What happen when you stir a cup of coffe? I have a cup of coffe, i add sugar to it and then i stir it. Why the flavor is homogeneous in all the liquid? I would expect to see the distribution of sugar following lines arround the fluid and not uniformlly distributed in the fluid.
A conceptual answer is fine but (if you have the time) a more mathematical answer is always welcome.
Thanks for reading!
 A: Sugar has a solubility in water of 909 g/1 L at 25 °C (wikipedia). Even if coffee is not water, let's take this as an estimate. In other words, if you do not heavily overload coffee with sugar, the sugar will get dissolved. The kinetics of this process are not known to me, but in general it seems fairly quick. The reason you stir is to distribute the water and sugar so that there are no local regions around the sugar where the sugar concentration is very high and dissolution thus very slow.
As soon as the sugar is dissolved, diffusion (in probably good approximation, Fickian diffusion $\dot{c}=D \Delta c$) sets in and distributes the dissolved sugar all throughout the cup as has been pointed out in the other answer.
If you want to see the effects of the fluids actual flow patterns, try putting something in that does not mix.
A: Querido beto, sugar not only get mixed by convection, or fluid transport, as you do when you revolve the spoon, if that were the case you would be right. But sugar also transport to the liquid through diffusion (more precise mathematical description here). Even if you do not revolve the coffee with a spoon, diffusion will act fast enough to, say, edulcorate your coffee in about 16 minutes.
