Chromatography and Distillation

Although you cannot separate homogeneous liquid mixtures using filtration, it is possible to separate them by using distillation.

Distillation

The technique of distillation uses the difference in boiling points of liquid solution components to separate those components from one another. 

You've heard of "bootleggers" using homemade stills to make alcohol out of fermented mixtures of fruits or vegetables. They didn't actually make alcohol, but rather they separated it from an aqueous solution. Boiling the solution accomplished the separation; as different fractions boiled off,, the gases were captured with cooling, which returned them to a liquid.