# Does this disprove diffusion?

Diffusion states that a solute moves from an area of high concentration to an area of low concentration until the solute is evenly distributed through the solution.

So when I make hot tea and the sugar melts, why does the majority of sweetness stay at the bottom instead of diffusing evenly through my tea? I know for a fact that the sugar is completely melted because when I finally empty my mug there is no grit at the bottom.

I don’t have the chemistry chops to tell you why, but I’m going to go out on a limb and say, “No, it doesn’t disprove diffusion.”

Just give it enough time. Maybe centuries.
Diffusion is a slow process, and it’s going to take even longer when you expect to evenly diffuse a relatively heavy molecule in water.

That’s why people stir

Is there a sweetness profile through the cross section of the tea? Is it changing through time? Does it accelerate when strong convection currents exist? if so then there is diffusion going on.

Diffusion in a liquid is much slower than you may think. If you have a cup of coffee 8 cm deep and all the sugar is at the bottom, how long will it take for it to diffuse to the top?

The formula for Diffusion is t=x[sup]2[/sup]/2D where

t = time
x = distance
D = Diffusion Coefficient

The Diffusion Coefficient for sucrose is .46 x 10[sup]-5[/sup]cm[sup]2[/sup]/s (PDF link here), so to move 8 cm it takes:

t = (8 cm)[sup]2[/sup]/(2*.46 x 10[sup]-5[/sup]cm[sup]2[/sup]/s)
t = 1 739 130 s
t = 20 days

Most of the mixing of the sugar comes from the stirring with a spoon and the sloshing as you take a drink.

Nice. Where does temp of the liquid factor in?

It doesn’t make that big a difference in this setting - the diffusion coefficient is slightly temperature dependent, but the liquid will cool to ambient much faster than any effects of the high temperature will be seen.

Temperature does control convection, though. If the surface cools faster than the liquid below it, for example, the increase in density on the surface will cause the warmer water below it to rise, displacing the cooler water and mixing the mug. Convective mixing distributes the dissolved sugar by moving the liquid that contains the molecules rather than the molecules themselves, and is usually a much faster and stronger process than diffusion.
ETA: The other thing the temperature controls is the rate of dissolution. If you’re dumping sugar and letting it dissolve slowly, that will happen faster in a hot mug than a cooler one. But again, that’s a faster process than diffusion is.