EXAMPLE 6.1A: SUGAR AT THE BOTTOM OF A CUP OF TEA: WAIT AND SEE (ELEMENTARY)

You put a layer of sugar in your hot tea and wait. At what time will the sugar reach the surface of your tea, if diffusion is the only transport mechanism? Use penetration theory for your estimate.

Data: diffusion coefficient of sugar in warm water

EXAMPLE 6.1B: TWO UNSTEADY FLAT LAYERS (MEDIUM)

Before you watch the example video, you can try to answer the question yourself!

Two flat plates are on top of each other: a wood (oak) one and a bituminous one. Both have a thickness of 1 cm. The oak plate (20°C) has a lower temperature than the bituminous plate (50°C).

Try to determine the temperature profile in each of the plates, after 10 seconds. Is the situation shortterms or longterms?

Data:

Oak:

EXAMPLE 6.1C: LEMON IN YOUR GLASS OF WATER: DON’T STIR (ADVANCED)

Suppose you want to mix yourself a fresh glass of water with a refreshing lemon taste. You juice a lemon and pour the lemon juice into a fresh glass of water. Normally, you would stir this mixture, to get the lemon evenly spread. What if you don’t stir, but wait? How long does it take for the lemon to spread out? Make a quick and dirty estimate using penetration theory.

BONUS: EXAMPLE 6.1D: TWO FLAT LAYERS TOWARDS STEADY STATE (MEDIUM)

If you wait longer, x becomes more than half of the depth of the plate. In this case, we do not speak of short-time anymore. So, the penetration will break down. What happens then? Can you calculate T_∞?

Data:

Oak: