How can we increase species exchange between two different liquid phase system?

Suppose that I have a neutral, polar species (say, a radical) in a two-phase liquid system (say, water and a nonpolar solvent). Now, consider if I have a catalyst that will create hydroxyl or hydrogen radical in water. What would you do to maximize the transport of those reactive species (which would be heavily solvated by water, I believe) to the nonpolar region? As much as possible, I would like to leave out the use of phase-transfer catalyst.|||The amounts in each phase will be controlled by the relevant Distribution Coefficient. You can get to that point by putting everything into a separating funnel, stoppering and shaking well.