If I have a mixture of glucose and fructose in aqueous solution, what is the simplest method to separate them? Heating to 110 °C to melt only the fructose would probably work theoretically, but this would cause a huge mess.
The most common industrial method is one of various types of liquid chromatographies, which is usually how glucose-fructose solutions are enriched in fructose. I did see a couple other possible methods though:
This one from 1965—before good LC methods existed—relies on the difference in solubility in partially water-miscible solvents like n-butanol to perform a liquid-liquid extraction. Unfortunately, the pdf seems to be incomplete, but basically the water-solvent-sugar system separates into two phases with each sugar partitioning more into a different phase. They calculated that it would take around 40 cycles to get 90% fructose from this method, but it doesn't seem to be very efficient due to slow diffusion of the sugars (and since LC is the dominant method today, it doesn't sound too promising on any reasonable scale). In the introduction, they also note that some of the other attempts of the era involved chemical means—specifically precipitation of the fructose as calcium fructosate, getting the fructose back out by reaction with carbon dioxide, oxalic acid, or sulfuric acid in what is known as Dubrunfaut's method. Again, this did not result in an industrially useful process.
This one involves careful fractional crystallization of glucose-fructose solutions, as fructose is far more soluble in water than glucose. The solution is cooled from room temperature to -20 °C fairly slowly (0.5 K/min) while being agitated and in the presence of small glucose seed crystals. Some of the glucose crystallizes out of the solution, which is separated by centrifugation, and the process is repeated going to -35 °C. The crystals they get are 89% glucose and 11% fructose, but a big red flag is they don't actually measure the concentrations in the liquid left behind (separating fructose is far more important industrially because pure glucose is easy to get by hydrolysis of starch). They say that "a concentrated solution of fructose containing a small amount of glucose was obtained", but don't actually prove it, and apparently it only works properly if you can maintain a total sugar concentration near 50%, so I'm pretty sceptical of the method's utility. You could probably do something similar at home if all you're interested in is getting some somewhat purified glucose.
Unfortunately, if there were a simple and effective way to do this, industrial production probably wouldn't bother with LC. If you just want to play around with separations, these might be some things to try, but if you just want glucose and/or fructose, I have seen both at bulk food stores. (glucose is often labelled as dextrose and fructose is sold as a low glycemic index sweetener)