At-home STEM Activities: Bubble Math
Blowing bubbles is a fun and simple activity for all ages. You dip a wand in bubble solution, blow through it, and create little spheres of soapy water. But have you ever thought about why bubbles are spherical?
Let’s explore the science and math behind bubbles, starting with making some bubble solution and experimenting with it!
DIY Bubble Solution and Wands
Materials:
Wands:
Pipe cleaners or wire
Scissors or wire cutters
Bubble Solution:
2 Tablespoons dish soap
3/4 cup water
Optional: 2 teaspoons corn syrup (for longer lasting bubbles)
Instructions:
Mix the dish soap, water, and corn syrup (if using) together. Bend the pipe cleaners into wands, experimenting with different shapes: circles, triangles, squares, spirals, etc. Also form some three-dimensional shapes with the pipe cleaners:
Tetrahedron:
A tetrahedron is a regular polyhedron with 4 faces, and each face is an equilateral triangle
Bend a pipe cleaner into a triangle.
Form a second triangle, to make a diamond-like shape, and trim the pipe cleaner.
You have two triangles that each have one open corner—connect the open corners with the remaining piece of pipe cleaner. Leave a long tail to dip the tetrahedron in the bubble solution.
Cube:
Bend a pipe cleaner or wire into a square.
Form a second square off of one side of the square you formed in step 1.
Repeat step 2, so that you have connected squares in a row.
Bend the first and third squares away from the second square at 90° angles. Connect the first and third squares at the top and bottom corners, forming a cube.
Blow some bubbles and observe what happens! How does the solution cling to the wands? Which shape is best for blowing bubbles?
Why are bubbles spheres?
In nature, in general, things want to take the form that uses the least energy and material. So when you blow a bubble, your air gets trapped inside and the soap bubble wants to minimize the amount of surface area it needs to enclose a specific volume. Let’s think about that a little more.
A three-dimensional shapes is measured by its surface area and volume. Surface area is the total area around the outside of the shape. Volume is the amount of space inside of a 3-D shape. So if we have a can of soup, for example, the surface area is how much aluminum we need to make the can, and the volume is how much soup we can fit inside.
Each three-dimensional shape has a different way of calculating its surface area and volume. Here are a few examples:
Note that we can solve for h1 and h2 in terms of x using the fact that each face of the tetrahedron is an equilateral triangle—if you have some experience with geometry, try to see why h1 = (x * sqrt(3))/2 and h2 = x * sqrt(2/3)
Now, if we want the volume of each of these shapes to be 1 cm3, let's see how that affects the surface area:
Of just these three shapes, we can see that the surface area of a sphere is less than the other two. In fact, of all three dimensional shapes, a sphere has the least surface area when all the shapes are enclosing the same volume.
This same concept explains the way the bubble solution clings to the wands, particularly with the three-dimensional shapes:
The way the bubbles sticks to the shapes uses the least possible amount of bubble solution.
