For instance, juice powder on water.

Is it better to make a vortex? Move the spoon back and forth? Move it randomly?


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.


As such, I'm also assuming that the solute can be dissolved in the solvent etc.

  • $\begingroup$ I know very little with regard to fluids, but my assumption is that at small volumes any method(s) used to mix solutions are nearly intelligible in terms of efficiency. Where this becomes most relevant is with larger volumes. Talk to a brewmeister? :) $\endgroup$
    – signus
    Commented Feb 13, 2017 at 20:47
  • $\begingroup$ People are voting to close, but I do believe this is on topic. Not the best of questions, perhaps, but on topic nonetheless. $\endgroup$
    – auden
    Commented Feb 13, 2017 at 22:16
  • $\begingroup$ What is efficiency her: Less energy input? Fastest mixing? When is the solution mixed (e.g., is there a % attached to the dissolved fraction?) $\endgroup$
    – Kyle Kanos
    Commented Feb 13, 2017 at 23:51
  • 2
    $\begingroup$ Doing a mental experiment: the vortex method would probably be one of the worst, considering the particles will essentially be moving in a uniform manner. You probably want to maximize turbulent mixing, such as when moving the spoon back and forth oriented obliquely to the flow. $\endgroup$
    – James
    Commented Feb 14, 2017 at 2:07

1 Answer 1


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.


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