
1 tblsp glycerine
2 tblsp dish soap
9 oz water   
Color Bubbles
1 cup liquid tempra paints
2 tblsp dish detergent
1 tblsp liquid starch

Hints for making bubble solutions
Mix up the recipes the day before for best results.
Glycerine is inexpensive and can be found in most drug stores.  The children think that the bubbles are so much better that it is worth keeping a small bottle on hand.   
Do NOT use the Sweet Bubbles recipe if you have bees or wasps in your yard.
Color Bubbles can be a bit messy.  Be sure to use paint that can wash out.  You can add a little water if the mix is too thick.

Bubble Wands
Children are often surprised when they realize they can do a craft project to make their own bubble wand.  A basic bubble wand can made from a stick with any type of loop on top.  Use any materials you have on hand, or try one of these ideas.  Once the children have seen the options, let them experiment with the craft supplies to make their own wands.
A 12 inch piece of coat hanger with 10 inch piece of string tied in a loop on one end.
Cut the center out of a plastic lid (yogurt or margarine container) and thumb tack it to a wooden chopstick.
Cut the top and bottom off a can of tuna, creating a 1 inch tube.  Check for sharp edges before letting the children have it.  Put the bubble solution in a pie plate to make it easy to dip the can.
Buy a set of 10 inch bubble wands and keep them from year to year.
Here are some ideas sent in by our visitors.
"We have had great luck making giant bubbles by using cotton string and straws to make wands. Cut two sections of straws, about 6 inches long. Cut a string about 24 inches long. Pull the string through the straws, tie the string in a knot, and hide the knot inside a straw. By putting your hands on the straws and pulling, you create a square or rectangle. Dip this form into the pan of bubble solution, and gently draw it through the air. Voila, a giant bubble."
"We made bubble wands using twigs found in our back yard. Have the children look for pine twigs that have recently fallen (flexibility is the key). Wrap the twig tightly with yarn starting from about 1/3 of the way up and wrapping to the tip. Bring the tip around to your starting point, making a circle, and tie it down by wrapping around where the twig crosses itself. The longer the twig, the bigger the circle, the larger the bubbles. Use any of the bubble recipes and enjoy. We used this as a childrens birthday party craft (for older children or adult assistance for younger children) and found it a nice way to bring all the kids together on a sunny day."
"At our preschool I purchased fly swatters for the children to use as bubble wands. Even the toddlers have great success making millions of bubbles."
"Use a fairly rigid drinking straw, the fancy reuseable ones work best. (You want straws with a fairly small diameter hole.) Have the child insert both ends of a 12" length of chenille into one end of the straw and form the loop into a 2-3" circle. You can make 20 - 50 bubbles from one dip of bubble mix!"
"Those little green baskets that strawberries come in make excellent bubble blowing tools. You can't blow very big bubbles, but kids can make lots and lots of little bubbles. Plus, it's recycling!"
"We had a lot of fun using plastic cookie cutters to blow bubbles. My daughter is fascinated by Count Von Count on Sesame Street, so we used big and small numbers. We tried lots of bubble solutions and had a blast in the back yard."

No Wands Needed
Here's an interesting idea for blowing bubbles sent in by one of our visitors.
After watching the clowns at the circus make bubbles with their hands, my son and I went home and tried it. It took a little practice, but now my 5 year old child does it with ease. You dip your hands in the bubble solution (shampoo in the bath is the cleanest) lock your two thumbs then slowly spread them to make a circle. Blow gentle and you will get massive bubbles.

I like to make my own bubble solution! Although the commercial solutions made by Tootsietoy (Mr. Bubbles), Imperial and Pustifix may be fine for general use, really big bubbles require lots of solution which can get quite expensive.

Detergents: During my world travels, I have tried hundreds of soaps and detergents as a basis for my mixtures. The best I've found are Joy and Dawn detergents, made in the USA. Ivory and Palmolive detergents are just ok. Since climate and other conditions vary widely, you must use recommendations made here only as a guide. You need to experiment to get the perfect mixture for your use.

Additives: When I need to make really colorful, sturdy bubbles, I add glycerine to the mix. Glycerine is available at most drug stores, but be forwarned, it is expensive! Glycerine sold in rose water or other solutions is pretty much worthless. A much more practical and less expensive additive is white Karo Syrup which is available at the grocery store.

Water: Water, a key ingredient, varies widely in its quality. One bubble solution manufacturer I know ships huge containers of water from the USA to its mixing plant in China where water quality doesn't meet the necessary standards. Soft water is good for bubbles. Hard water, well water, and any water containing high levels of iron is bad for bubbles. To get the best mixture, try using distilled water which is available at the grocery store. The tap water where I live is good so I usually use it in my mixtures.

Bubble Formula # 1
Dawn Ultra or Joy Ultra    Water
(Distilled Water Works Best)    Glycerine or White Karo Syrup
1 Part    15 Parts    .25 Parts
Bubble Formula # 2
Regular Dawn or Joy     Water
(Distilled Water Works Best)    Glycerine or White Karo Syrup
1 Part    10 Parts    .25 Parts
Bubble Formula # 3 (Super Bubbles)
Regular Dawn or Joy     Glycerine    White Karo Syrup
2 Parts    4 Parts    1 Part
Stuff to Create With
All recipes for Bubbles are from Jane Harris from the ECELoop!  Thanks Jane!

Jane’s favorite
2 C Dawn
4 oz glycerin
Enough water to fill jug.
Place Dawn and glycerin in 1 gal container add enough water to fill. Let set at least over night.

Joyful bubbles
2 C Joy
6 C water
¾ C Karo syrup
Mix together, let set over night

Preschool bubbles
1 C Dawn
10-12 C water
1 T glycerin
Mix as above
Long Last Bubbles
1 oz Dawn
1 Oz Glycerin
1 C water
This mixture can be used at once. It is very thick
From the Home Child care providers
1 C water
2 T Karo syrup
4 T Dishwashing liquid
Professor Bubbles
1 C Regular Joy
10 C water
¼ C glycerin

Beluga Bubbles
1 T salt
1 C warm water
¼ C Blue Dish soap
Combine water and salt , gentle add dish soap. Stir gently until salt is dissolved.

Desperation Bubbles
½ C warm water
½ C liquid detergent
1 T cooking oil
Stir together and use.
Although these are not the very best bubbles they can be made from things found in any kitchen.

Sugar Bubbles
4 C hot water
10 T white sugar
¾ C Dawn or Joy
Combine hot water and sugar, gently stir in soap.

A variation on a theme
1 C Joy Dawn or Ajax
1 gal water
1 T glycerin
Mix together and let settle before using.

Tears no more Bubbles
¼ C Baby shampoo
¾ C water
3 T corn syrup
Mix together let set a few hours.

Ultra Bubbles
1 C Ultra Joy or Dawn
15 C water
¼ C Glycerin

Super Bubbles
2 parts Dawn
4 parts glycerin
1 part corn syrup.
I have never tried this. It is supposed to be for very long last bubbles
(Like for days)

Long Lasting Bubbles
1/3 C commercial bubbles
1/3 C water
1/3 C liquid soap.
A simple solution
8 T dish soap
1 Quart water

Notes and Comments
1. If bubbles pop easily or solution does not work well, add more water.
2. Dawn and Joy seem to be the best choices for bubbles. It is the antigrease agent.
3. Bubbles work best on an over cast day.
4. Bubbles love moisture so right after a rain also works well.
5. To catch a bubble just get your hand wet.
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