What is the most time efficient way to mix a solution using a spoon? For instance, juice powder on water.
Is it better to make a vortex? Move the spoon back and forth? Move it randomly?
edit:
I'm most interested in a time efficient way of mixing.
For a "mixed solution" I'm using this definition of solution in Chemistry: 

  
*
  
*A solution is a homogeneous mixture of two or more substances.
  
*The particles of solute in a solution cannot be seen by the naked eye.
  
*A solution does not allow beams of light to scatter.
  
*A solution is stable.
  
*The solute from a solution cannot be separated by filtration (or mechanically).
  
*It is composed of only one phase.
  

https://en.wikipedia.org/wiki/Solution
As such, I'm also assuming that the solute can be dissolved in the solvent etc.
 A: This is indeed a very interesting question, even if perhaps not perfectly expressed. The question of advection and mixing in fluids has been studied extensively, and has clear and important practical applications. Given that diffusive mixing is often negligibly slow in technically important parameter ranges, people have spent a lot of time understanding chaotic advection of fluid particles, which is an area of dynamical systems theory. The Wikipedia article on Chaotic Mixing has a lot of material, plus references to some pertinent pieces of literature.
In short, random motion is pretty good, but a simple periodic back-and-forth motion might work almost as well or better. Rotating the spoon at constant angular velocity, on the other hand, is not usually a good idea. Jean-Luc Thiffeault has given a great talk related to this subject for a memorial lecture for Hassan Aref, which can be downloaded here. (Note: For some reason Adobe Acrobat has problems with this PDF; you may need to find a different PDF reader if this happens to you). Of course, Aref's seminal paper "Stirring by Chaotic Advection" is the classic in that field.
