[Jugurtha]

>This ge really means that when you stir with a spoon you create a vortex concentrating the solute in the bottom center of the cup.

This is considered improper with regards to "table manners". Many people do a circular motion with the spoon moving around the glass/cup wall. This creates a big stable vortex. The mass of the liquid is pushed against the wall and moves as a whole, similar to an annular flow, as you describe.

Another technique, the one I use (which appears to be "considered" proper, but our focus is on efficiency here), is a linear back and forth motion where the spoon moves forward and backward creating four unstable vortices every motion's period (T): two vortices on the left and right of the spoon when it moves forward (T/2), then two vortices on its left and right when it moves backwards (second half period, at date T, for a total of four vortices). These are quickly broken as they collide against one another every half period, and I suppose each particle's trajectory is more irregular with respect to a neighboring particle, which would mean a faster dissolution and a faster change in the concentration gradient.

That's how I've always thought about it. I'm not certain.