Brownian Motion was discovered by Robert Brown in 1827. He was studying plant pollen under a microscope, but he was frustrated because the pollen was moving. The water molecules were bumping the pollen molecules, therefore causing the movement that Brown saw. We tried to see Brownian Motion with talcum powder and dirt suspended in water, but we think our microscope wasn't strong enough.
Brownian Motion can also cause diffusion. Diffusion happens when molecules are bumped from an area of more concentration to less concentration. The movement is called concentration gradient. We experimented with diffusion by putting dye in water and watch it spread out, or diffuse. We put dye in cold water, hot water, and in stirred up water. The dye in the stirred water diffused immediately because the water molecules were bumping into the dye molecules very quickly. The dye in the cold water diffused more slowly, and the dye in the hot water diffused quickly, because when water molecules are heated, they move faster, therefore diffusing the dye molecules more quickly.
We also tried chocolate syrup in water. That took very long to diffuse, and it didn't completely diffuse, but mostly sank to the bottom. The syrup was too dense to be diffused by the water molecules, even when we left the sample out over night. The cold green dye sample did diffuse completely overnight, reaching a state of equilibrium. Equilibrium does not mean diffusion really stops, just that there is no more empty space for the dye to be bounced into by water molecules.
Diffusion happens in our lungs every day. The oxygen we breathe goes through the alveoli and diffuses into the blood, which then goes all around your body.