Well, that is an interesting task that I definitely want to hear the result of :)
I would start out by simply defining how large (or small, if you will) the individual gel "blobs" must be, before you would consider the mixture homogeneous. For a hypersimplified example, lets say you have 10^-3 moles of your gel, your mixer splits every gel blob in two equal parts every rotation, and once the blobs reach a size of 100 molecules or less, you would call that mixture homogeneous.
blobsize=6.023e23/1000;
timer=0;
while blobsize>100
blobsize=floor(blobsize/2);
timer=timer+1;
end
It comes out to 63 rotations of the mixer - extremely oversimplified of course :)
Next, you will want to introduce more terms gradually, like the probability of your mixer paddle colliding with each individual gel blob each rotation / time unit. This probability depends on the shape of the mixer, and might be close to 1 when you start the simulation, but the probability of an individual blob being hit decreases rapidly when the blob sizes decrease. However, you have more and more blobs, so the chance of just hitting any blob might be higher and higher! And of course, the paddle colliding with any gel blob might simply "bounce off" and not reduce the blob, it might split the blob into two blobs 50:50, into 3 blobs 33:33:34 or maybe even into 2 small blobs and a large blob 20:20:60. And all the while, the movement of the water/gel mixture will also cause dissolution in the gel/water interface - the rate of which will depend on your total blob surface area, which will increase super rapidly when the blob sizes decrease! There are so many terms you can introduce - take it little by little, make one thing work before introducing the next thing. In the end, you might end up with a large array of different blob sizes - and when your average blob size reaches the goal, you stop the simulation.
