Since the coloring agents are generally of the same specific gravity and share a common base, there is little to keep diffusion from eventually mixing the colors.
The most obvious way to counter this is to use a viscous base and use the paint before diffusion has a chance to mix. Since the base is often viscous anyway, simply pouring one color into the same container as the others should give you separated colors that will remain separated plenty long enough to work with.
But the photo you show looks like a water-based fluid. For non-viscous liquids, try dying oil with one color and water with a second color. The colors will still bleed, but for a while, they will stay in their own layer.
Ideally, you might be able to find liquids that don't mix and keep their color without bleeding. Perhaps one of the chemical engineers can help with that.
What exactly are you trying to do?
